ALBERT

Description: Despite a considerable push by policy-makers to incentivize green business practices, take-up of environmental initiatives amongst North American retailers has been highly uneven. While some “big-box” retailers have launched ambitious environmental initiatives, others continue to conduct business as usual. This paper asks: why do some mega-retailers commit to ambitious environmental agendas while others in the same sector do not? And how can the answer to this question improve public policy? I investigate these questions using comparative case studies of four North American big-box retailers: Wal-Mart, Target, Costco and Kroger. My findings suggest that the socialization of senior executives through multi-stakeholder sustainability networks is the critical variable accounting for progressive environmental practices in some corporations and not others. This finding suggests that existing public policies that focus on making the business case for sustainability are based on incomplete assumptions about why companies “go green.” It further suggests that socialization theory can help explain broader instances of corporate social responsibility and proposes that scholars in this field should devote more attention to the composition of socializing groups.

Description: The economic success of state-led forms of capitalism in Russia, China and some other autocracies is one of the most challenging developments for existing typologies of comparative political economy research. For the OECD-World complex theories and models assess the interrelation of polity and economy (e.g., Hall/Soskice), while well defined and systematic approaches for autocracies are seldomly found. Most of the existing work are rather idiosyncratic case studies. We argue that by climbing up the ladder of abstraction (Sartori), we gain analytical leverage and comparability between cases and regions. That's why we've developped an idealtype called “incorporated capitalism.” By looking at state-capitalist developments in China, Singapore, Saudi-Arabia or Russia, there is strong empirical evidence for a variety of “incorporated capitalism”: bureaucratic market economies and patrimonial market economies. Why are those types of capitalism so successful? In order to answer this question correctly, we have to consider other questions first: 1) Which are the specific patterns of interaction between polity and economy? 2) What are the unique governance mechanisms in those incorporated capitalisms? Using mainly qualitative methods we will empirically proof our theoretical findings in order to decode the special complementarities of the bureaucratic and patrimonial market economy in those four real types mentioned above.

Description: Since deregulation in 1980, there has been a major shift in antitrust enforcement to the states, specifically to state attorneys general (AGs). For advocates of deregulation, this move has had important unintended consequences. Specifically, it has allowed antitrust litigation to become hitched to the political incentives of AGs. Analysis of a panel dataset of all state antitrust actions between 1990 and 2008 suggests that antitrust enforcement by state attorneys general appears to follow electoral cycles, which is especially pronounced depending on specific institutional constraints that exist between the states.

Description: Analyses of transnational governance formation point to the destabilizing effects transnational standard setters have upon national institutional configurations. Isomorphic pressures, it is argued, lead to the standardization of procedures used and actors involved in standard setting processes. What is not clear, however, is to what extent this meta-standardization increases the chances for convergence of national with transnational standards. This article explores this question for the case of the international accounting standard for off-balance-sheet financing in the Netherlands, France and Germany. It argues that the reconfiguration of domestic governance architectures had a decisive impact on convergence processes. Counter-intuitively, copying goals, membership and procedures of the transnational, private International Accounting Standards Committee limited the chances of rule convergence, as it threatened to deinstitutionalize the standard-setting role of an important national champion of rule-convergence, the banking regulator. The institutional template developed at the transnational level created actor-mismatch at the national level between those formulating and those implementing the rules, thereby weakening the coalition for rule change. A strong coalition, however, is needed to overcome vested business interests that favor convergence with transnational templates for legitimacy gains at the same time that they oppose convergence to contentious rules that limit their business activities.

Description: While the West is struggling to find a way out of recession, emerging markets present myriad opportunities for growth. This paper offers a new perspective on how global economic triangulation facilitates trade between regions. Triangulation occurs where barriers exist to trade and investment between two countries and a third party (e.g., a country) acts as a facilitator or bridge. The “bridge model,” as we call it, shifts the focus away from national policy as a facilitator of international trade and emphasizes the role of companies. Corporate bridge-building is essentially a form of economic triangulation, and we use the terms “bridge” and “triangulation” interchangeably. Various examples are cited to show how Spanish multinational companies have served as a bridge connecting Asia and Latin America, and in so doing have expanded their own business. Thanks to their links with both regions they create business relationships that might otherwise be impeded by cultural or language barriers, facilitating the flow of products, knowledge and financial resources. In this way firms in otherwise stagnating economies have an opportunity to grow by facilitating trade and investment between emerging markets via the bridge model.

Description: Over time and across countries, researchers have noted frequent and mostly unexplained gender differences in the levels of support for policies of free or freer trade: according to aggregate results from many surveys, women tend to be less favorable toward policies of liberalizing trade than men. Positing an economic security explanation based largely on a mobile factors approach, we ask if it is women generally who are more negative toward trade or rather women who are more economically vulnerable – i.e., women from the scarce labor factor. We utilize data from two recent surveys on individuals’ attitudes toward different facets of trade and its effects to examine this hypothesis empirically. Rejecting a monolithic definition of “women,” we find that disaggregating by education level illuminates to some extent what underlying characteristics might be helping to drive some of these findings. Lower-skilled women in the US are much less likely to support free trade compared to higher-skilled women and this may largely explain previous negative findings. The low versus high-skill dynamic is, however, much less clear in the findings using survey data from a small sample of developing countries.

Description: Emerging markets are rapidly gaining importance in the world economy and many multinational corporations (MNCs) are taking advantage of this economic development by expanding their activities there. Due to the high level of perceived uncertainty and lack of formal institutions in these markets, firms cope by relying on network relationships with other organizational actors – including societal and political actors – in their environment. In these uncertain environments, where political and economic change is frequent, firms may have to negotiate their relationships frequently – building new ties and severing old ones. In this paper, findings from a case study of Turkey reveal that while the role of political actors in emerging markets should not be neglected, the value of political ties are contingent on the market environment and can change in the face of state policy change. Hence, MNCs tend to buffer the political hazards through their connections to the business and civil society organizations. Consequently, we suggest that researchers in this field might improve the explanatory power of their models by including consideration of the context that firms are embedded in. Then the focus needs to be shifted towards the interplay between different actors and the indirect impact of network ties along with the direct effects.

Description: This paper explores the plurality of institutional environments in which standards for the service sector are expected to support the rise of a global knowledge-based economy. A wide range of international bodies is able to define standards affecting the internationalization of services. Relying on global political economy approaches, the analysis uncovers the power relations underpinning the various forms of standards supporting a deeper integration of the market for services. Service standards are conceived as heterogeneous forms of transnational hybrid authority. The empirical study focuses on recent developments in the International Organization for Standardization (ISO), the European Union, and the US. In contrast to conventional views opposing the American system to the ISO/European framework, the paper argues that institutional developments of service standards are likely to face trade-offs and compromises reflecting contrasting models of standardization, not only between, but also across, those systems. While this undermines the conventional analysis of a transatlantic divide in standardization, it also shows that the variance between product and service standards is much greater in the European context and the ISO system than in the US, where it is hardly debated.

Description: Wind power remains one of the fastest growing energy sources in the world, even as countries have struggled to come back from the global economic crisis of 2008. Yet the sector's rise has been the product of a crucial shift in how governments approach renewable energy. To build political support for wind power, governments have added industrial policy instruments to traditional renewable energy deployment mechanisms. This paper argues that we are witnessing a rise in protectionism in the wind power sector growing out of specific political and economic challenges at the national level that have arisen in the period following the 2008 crisis. In addition, this paper demonstrates that protectionism, justified by a rationale of promoting local economic development, takes many forms, and countries have come up with ever more varied and sophisticated methods of using industrial policy to establish and protect nascent, strategic industries. Finally, it challenges conventional wisdom that protectionism is reserved for the emerging economies as either a strategy to improve economic competitiveness or as a short cut to technological innovation. It demonstrates that while these strategies do indeed persist in emerging economies, North America and Western Europe continue to protect their own wind industries, even as they initiate disputes with countries for implementing similar measures.

Description: Globalization is often described as a chaotic process which signals the end of national institutions’ ability to regulate markets. However, a closer look reveals a new world of standards and regulations, often with a transnational scope and reach. Contemporary rule making and rule monitoring increasingly take place in the context of transnational arenas that bring around the table many different types of actors, all of whom have or feel to have a “stake” in the regulatory project at hand, yet often for quite diverse reasons and with varying interests. While standardization would seem to suggest regularity, rationalization, and a reduction of diversity if not the advance of homogeneity and convergence, we can easily document a surprising multiplicity and plurality in our transnational world of standards. In most industries, fields and arenas, we find multiple standards and standard setting coalitions. Even so, scholars have only barely started to explore this multiplicity and plurality. Building upon what we know on technical standards, this Symposium describes and explains important patterns in the world of transnational standard-setting, revealing the nature of this plurality and the ways in which it impacts upon and is impacted by different groups of actors involved.

Description: Mining companies are increasingly seen as co-governors of sub-Saharan Africa's gold mining industries, sharing sovereignty with states through private governance initiatives. Using interviews with company executives from the continent's largest gold mining firms this paper highlights the private authority of these firms vis-à-vis the state. This paper firstly examines the globalization and governance literature, focusing on why states share sovereignty with non-state actors. Secondly, a “three faces of power” framework is employed to understand how authority is exercised. Thirdly, private governance regimes specific to the mining industry are outlined. Finally, individuals’ and firms’ attitudes towards these private governance regimes are examined through an analysis of elite interviews. The theoretical and empirical analysis demonstrates that firms are formulating rules in order to increase certainty and reduce investment risk. These firms are engaging in private governance initiatives to build reputations as industry experts thereby controlling the regulation of their sector, rather than sharing authority with states.

Description: In the wake of the 2008 financial crisis, governments turned to protectionist policies to support their financial sectors. Yet these policy choices have been highly variegated, and like many recent protectionist policies reflect a process of adaptation to changing circumstances. Using data on a variety of government interventions in the financial sector since the crisis, I show that financial protectionism comes in at leastthreetypes, only two of which have witnessed a traceable increase since the global financial crisis. These are protection through market entry restrictions (Type 1), through asymmetrically applied regulation (Type 2) and protection through subsidies (Type 3). While Type 1 has not appeared to change significantly since the crisis, Type 2 and Type 3 have. I present empirical evidence which suggests that while Type 3 financial protectionism proliferated during and shortly after the crisis, it is unlikely to continue. Type 2 financial protectionism, I conclude, is more likely to take off into the future because of the nature of interest group effects associated with asymmetric regulation as a form of government intervention.

Description: Apart from being one of the hardest hit sectors during the 2008 financial crisis, the auto sector is also a prominent sector where emerging auto markets such as China have fared relatively well compared to their competitors in North America and Europe. This paper examines various ways that nations have shifted their policy gears to revive and restructure the automotive industry by using the case studies of the USA, France, and China. New sets of policy initiatives are contingent on particular industrial and institutional contexts, but both developed and developing countries have employed wide range of “murky” protectionist measures. This makes it unlikely for the WTO member countries to take a naming and shaming approach and file a case at the WTO level, which poses challenges to the WTO rules and trade liberalization.

Description: The Lobbying and Disclosure Act of 1995 requires lobbyists to disclose information about their lobbying activities. The resulting data is used by the websiteOpenSecrets.org(run by the Center for Responsive Politics) to give snapshot pictures of the amount of lobbying groups do. The same data has also been used by scholars to measure the impact of lobbying and to evaluate rent-seeking expenditures by firms. Unfortunately, users of the data are unaware of a reporting option for organizations under the LDA that has consequences for the validity of the data. LDA data does not accurately reflect the amount of money that an organization has spent trying to influence federal law because organizations may choose a reporting requirement under which they must also disclose the amount of money they spent to influence state laws. In this article I analyze the implications of this fact. I begin with a discussion of the problem's scope and then show how it misleads scholars.

Description: The creation of the World Trade Organization (WTO) in 1995 was a landmark in the development of the liberal international economic order. Yet the global economic crisis of 2008 put the spotlight on the longstanding question whether WTO membership limited the policy choices of governments coping with distress. This Special Issue ofBusiness and Politicsuses the crisis as a “stress test” for evaluating the prominent thesis that multilateral trade rules presently impose sharp limits on national industrial policies. The evidence from a wide range of sectoral and national contexts suggests that the WTO's ability to constrain member governments’ use of industrial policy is highly exaggerated. As we argue in this introductory essay, and as the studies in this Issue show, assertions of the WTO's strength do not reflect the incomplete and contested nature of its accords and the imperatives of policymaking in an era when many governments simultaneously intervene in national economies.

Description: We argue that international trade affects party systems but that this impact is conditioned on the types of societal interests trade brings about. When factor mobility is high, trade promotes class-based grievances that are unlikely to affect the structure of the party system. However, when factor mobility is low, trade will increase the diversity of group interests and policy preferences, thereby pressuring structural change in the party system. A consequence is an increase in the effective number of political parties. The empirical analysis supports these expectations. This paper contributes to our understanding of the political impact of economic liberalization on representative democracy.

Description: Partisanship and institutionalization are more important to group formation and dynamics than is often recognized in the literature on interest groups. This study examines the contrasting cases of small business group formation and dynamics in Japan and the United States to demonstrate how opposition to the party or parties in power was crucial to the timing and nature of the largest small business organizations formed in both countries. Parties are also important to subsequent developments in the organization and institutional interactions of the sector. It is these processes which explain the divergent outcome whereby the US small business sector is identified with the political right and the small business in Japan with the political left.

Description: Industry lobbying is traditionally thought of as a non-excludable good subject to collective action problems that are most easily solved by concentrated industries. However, there is very little empirical support for this hypothesis. In this paper, we address a major shortcoming of existing work on the topic: Its near-exclusive reliance on data from the US. Using comparative firm-level survey data from up to 74 countries, we construct an industry-level indicator of concentration and test its effect on firms’ lobbying activity. Using multilevel Extreme Bounds Analysis and Bayesian Variable Selection techniques to account for model uncertainty, we find no evidence that industry concentration is a predictor of lobbying activity. We discuss the implications of these non-findings for the literature and outline possible avenues for further research.

Description: The dual pressures of the global economic crisis in 2008 and high crude prices through the subsequent recovery period have prompted oil-producing countries to adopt a wide range of protectionist measures including subsidies in all forms and trade and investment restrictions. Focusing on fiscal and industrial policy adjustments in the UK and the People's Republic of China since 2008, this paper argues that both governments have sought an increase in tax contributions from the corporate sector in exchange for intensified, targeted support for specific capital investments that will address the challenges of overall decline in domestic oil production and new field exploration and oil recovery opportunities. These novel “rent-sharing” schemes – inadequately captured in recent academic debates over precise measurements of fuel subsidies – raise concerns for fair competition in the upstream market and politicians’ long-term commitment to the transitioning of energy mix toward green and renewable sources.

Description: Standards for “ethical” goods provide activists and mission-driven producers with opportunities to clarify decisions for so-called “ethical consumers” and spur growth in these new markets. But certification schemes also raise monitoring challenges, and may confuse consumers and create opportunities for cooptation by large corporate competitors. In this interview-based study, we examined the localism movement to understand why social movement leaders might resist harmonization of standards. We find that leaders define “local” in at least five ways, and argue that they resist harmonization of local for pragmatic, philosophical, and strategic reasons. We conclude that tolerance for multiple standards could be beneficial for core activists in market-oriented social movements. If and when these groups turn more systematically to the political system, maintaining loose and multiple standards may impede policy success. The “buy local” case suggests, however, that as long as the market remains activists’ primary mechanism for social change, decentralized governance and multiple standards in ethical markets allow activists to maintain a powerful voice in defining ethical products and business practices.

Description: Amid concerns for a regulatory void in transnational fields, the principle of private regulation has become institutionalized. Many sectors have seen the emergence of multiple and overlapping standards. When comparing the sectors, there is considerable variation in standard multiplicity. We build on three institutional perspectives that have been put forward to explain the emergence of sustainability standards – the economic, idealist and political-institutional perspectives – to analyze the phenomenon of standard multiplicity. Each perspective reflects a different kind of action logic and is simultaneously present and accessible to various parties involved. Based on a cross-sector analysis of standards multiplicity in the forestry, coffee and textile sectors, this article seeks to make two contributions. First, whereas these three perspectives have been presented as competing, we propose that they are complementary in offering partial explanations for different episodes in the dynamics underlying standards multiplicity in different sectors. Second, whereas most studies have analyzed standard setting in single sectors and thus have understood it as being an intra-sector phenomenon, our cross-sector analysis of the dynamics of standard setting suggests that it is propelled by both sector-specific contingencies and experiences as well as by the experiences from other sectors.

Description: The commercial aircraft industry is no stranger to trade friction, which has brought bitter international disputes over industrial policy to the World Trade Organization (WTO). Yet despite the fact that several countries, notably China, Japan and Russia have stated their intentions to develop aircraft that can compete with other countries, these efforts have not led to a trade dispute. What explains this pattern? Drawing on sources such as the Global Trade Alert database, this paper argues that that the complexity of the aircraft industry generates considerable barriers to entry. Moreover, emerging aerospace states have not repeated earlier efforts of direct subsidy, but rather, they have sought to position themselves in the global aerospace value chain, with selective government interventions designed to help national champions accumulate the necessary technical experience though collaboration with incumbent firms. However, the very diversity of government supports may make protectionist measures more difficult to identify.

Description: Scholars and policymakers tend to see economic sanctions as an important tool of coercive diplomacy, even if the effectiveness of sanctions in changing the policies of target states remains highly contested. Though much of the research on sanctions focuses on their effects at the state level, this article argues that analyzing their effectiveness must begin with the industrial sectors they are meant to affect. Through analysis of restrictive measures currently in place against Iran, this article explores the impact of sanctions at the working level within the insurance industry, drawing on qualitative data gathered as part of a recent workshop funded by the UK Economic and Social Research Council (ESRC) and industry partners.

Description: We propose an analytical model for the determination of the microstructure and stresses in a sheared suspension that consists of a dense monolayer of identical spheres in a viscous fluid. We calculate the anisotropy in the orientational distribution of spheres, associated with a short-range repulsive force assumed to act between the spheres, and a particle pressure and normal stress difference that result from this anisotropy. The microstructure and stresses are similar to those measured in Stokesian dynamics simulations. © Cambridge University Press 2014.

Description: We investigate the forces and unsteady flow structures associated with harmonic oscillations of an airfoil in the streamwise (surging) and transverse (plunging) directions in two-dimensional simulations at low Reynolds number. For the surging case, we show that there are specific frequencies where the wake instability synchronizes with the unsteady motion of the airfoil, leading to significant changes in the mean forces. Resonant behaviour of the time-averaged forces is observed near the vortex shedding frequency and its subharmonic; the behaviour is reminiscent of the dynamics of the generic nonlinear oscillator known as the Arnol'd tongue or the resonance horn. Below the wake instability frequency, there are two regimes where the fluctuating forces are amplified and attenuated, respectively. A detailed study of the flow structures associated with leading-edge vortex (LEV) growth and detachment are used to relate this behaviour with the LEV acting either in phase with the quasi-steady component of the forces for the amplification case, or out of phase for the attenuation case. Comparisons with wind tunnel measurements show that phenomenologically similar dynamics occur at higher Reynolds number. Finally, we show that qualitatively similar phenomena occur during both surging and plunging. © 2014 Cambridge University Press.

Description: We study the motion of a bubble driven by buoyancy and thermocapillarity in a tube with a non-uniformly heated walls, containing a so-called 'self-rewetting fluid'; the surface tension of the latter exhibits a parabolic dependence on temperature, with a well-defined minimum. In the Stokes flow limit, we derive the conditions under which a spherical bubble can come to rest in a self-rewetting fluid whose temperature varies linearly in the vertical direction, and demonstrate that this is possible for both positive and negative temperature gradients. This is in contrast to the case of simple fluids whose surface tension decreases linearly with temperature, for which bubble motion is arrested only for negative temperature gradients. In the case of self-rewetting fluids, we propose an analytical expression for the position of bubble arrestment as a function of other dimensionless numbers. We also perform direct numerical simulation of axisymmetric bubble motion in a fluid whose temperature increases linearly with vertical distance from the bottom of the tube; this is done for a range of Bond and Galileo numbers, as well as for various parameters that govern the functional dependence of surface tension on temperature. We demonstrate that bubble motion can be reversed and then arrested only in self-rewetting fluids, and not in linear fluids, for sufficiently small Bond numbers. We also demonstrate that considerable bubble elongation is possible under significant wall confinement, and for strongly self-rewetting fluids and large Bond numbers. The mechanisms underlying the phenomena observed are elucidated by considering how the surface tension dependence on temperature affects the thermocapillary stresses in the flow. © 2014 Cambridge University Press.

Description: Numerical simulation is used to document the statistical structure and better understand energy transfers in a low-Reynolds-number turbulent flow generated by negative axial buoyancy in a long circular tilted pipe under the Boussinesq approximation. The flow is found to exhibit specific features which strikingly contrast with the familiar characteristics of pressure-driven pipe and channel flows. The mean flow, dominated by an axial component exhibiting a uniform shear in the core, also comprises a weak secondary component made of four counter-rotating cells filling the entire cross-section. Within the cross-section, variations of the axial and transverse velocity fluctuations are markedly different, the former reaching its maximum at the edge of the core while the latter two decrease monotonically from the axis to the wall. The negative axial buoyancy component generates long plumes travelling along the pipe, yielding unusually large longitudinal integral length scales. The axial and crosswise mean density variations are shown to be respectively responsible for a quadratic variation of the crosswise shear stress and density flux which both decrease from a maximum on the pipe axis to near-zero values throughout the near-wall region. Although the crosswise buoyancy component is stabilizing everywhere, the crosswise density flux is negative in some peripheral regions, which corresponds to apparent counter-gradient diffusion. Budgets of velocity and density fluctuations variances and of crosswise shear stress and density flux are analysed to explain the above features. A novel two-time algebraic model of the turbulent fluxes is introduced to determine all components of the diffusivity tensor, revealing that they are significantly influenced by axial and crosswise buoyancy effects. The eddy viscosity and eddy diffusivity concepts and the Reynolds analogy are found to work reasonably well within the central part of the section whereas non-local effects cannot be ignored elsewhere. © 2014 Cambridge University Press.

Description: Analysis of bioconvection in dilute suspensions of bottom-heavy but randomly swimming micro-organisms is commonly based on a model introduced in 1990. This couples the Navier–Stokes equations, the cell conservation equation and the Fokker–Planck equation (FPE) for the probability density function for a cell’s swimming direction ${p}$, which balances rotational diffusion against viscous and gravitational torques. The results have shown qualitative agreement with observation, but the model has not been subjected to direct quantitative testing in a controlled experiment. Here, we consider a simple configuration in which the suspension is contained in a circular cylinder of radius $R$, which rotates at angular velocity ${ mOmega}$ about a horizontal axis. We solve the FPE and calculate the cells’ mean swimming velocity, which proves to be horizontal when $B{mOmega}gg 1$, where $B$ is the gyrotactic reorientation time scale. Then we compute the cell concentration distribution, which is non-uniform only in a thin boundary layer near the cylinder wall when ${it eta}^{2}={mOmega}R^{2}/Dgg 1$, where $D$ is the cells’ translational diffusivity. The fact that cells are denser than water means that this concentration distribution drives a perturbation to the underlying solid-body rotational flow which can be calculated analytically. The predictions of the theory are evaluated in terms of a proposed experimental realisation of the configuration, using suspensions of the alga Chlamydomonas nivalis or Chlamydomonas reinhardtii or the algal colony Volvox.

Description: We study a partial dewetting corner flow with a moving contact line at a finite Reynolds number, $01$ and furthermore shows that the dynamic pressure effects become dominant at a small half-opening angle. Additionally, this model provides analytical results for the internal flow, which is a self-similar flow pattern. To validate the analytical results, we perform high-speed shadowgraphy and tomographic particle image velocimetry (PIV). We find a good agreement between the theoretical and the experimental results.

Description: Longitudinal and transverse structure functions, Dll = (δulδui) and Dll = (δμlδμi), can be calculated from aircraft data. Here, δ denotes the increment between two points separated by a distance r, ul and ut the velocity components parallel and perpendicular to the aircraft track respectively and () an average. Assuming statistical axisymmetry and making a Helmholtz decomposition of the horizontal velocity, u =ur+ud, where ur is the rotational and ud the divergent component of the velocity, we derive expressions relating the structure functions Drr= (δur.δur) and Ddd=(δud .δud to Dll and Dtt. Corresponding expressions are also derived in spectral space. The decomposition is applied to structure functions calculated from aircraft data. In the lower stratosphere, Drr and Ddd both show a nice r2=3-dependence for r 2 T2; 20U km. In this range, the ratio between rotational and divergent energy is a little larger than unity, excluding gravity waves as the principal agent behind the observations. In the upper troposphere, Drr and Ddd show no clean r2=3-dependence, although the overall slope of Ddd is close to 2=3 for r 2 T2; 400U km. The ratio between rotational and divergent energy is approximately three for r 〈100 km, excluding gravity waves also in this case. We argue that the possible errors in the decomposition at scales of the order of 10 km are marginal. © 2014 Cambridge University Press.

Description: By means of extensive lattice Boltzmann simulations, we investigate the process of growth and coalescence of liquid clusters in a granular material as the amount of liquid increases. A homogeneous grain-liquid mixture is obtained by means of capillary condensation, thus providing meaningful statistics on the liquid distribution inside the granular material. The tensile stress carried by the grains as a function of the amount of condensed liquid reveals four distinct states, with a peak stress occurring at the transition from a primary coalescence process, where the cohesive strength is carried mostly by the grains, to a secondary process governed by the increase of the liquid cluster volumes. We show that the evolution of capillary states is correctly captured by a simple model accounting for the competing effects of the Laplace pressure and grain-liquid interface. © 2014 Cambridge University Press.

Description: The stirring of a passive scalar by grid-generated turbulence in the presence of a mean scalar gradient is studied by direct numerical simulations (DNS) for six different grids: one fractal square grid with three fractal iterations, one fractal square grid with four fractal iterations, one fractal I grid and three different regular grids. Our results can be summarised as follows. (i) For all these grids, the turbulence intensity averaged over time and over a plane parallel to the grid takes its peak value when the streamwise position of this plane is between $0.75M〈inf〉eff〈/inf〉 and 1.5M〈inf〉eff〈/inf〉 where M〈inf〉eff〈/inf〉 is the effective mesh size introduced by Hurst & Vassilicos (Phys. Fluids, vol. 19, 2007, 035103). (ii) Downstream of the location of this peak, the turbulence intensity averaged in this way is greatly enhanced by the fractal grids relative to the regular grids even though the fractal grids have comparable or even lower blockage ratios. The novelty of this result lies in the fact that it concerns turbulence intensities averaged over lateral planes (as well as time). (iii) The pressure drop is about the same across grids of the same blockage ratio whether fractal or not, but the pressure recovery is longer for the fractal grids. (iv) Even so, the fractal grids enhance turbulent scalar fluxes by up to an order of magnitude in the region downstream of the aforementioned peak and they also greatly enhance the streamwise growth of the fluctuating scalar variance in that region. (v) We demonstrate on a simple planar model problem that the cause of this phenomenon lies in the fractality of the grids. (vi) The turbulence scalar flux coefficient is constant far enough downstream of all the present grids and is significantly dependent on the nature and details of the turbulence-generating grid. © 2014 Cambridge University Press.

Description: We consider the axisymmetric arrangement of an annular liquid film, coating the inner surface of a narrow cylindrical tube, in interaction with an active core fluid. We introduce a low-dimensional model based on the two-phase weighted residual integral boundary layer (WRIBL) formalism (Dietze & Ruyer-Quil, J. Fluid Mech., vol. 722, 2013, pp. 348–393) which is able to capture the long-wave instabilities characterizing such flows. Our model improves upon existing works by fully representing interfacial coupling and accounting for inertia as well as streamwise viscous diffusion in both phases. We apply this model to gravity-free liquid-film/core-fluid arrangements in narrow capillaries with specific attention to the dynamics leading to flooding, i.e. when the liquid film drains into large-amplitude collars that occlude the tube cross-section. We do this against the background of linear stability calculations and nonlinear two-phase direct numerical simulations (DNS). Due to the improvements of our model, we have found a number of novel/salient physical features of these flows. First, we show that it is essential to account for inertia and full interphase coupling to capture the temporal evolution of flooding for fluid combinations that are not dominated by viscosity, e.g. water/air and water/silicone oil. Second, we elucidate a viscous-blocking mechanism which drastically delays flooding in thin films that are too thick to form unduloids. This mechanism involves buckling of the residual film between two liquid collars, generating two very pronounced film troughs where viscous dissipation is drastically increased and growth effectively arrested. Only at very long times does breaking of symmetry in this region (due to small perturbations) initiate a sliding motion of the liquid film similar to observations by Lister et al. (J. Fluid Mech., vol. 552, 2006, pp. 311–343) in thin non-flooding films. This kickstarts the growth of liquid collars anew and ultimately leads to flooding. We show that streamwise viscous diffusion is essential to this mechanism. Low-frequency core-flow oscillations, such as occur in human pulmonary capillaries, are found to set off this sliding-induced flooding mechanism much earlier.

Description: We investigate the statistical properties of Lagrangian tracers transported by a time-correlated compressible renewing flow. We show that the preferential sampling of the phase space performed by tracers yields significant differences between the Lagrangian statistics and its Eulerian counterpart. In particular, the effective compressibility experienced by tracers has a non-trivial dependence on the time correlation of the flow. We examine the consequence of this phenomenon on the clustering of tracers, focusing on the transition from the weak- to the strong-clustering regime. We find that the critical compressibility at which the transition occurs is minimum when the time correlation of the flow is of the order of the typical eddy turnover time. Further, we demonstrate that the clustering properties in time-correlated compressible flows are non-universal and are strongly influenced by the spatio-temporal structure of the velocity field. © 2014 Cambridge University Press.

Description: Microdroplet deposition is a technology that spans applications from tissue engineering to microelectronics. Our new high-speed imaging measurements reveal how sequential linear deposition of overlapping droplets on flat uniform substrates leads to striking non-uniform morphologies for moderate contact angles. We develop a simple physical model, which for the first time captures the post-impact dynamics drop-by-drop: surface-tension drives liquid redistribution, contact-angle hysteresis underlies initial non-uniformity, while viscous effects cause subsequent periodic variations. © 2014 Cambridge University Press.

Description: Liquid-bubble interaction, especially in complex two-phase bubbly flow under breaking waves, is still poorly understood. In the present study, we perform a large-eddy simulation using a Navier-Stokes solver extended to incorporate entrained bubble populations, using an Eulerian-Eulerian formulation for a polydisperse bubble phase. The volume-of-fluid method is used for free-surface tracking. We consider an isolated unsteady deep water breaking event generated by a focused wavepacket. Bubble contributions to dissipation and momentum transfer between the water and air phases are considered. The model is shown to predict free-surface evolution, mean and turbulent velocities, and integral properties of the entrained dispersed bubbles fairly well. We investigate turbulence modulation by dispersed bubbles as well as shear- and bubble-induced dissipation, in both spilling and plunging breakers. We find that the total bubble-induced dissipation accounts for more than 50 % of the total dissipation in the breaking region. The average dissipation rate per unit length of breaking crest is usually written as bρg-1c〈inf〉b〈/inf〉5, where ρ is the water density, g is the gravitational acceleration and c〈inf〉b〈/inf〉 is the phase speed of the breaking wave. The breaking parameter, b, has been poorly constrained by experiments and field measurements. We examine the time-dependent evolution of b for both constant-steepness and constant-amplitude wavepackets. A scaling law for the averaged breaking parameter is obtained. The exact two-phase transport equation for turbulent kinetic energy (TKE) is compared with the conventional single-phase transport equation, and it is found that the former overpredicts the total subgrid-scale dissipation and turbulence production by mean shear during active breaking. All of the simulations are also repeated without the inclusion of a dispersed bubble phase, and it is shown that the integrated TKE in the breaking region is damped by the dispersed bubbles by approximately 20 % for a large plunging breaker to 50 % for spilling breakers. In the plunging breakers, the TKE is damped slightly or even enhanced during the initial stage of active breaking. © 2014 Cambridge University Press.

Description: The development of incompressible turbulent flow through a pipe of wavy cross-section was studied numerically by direct integration of the Navier-Stokes equations. Simulations were performed at Reynolds numbers of 4.5 × 103 and 104 based on the hydraulic diameter and the bulk velocity. Results for the pressure resistance coefficient λ were found to be in excellent agreement with experimental data of Schiller (Z. Angew. Math. Mech., vol. 3, 1922, pp. 2-13). Of particular interest is the decrease in λ below the level predicted from the Blasius correlation, which fits almost all experimental results for pipes and ducts of complex cross-sectional geometries. Simulation databases were used to evaluate turbulence anisotropy and provide insights into structural changes of turbulence leading to flow relaminarization. Anisotropy-invariant mapping of turbulence confirmed that suppression of turbulence is due to statistical axisymmetry in the turbulent stresses. © 2014 Cambridge University Press.

Description: A single, simply stated approximation transforms the equations for a two-dimensional perfect fluid into a form that is closely analogous to Maxwell's equations in classical electrodynamics. All the fluid conservation laws are retained in some form. Waves in the fluid interact only with vorticity and not with themselves. The vorticity is analogous to electric charge density, and point vortices are the analogues of point charges. The dynamics is equivalent to an action principle in which a set of fields and the locations of the point vortices are varied independently. We recover classical, incompressible, point vortex dynamics as a limiting case. Our full formulation represents the generalization of point vortex dynamics to the case of compressible flow. © 2014 Cambridge University Press.

Description: In the present treatise, the stability of the boundary layer under solitary waves is analysed by means of the parabolized stability equation. We investigate both surface solitary waves and internal solitary waves. The main result is that the stability of the flow is not of parametric nature as has been assumed in the literature so far. Not only does linear stability analysis highlight this misunderstanding, it also gives an explanation why Sumer et al. (J. Fluid Mech., vol. 646, 2010, pp. 207-231), Vittori & Blondeaux (Coastal Engng, vol. 58, 2011, pp. 206-213) and Ozdemir et al. (J. Fluid Mech., vol. 731, 2013, pp. 545-578) each obtained different critical Reynolds numbers in their experiments and simulations. We find that linear instability is possible in the acceleration region of the flow, leading to the question of how this relates to the observation of transition in the acceleration region in the experiments by Sumer et al. or to the conjecture of a nonlinear instability mechanism in this region by Ozdemir et al. The key concept for assessment of instabilities is the integrated amplification which has not been employed for this kind of flow before. In addition, the present analysis is not based on a uniformization of the flow but instead uses a fully nonlinear description including non-parallel effects, weakly or fully. This allows for an analysis of the sensitivity with respect to these effects. Thanks to this thorough analysis, quantitative agreement between model results and direct numerical simulation has been obtained for the problem in question. The use of a high-order accurate Navier-Stokes solver is primordial in order to obtain agreement for the accumulated amplifications of the Tollmien-Schlichting waves as revealed in this analysis. An elaborate discussion on the effects of amplitudes and water depths on the stability of the flow is presented. © 2014 Cambridge University Press.

Description: We perform a local stability analysis of rotational flows in the presence of a constant vertical magnetic field and an azimuthal magnetic field with a general radial dependence. Employing the short-wavelength approximation we develop a unified framework for the investigation of the standard, helical and azimuthal version of the magnetorotational instability (MRI), as well as of current-driven kink-type instabilities. Considering the viscous and resistive setup, our main focus is on the case of small magnetic Prandtl numbers which applies e.g. to liquid-metal experiments but also to the colder parts of accretion disks. We show that the inductionless versions of MRI that were previously thought to be restricted to comparatively steep rotation profiles extend well to the Keplerian case if only the azimuthal field slightly deviates from its current-free (in the fluid) profile. We find an explicit criterion separating the pure azimuthal inductionless MRI from the regime where this instability is mixed with the Tayler instability. We further demonstrate that for particular parameter configurations the azimuthal MRI originates as a result of a dissipation-induced instability of Chandrasekhar's equipartition solution of ideal magnetohydrodynamics. © 2014 Cambridge University Press.

Description: The nonlinear instability of the density-inverted granular Leidenfrost state and the resulting convective motion in strongly shaken granular matter are analysed via a weakly nonlinear analysis of the hydrodynamic equations. The base state is assumed to be quasi-steady and the effect of harmonic shaking is incorporated by specifying a constant granular temperature at the vibrating plate. Under these mean-field assumptions, the base-state temperature decreases with increasing height away from the vibrating plate, but the density profile consists of three distinct regions: (i) a collisional dilute layer at the bottom, (ii) a levitated dense layer at some intermediate height and (iii) a ballistic dilute layer at the top of the granular bed. For the nonlinear stability analysis (Shukla & Alam, J. Fluid Mech., vol. 672, 2011b, pp. 147-195), the nonlinearities up to cubic order in the perturbation amplitude are retained, leading to the Landau equation, and the related adjoint stability problem is formulated taking into account appropriate boundary conditions. The first Landau coefficient and the related modal eigenfunctions (the fundamental mode and its adjoint, the second harmonic and the base-flow distortion, and the third harmonic and the cubic-order distortion to the fundamental mode) are calculated using a spectral-based numerical method. The genesis of granular convection is shown to be tied to a supercritical pitchfork bifurcation from the density-inverted Leidenfrost state. Near the bifurcation point the equilibrium amplitude (A〈inf〉e〈/inf〉) is found to follow a square-root scaling law, A〈inf〉e〈/inf〉 ∼ Δ, with the distance Δ from the bifurcation point. We show that the strength of convection (measured in terms of velocity circulation) is maximal at some intermediate value of the shaking strength, with weaker convection at both weaker and stronger shaking. Our theory predicts that at very strong shaking the convective motion remains concentrated only near the top surface, with the bulk of the expanded granular bed resembling the conduction state of a granular gas, dubbed as a floating-convection state. The linear and nonlinear patterns of the density and velocity fields are analysed and compared with experiments qualitatively. Evidence of 2:1 resonance is shown for certain parameter combinations. The influences of bulk viscosity, effective Prandtl number, shear work and free-surface boundary conditions on nonlinear equilibrium states are critically assessed. © 2014 Cambridge University Press.

Description: The motion of gravity-driven deformable drops (Bond number, Bo ∼0:8-11) through a circular confining orifice (ratio of orifice diameter to drop diameter, d/D 〈 1) was studied using high-speed imaging. Drops of water/glycerin, surrounded by silicone oil, fall toward and encounter the orifice plate after reaching terminal speed. The effects of surface wettability were investigated for both round-edged and sharp-edged orifices. For the round-edged case, a thin film of surrounding oil prevents the drop fluid from contacting the orifice surface, such that the flow outcomes of the drops are independent of surface wettability. For d/D 〈 0.8, the boundary between drop capture and release depends on a modified Bond number relating drop gravitational time scale to orifice surface tension time scale and is independent of viscosity ratio. Drops that release break into multiple fragments for larger Bo and smaller d/D. For the sharp-edged case, a contact is initiated at the orifice edge immediately upon impact, such that surface wettability influences the drop outcome. When the surface is hydrophobic, the contact line motion through the orifice enhances penetration of the drop fluid, but the trailing interface becomes pinned at the orifice edge, inhibiting drop release. When the surface is hydrophilic, a fraction of the drop fluid is always captured because the drop fluid spreads on both the upper and lower plate surfaces. © Cambridge University Press 2014.

Description: A sessile droplet partially wets a planar solid support. We study the linear stability of this spherical-cap base state to disturbances whose three-phase contact line is (i) pinned, (ii) moves with fixed contact angle and (iii) moves with a contact angle that is a smooth function of the contact-line speed. The governing hydrodynamic equations for inviscid motions are reduced to a functional eigenvalue problem on linear operators, which are parameterized by the base-state volume through the static contact angle and contact-line mobility via a spreading parameter. A solution is facilitated using inverse operators for disturbances (i) and (ii) to report frequencies and modal shapes identified by a polar k and azimuthal l wavenumber. For the dynamic contact-line condition (iii), we show that the disturbance energy balance takes the form of a damped-harmonic oscillator with 'Davis dissipation' that encompasses the dynamic effects associated with (iii). The effect of the contact-line motion on the dissipation mechanism is illustrated. We report an instability of the super-hemispherical base states with mobile contact lines (ii) that correlates with horizontal motion of the centre-of-mass, called the 'walking' instability. Davis dissipation from the dynamic contact-line condition (iii) can suppress the instability. The remainder of the spectrum exhibits oscillatory behaviour. For the hemispherical base state with mobile contact line (ii), the spectrum is degenerate with respect to the azimuthal wavenumber. We show that varying either the base-state volume or contact-line mobility lifts this degeneracy. For most values of these symmetry-breaking parameters, a certain spectral ordering of frequencies is maintained. However, because certain modes are more strongly influenced by the support than others, there are instances of additional modal degeneracies. We explain the physical reason for these and show how to locate them. © 2014 Cambridge University Press.

Description: We report on the structure and dynamics of gaseous detonation stabilized in a supersonic flow emanating radially from a central source. The steady-state solutions are computed and their range of existence is investigated. Two-dimensional simulations are carried out in order to explore the stability of the steady-state solutions. It is found that both collapsing and expanding two-dimensional cellular detonations exist. The latter can be stabilized by putting several rigid obstacles in the flow downstream of the steady-state sonic locus. The problem of initiation of standing detonation stabilized in the radial flow is also investigated numerically. © 2014 Cambridge University Press.

Description: Mixing induced through the life-cycle of Kelvin–Helmholtz (KH) billows is studied for a range of low and intermediate Reynolds numbers using direct numerical simulations (DNS). The amount of stirring, and therefore mixing, is significantly controlled by the process of vortex pairing of two KH billows. For low Reynolds numbers, vortex pairing of the billows is complete in the pre-turbulent stage or early stages of turbulence, generating a high amount of stirring. At higher Reynolds numbers, vortex pairing is suppressed by the growth of three-dimensional instabilities, and the amount of stirring is significantly reduced. For single KH billows, as the Reynolds number increases, there is a transition in the characteristics of the mixing, similar to the laboratory measurements of Breidenthal (J. Fluid Mech., vol. 109, 1981, pp. 1–24) and Koochesfahani & Dimotakis (J. Fluid Mech., vol. 170, 1986, pp. 83–112). The transition in mixing is associated with the growth and sustainability of three-dimensional motions at sufficiently high Reynolds numbers. We examine this ‘mixing transition’ and the influence of vortex pairing on it by examining the flow properties at different stages and the exchange between the energy partitions. As the Reynolds number increases, three-dimensional motions develop over a wider range of length scales, and smaller scale eddies form. However, this does not necessarily result in a greater amount of mixing. The maximum total amount of mixing induced over the lifetime of a KH instability, for billows both with and without vortex pairing, occurs when the large-scale eddies that cause the stirring are the most energetic. The mixing efficiency reveals a non-monotonic dependence on the Reynolds number.

Description: The chaotic advection of passive tracers in a two-dimensional confined convection flow is addressed numerically near the onset of the oscillatory regime. We investigate here a differentially heated cavity with aspect ratio 2 and Prandtl number 0.71 for Rayleigh numbers around the first Hopf bifurcation. A scattering approach reveals different zones depending on whether the statistics of return times exhibit exponential or algebraic decay. Melnikov functions are computed and predict the appearance of the main mixing regions via the break-up of the homoclinic and heteroclinic orbits. The non-hyperbolic regions are characterised by a larger number of Kolmogorov-Arnold-Moser (KAM) tori. Based on the numerical extraction of many unstable periodic orbits (UPOs) and their stable/unstable manifolds, we suggest a coarse-graining procedure to estimate numerically the spatial fraction of chaos inside the cavity as a function of the Rayleigh number. Mixing is almost complete before the first transition to quasi-periodicity takes place. The algebraic mixing rate is estimated for tracers released from a localised source near the hot wall. © © 2014 Cambridge University PressÂ.

Description: We study here Green-Naghdi type equations (also called fully nonlinear Boussinesq, or Serre equations) modelling the propagation of large-amplitude waves in shallow water without a smallness assumption on the amplitude of the waves. The novelty here is that we allow for a general vorticity, thereby allowing complex interactions between surface waves and currents. We show that the a priori (2 + 1)-dimensional dynamics of the vorticity can be reduced to a finite cascade of two-dimensional equations. With a mechanism reminiscent of turbulence theory, vorticity effects contribute to the averaged momentum equation through a Reynolds-like tensor that can be determined by a cascade of equations. Closure is obtained at the precision of the model at the second order of this cascade. We also show how to reconstruct the velocity field in the (2 + 1)-dimensional fluid domain from this set of two-dimensional equations and exhibit transfer mechanisms between the horizontal and vertical components of the vorticity, thus opening perspectives for the study of rip currents, for instance. © Cambridge University Press 2014.

Description: A novel approach to the study of the kinematics and dynamics of turbulent flows is presented. The method involves tracking in time coherent structures, and provides all of the information required to characterize eddies from birth to death. Spatially and temporally well-resolved DNSs of channel data at Reτ = 930-4200 are used to analyse the evolution of three-dimensional sweeps, ejections (Lozano-Durán et al., J. Fluid Mech., vol. 694, 2012, pp. 100-130) and clusters of vortices (del Álamo et al., J. Fluid Mech., vol. 561, 2006, pp. 329-358). The results show that most of the eddies remain small and do not last for long times, but that some become large, attach to the wall and extend across the logarithmic layer. The latter are geometrically and temporally self-similar, with lifetimes proportional to their size (or distance from the wall), and their dynamics is controlled by the mean shear near their centre of gravity. They are responsible for most of the total momentum transfer. Their origin, eventual disappearance, and history are investigated and characterized, including their advection velocity at different wall distances and the temporal evolution of their size. Reinforcing previous results, the symmetry found between sweeps and ejections supports the idea that they are not independent structures, but different manifestations of larger quasi-streamwise rollers in which they are embedded. Spatially localized direct and inverse cascades are respectively associated with the splitting and merging of individual structures, as in the models of Richardson (Proc. R. Soc. Lond. A, vol. 97(686), 1920, pp. 354-373) or Obukhov (Izv. Akad. Nauk USSR, Ser. Geogr. Geofiz., vol. 5(4), 1941, pp. 453-466). It is found that the direct cascade predominates, but that both directions are roughly comparable. Most of the merged or split fragments have sizes of the order of a few Kolmogorov viscous units, but a substantial fraction of the growth and decay of the larger eddies is due to a self-similar inertial process in which eddies merge and split in fragments spanning a wide range of scales. © Cambridge University Press 2014.

Description: The incompressible, inviscid and axisymmetric dynamics of perturbations on a solid-body rotation flow with a uniform axial velocity in a rotating, finite-length, straight, circular pipe are studied via global analysis techniques and numerical simulations. The investigation establishes the coexistence of both axisymmetric wall-separation and vortex-breakdown zones above a critical swirl level, ω1. We first describe the bifurcation diagram of steady-state solutions of the flow problem as a function of the swirl ratio ω. We prove that the base columnar flow is a unique steady-state solution when ω is below ω1. This state is asymptotically stable and a global attractor of the flow dynamics. However, when ω 〉 ω1, we reveal, in addition to the base columnar flow, the coexistence of states that describe swirling flows around either centreline stagnant breakdown zones or wall quasi-stagnant zones, where both the axial and radial velocities vanish. We demonstrate that when ω 〉 ω1, the base columnar flow is a min-max point of an energy functional that governs the problem, while the swirling flows around the quasi-stagnant and stagnant zones are global and local minimizer states and become attractors of the flow dynamics. We also find additional min-max states that are transient attractors of the flow dynamics. Numerical simulations describe the evolution of perturbations on above-critical columnar states to either the breakdown or the wall-separation states. The growth of perturbations in both cases is composed of a linear stage of the evolution, with growth rates accurately predicted by the analysis of Wang & Rusak (Phys. Fluids, vol. 8, 1996a, pp. 1007-1016), followed by a stage of saturation to either one of the separation zone states. The wall-separation states have the same chance of appearing as that of vortex-breakdown states and there is no hysteresis loop between them. This is strikingly different from the dynamics of vortices with medium or narrow vortical core size in a pipe. © Cambridge University Press 2014.

Description: A vertically vibrating liquid layer produces liquid ligaments that disintegrate to form a spray with drops of a controllable size. Previous experimental investigations of ultrasonic atomisation have shown that when such a spray forms, there exists a predominant surface-wave mode from which drops are generated with a mean diameter that follows Lang's equation. In this paper, we determined this predominant surface-wave mode physically and, by utilising the coupled level-set and volume-of-fluid method, we numerically studied the threshold condition for spray formation based on a cell model of the predominant surface wavelength that excludes the effects of the container walls. We defined a condition whereby the broken drop holds a zero area-averaged vertical velocity in the laboratory reference frame as the criterion for the formation of a spray. The results of our calculations indicated that the onset of a spray occurs in the subharmonic unstable region for a threshold dimensionless forcing strength βc = (ρlΔ03Ω2)/σ ∼ O(1), where ρl and σ denote the liquid density and surface tension coefficient, respectively, Δ0 is the forcing displacement amplitude and Ω is the forcing angular frequency. Spray formation due to the Faraday instability can be considered as a process whereby the liquid layer absorbs energy from the inertial force, and releases it by producing drops that leave the surface of the liquid layer. We demonstrated that for a deep liquid layer, the threshold condition for the formation of a spray is determined only by the forcing strength, and is independent of the initial conditions of the liquid surface. © Cambridge University Press 2014.

Description: We present the first full-scale computational evidence of intermittent and synchronized dynamics of red blood cells in shear flow. These dynamics are characterized by the coexistence of a tumbling motion in which the cell behaves like a rigid body and a tank-treading motion in which the cell behaves like a liquid drop. In the intermittent dynamics, we observe sequences of tumbling interrupted by swinging, as well as sequences of swinging interrupted by tumbling. In the synchronized dynamics, the tumbling and membrane rotation are observed to occur simultaneously with integer ratios of the rotational frequencies. These dynamics are shown to be dependent on the stress-free state of the cytoskeleton, and are explained based on the cell membrane energy landscape. © Cambridge University Press 2014.

Description: This paper describes experimentally, numerically and theoretically how the three-dimensional instabilities of a cylinder wake are modified by the presence of a linear density stratification. The first part is focused on the case of a cylinder with a small tilt angle between the cylinder's axis and the vertical. The classical mode A well-known for a homogeneous fluid is still present. It is more unstable for moderate stratifications but it is stabilized by a strong stratification. The second part treats the case of a moderate tilt angle. For moderate stratifications, a new unstable mode appears, mode S, characterized by undulated layers of strong density gradients and axial flow. These structures correspond to Kelvin-Helmholtz billows created by the strong shear present in the critical layer of each tilted von Kármán vortex. The last two parts deal with the case of a strongly tilted cylinder. For a weak stratification, an instability (mode RT) appears far from the cylinder, due to the overturning of the isopycnals by the von Kármán vortices. For a strong stratification, a short wavelength unstable mode (mode L) appears, even in the absence of von Kármán vortices. It is probably due to the strong shear created by the lee waves upstream of a secondary recirculation bubble. A map of the four different unstable modes is established in terms of the three parameters of the study: the Reynolds number, the Froude number (characterizing the stratification) and the tilt angle. © Cambridge University Press 2014.

Description: We have established a parallel, adaptive interface-tracking framework in order to conduct, based on the framework, direct simulation of binary head-on droplet collision in the high-Weber-number regime (from 200 to 1500) that exhibits complex topological changes and substantial length scale variations. The overall algorithms include a combined Eulerian and Lagrangian solver to track moving interfaces, conservative Lagrangian mesh modification and reconstruction, cell-based unstructured adaptive mesh refinement (AMR) in the Eulerian solver, and associated Eulerian and Lagrangian domain partitions to minimize communication overhead. Based on the combined computational and experimental efforts, we have resolved for the first time the free-surface instabilities of the colliding droplets at such high Weber number. We detail the characteristics of coalescence, stretch, end pinching, fingering, free-surface movement and drop breakup. The Taylor-Culick rim is present soon after the collision. Furthermore, we observe two types of longitudinal instabilities on the rim, namely, the Rayleigh-Taylor (RT)-type instability in the initial deceleration phase of the circular sheet right after droplet coalescence, and later the Rayleigh-Plateau (RP) instabilities. As the Taylor-Culick rim disintegrates in the retraction phase, fingering effect is profound and resulting in wider droplet size distribution. © Cambridge University Press 2014.

Description: Many experimental studies have demonstrated that ducted premixed flames exhibit stable limit cycles in some regions of parameter space. Recent experiments have also shown that these (period-1) limit cycles subsequently bifurcate to period-2n, quasiperiodic, multiperiodic or chaotic behaviour. These secondary bifurcations cannot be found computationally using most existing frequency domain methods, because these methods assume that the velocity and pressure signals are harmonic. In an earlier study we have shown that matrix-free continuation methods can efficiently calculate the limit cycles of large thermoacoustic systems. This paper demonstrates that these continuation methods can also efficiently calculate the bifurcations from the limit cycles. Furthermore, once these bifurcations are found, it is then possible to isolate the coupled flame-acoustic motion that causes the qualitative change in behaviour. This information is vital for techniques that use selective damping to move bifurcations to more favourable locations in the parameter space. The matrix-free methods are demonstrated on a model of a ducted axisymmetric premixed flame, using a kinematic G-equation solver. The methods find limit cycles and period-2 limit cycles, and fold, period-doubling and Neimark-Sacker bifurcations as a function of the location of the flame in the duct, and the aspect ratio of the steady flame. © Cambridge University Press 2014.

Description: In this article, we introduce techniques to build a reduced-order model of a fluid system that accurately predicts the dynamics of a flow from local wall measurements. This is particularly difficult in the case of noise amplifiers where the upstream noise environment, triggering the flow via a receptivity process, is not known. A system identification approach, rather than a classical Galerkin technique, is used to extract the model from time-synchronous velocity snapshots and wall shear-stress measurements. The technique will be illustrated for the case of a transitional flat-plate boundary layer, where the snapshots of the flow are obtained from direct numerical simulations. Particular attention is directed to limiting the processed data to data that would be readily available in experiments, thus making the technique applicable to an experimental set-up. The proposed approach combines a reduction of the degrees of freedom of the system by a projection of the velocity snapshots onto a proper orthogonal decomposition basis combined with a system identification technique to obtain a state-space model. This model is then used in a feedforward control set-up to significantly reduce the kinetic energy of the perturbation field and thus successfully delay transition. © Cambridge University Press 2014.

Description: Recent directional solidification experiments with aqueous suspensions of alumina particles (Anderson & Worster, Langmuir, vol. 28 (48), 2012, pp. 16512-16523) motivate a model for freezing colloidal suspensions that builds upon a theoretical framework developed by Rempel et al. (J. Fluid Mech., vol. 498, 2004, pp. 227-244) in the context of freezing soils. Ice segregates from the suspension at slow freezing rates into discrete horizontal layers of particle-free ice, known as ice lenses. A portion of the particles is trapped between ice lenses, while the remainder are pushed ahead, forming a layer of fully compacted particles separated from the bulk suspension by a sharp compaction front. By dynamically modelling the compaction front, the growth kinetics of the ice lenses are fully coupled to the viscous flow through the evolving compacted layer. We examine the periodic states that develop at fixed freezing rates in a constant, uniform temperature gradient, and compare the results against experimental observations. Congruent with the experiments, three periodic regimes are identified. At low freezing rates, a regular periodic sequence of ice lenses is obtained; predictions for the compacted layer thickness and ice-lens characteristics as a function of freezing rate are consistent with experiments. At intermediate freezing rates, multiple modes of periodic ice lenses occur with a significantly diminished compacted layer. When the cohesion between the compacted particles is sufficiently strong, a sequence of mode-doubling bifurcations lead to chaos, which may explain the disordered ice lenses observed experimentally. Finally, beyond a critical freezing rate, the regime for sustained ice-lens growth breaks down. This breakdown is consistent with the emergence of a distinct regime of ice segregation found experimentally, which exhibits a periodic, banded structure that is qualitatively distinct from ice lenses. © Cambridge University Press 2014.

Description: Closed-loop control of an amplifier flow is experimentally investigated. A feed-forward algorithm is implemented to control the flow downstream of a backward-facing step (BFS) perturbed by upstream perturbations. Upstream and downstream data are extracted from real-time velocity fields to compute an ARMAX model used to effect actuation. This work, done at Reynolds number 430, investigates the practical feasibility of this approach which has shown great promise in a recent numerical study by Hervé et al. (J. Fluid Mech., vol. 702, 2012, pp. 26-58). The linear nature of the regime is checked, two-dimensional upstream perturbations are introduced, and the degree to which the flow can be controlled is quantified. The resulting actuation is able to effectively reduce downstream energy levels and fluctuations. The limitations and difficulties of applying such an approach to an experiment are also discussed. © Cambridge University Press 2014.

Description: Shallow flow past successive cavities is characterized by means of high-image-density particle image velocimetry (PIV). Highly coherent, self-sustained oscillations arise due to coupling between the inherent instability of the separated shear layer along the opening of each sequential cavity; and a gravity standing wave mode within each cavity. The globally coupled nature of the flow structure is evident through dominance of the same spectral component in the undulating vorticity layers along each of the successive cavities and the wall pressure fluctuations within the cavities. Unlike coupled phenomena associated with flow past a single cavity, optimal coupling for successive cavities requires a defined phase shift between the gravity standing wave patterns in adjacent cavities and, furthermore, an overall phase shift of the undulating shear layer along the cavity openings. The magnitudes of these phase shifts depend on the mode of the gravity standing wave in each cavity, i.e. longitudinal or transverse mode, which is respectively aligned with or normal to the main stream. Such phase shifts result in corresponding displacements of patterns of phase-referenced vorticity concentrations along the cavity openings and changes in the timing of impingement of these concentrations upon the downstream corners of successive cavities. All of the foregoing aspects are related to the unsteady recirculation flow within the cavity, the time-dependent streamline topology, and concentrations of Reynolds stress along the cavity opening. © Cambridge University Press 2014.

Description: Measurements are presented of the structural response and wake of a two-degree-of-freedom (2-DOF) pivoted cylinder undergoing streamwise vortex-induced vibrations (VIV), which were carried out using particle-image velocimetry (PIV). The results are compared with those of previous studies performed in the same experimental facility examining a cylinder free to move only in the streamwise direction (1-DOF). The aim of this study is to examine to what extent the results of previous work on streamwise-only VIV can be extrapolated to the more practical, multi-DOF case. The response regimes measured for the 1- and 2-DOF cases are similar, containing two response branches separated by a low-amplitude region. The first branch is characterised by negligible transverse motion and the appearance of both alternate and symmetric vortex shedding. The two wake modes compete in an unsteady manner; however, the competition does not appear to have a significant effect on either the streamwise or transverse motion. Comparison of the phase-averaged vorticity fields acquired in the second response branch also indicates that the additional DOF does not alter the vortex-shedding process. However, the additional DOF affects the cylinder-wake system in other ways; for the 1-DOF case the second branch can appear in three different forms (each associated with a different wake mode), while for the 2-DOF case the second branch only exists in one form, and does not exhibit hysteresis. The cylinder follows a figure-of-eight trajectory throughout the lock-in range. The phase angle between the streamwise and transverse motion decreases linearly with reduced velocity. This work highlights the similarities and differences between the fluid-structure interaction and wake dynamics associated with 1- and 2-DOF cylinders throughout the streamwise response regime, which has not received attention to date. © Cambridge University Press 2014.

Description: Linear stability of the Stuart vortices in the presence of an axial flow is studied. The local stability equations derived by Lifschitz & Hameiri (Phys. Fluids A, vol. 3 (11), 1991, pp. 2644-2651) are rewritten for a three-component (3C) two-dimensional (2D) base flow represented by a 2D streamfunction and an axial velocity that is a function of the streamfunction. We show that the local perturbations that describe an eigenmode of the flow should have wavevectors that are periodic upon their evolution around helical flow trajectories that are themselves periodic once projected on a plane perpendicular to the axial direction. Integrating the amplitude equations around periodic trajectories for wavevectors that are also periodic, it is found that the elliptic and hyperbolic instabilities, which are present without the axial velocity, disappear beyond a threshold value for the axial velocity strength. Furthermore, a threshold axial velocity strength, above which a new centrifugal instability branch is present, is identified. A heuristic criterion, which reduces to the Leibovich & Stewartson criterion in the limit of an axisymmetric vortex, for centrifugal instability in a non-axisymmetric vortex with an axial flow is then proposed. The new criterion, upon comparison with the numerical solutions of the local stability equations, is shown to describe the onset of centrifugal instability (and the corresponding growth rate) very accurately. © Cambridge University Press 2014.

Description: Gas flow through fractured nanoporous shale formations is complicated by a hierarchy of structural features (ranging from nanopores to microseismic and hydraulic fractures) and by several transport mechanisms that differ from the standard viscous flow used in reservoir modelling. In small pores, self-diffusion becomes more important than advection; also, slippage effects and Knudsen diffusion might become relevant at low densities. We derive a nonlinear effective diffusion coefficient that describes the main transport mechanisms in shale-gas production. In dimensionless form, this coefficient depends only on a geometric factor (or dimensionless permeability) and on the kinetic model that describes the gas. To simplify the description of the complex structure of fractured shales, we observe that the production rate is controlled by the flow from the shale matrix (which has the smallest diffusivity) into the fracture network, which is assumed to produce instantaneously. Therefore, we propose to model the flow in the shale matrix and estimate the production rate with a simple bundle-of-dual-tubes model (BoDTM), in which each tube is characterized by two diameters (one for transport and the other for storage). The solution of a single tube is approximately self-similar at early time, but not at late time, when the gas flux decays exponentially owing to the finite length of the tube. To construct a BoDTM, a reliable estimate of the joint statistics of the matrix-porosity parameters is required. This can be either inferred from core measurements or postulated on the basis of somea prioriassumptions when information from laboratory and field measurements is scarce. By comparison with field production data from the Barnett shale-gas field, we demonstrate that BoDTM can be calibrated to estimate structural parameters of the shale formation and to predict the cumulative production of shale gas. Our framework has enough flexibility to construct models of increasing complexity that can be employed in the presence of a complex dataset or when more information is available.

Description: Much of our understanding of the transition to turbulence in flows without a linear instability came with the discovery and characterization of fully three-dimensional solutions to the Navier-Stokes equation. The first examples in plane Couette flow were periodic in both spanwise and streamwise directions, and could explain the transitions in small domains only. The presence of localized turbulent spots in larger domains, the spatiotemporal decoherence on larger scales and the ability to trigger turbulence with pointwise perturbations require solutions that are localized in both directions, like the one presented by Brand & Gibson (J. Fluid Mech., vol. 750, 2014, R3). They describe a steady solution of the Navier-Stokes equations and characterize in unprecedented detail, including an analytic computation of its localization properties. The study opens up new ways to describe localized turbulent patches. © Cambridge University Press 2014.

Description: To contribute to the understanding of flow phenomena in abdominal aortic aneurysms, numerical computations of pulsatile flows through aneurysm models and a stability analysis of these flows were carried out. The volume flow rate waveforms into the aneurysms were based on measurements of these waveforms, under rest and exercise conditions, of patients suffering abdominal aortic aneurysms. The Reynolds number and Womersley number, the dimensionless quantities that characterize the flow, were varied within the physiologically relevant range, and the two geometric quantities that characterize the model aneurysm were varied to assess the influence of the length and maximal diameter of an aneurysm on the details of the flow. The computed flow phenomena and the induced wall shear stress distributions agree well with what was found in PIV measurements by Salsac et al. (J. Fluid Mech., vol. 560, 2006, pp. 19-51). The results suggest that long aneurysms are less pathological than short ones, and that patients with an abdominal aortic aneurysm are better to avoid physical exercise. The pulsatile flows were found to be unstable to three-dimensional disturbances if the aneurysm was sufficiently localized or had a sufficiently large maximal diameter, even for flow conditions during rest. The abdominal aortic aneurysm can be viewed as acting like a 'wavemaker' that induces disturbed flow conditions in healthy segments of the arterial system far downstream of the aneurysm; this may be related to the fact that one-fifth of the larger abdominal aortic aneurysms are found to extend into the common iliac arteries. Finally, we report a remarkable sensitivity of the wall shear stress distribution and the growth rate of three-dimensional disturbances to small details of the aneurysm geometry near the proximal end. These findings suggest that a sensitivity analysis is appropriate when a patient-specific computational study is carried out to obtain a quantitative description of the wall shear stress distribution. © Cambridge University Press 2014.

Description: This paper presents three-dimensional numerical simulations of non-Brownian concentrated suspensions in a Couette flow at zero Reynolds number using a fictitious domain method. Contacts between particles are modelled using a discrete element method (DEM)-like approach, which allows for a more physical description, including roughness and friction. This work emphasizes the effect of friction between particles and its role on rheological properties, especially on normal stress differences. Friction is shown to notably increase viscosity and second normal stress difference |N2| and decrease |N1|, in better agreement with experiments. The hydrodynamic and contact contributions to the overall particle stress are particularly investigated. This shows that the effect of friction is mostly due to the additional contact stress since the hydrodynamic stress remains unaffected by friction. Simulation results are also compared with experiments, such as normal stresses or effective friction coefficient μ (Iv), and the agreement is improved when friction is accounted for. This suggests that friction is operative in actual suspensions. © 2014 Cambridge University Press.

Description: The generation, redistribution and, importantly, conservation of vorticity and circulation is studied for incompressible Newtonian fluids in planar and axisymmetric geometries. A generalised formulation of the vorticity at the interface between two fluids for both no-slip and stress-free conditions is presented. Illustrative examples are provided for planar Couette flow, Poiseuille flow, the spin-up of a circular cylinder, and a cylinder below a free surface. For the last example, it is shown that, although large imbalances between positive and negative vorticity appear in the wake, the balance is found in the vortex sheet representing the stress-free surface. © Cambridge University Press 2014.

Description: The interaction of a planar shock wave with a polygonal N〈inf〉2〈/inf〉 volume surrounded by SF〈inf〉6〈/inf〉 is investigated experimentally and numerically. Three polygonal interfaces (square, triangle and diamond) are formed by the soap film technique developed in our previous work, in which thin pins are introduced as angular vertexes to connect adjacent sides of polygonal soap films. The evolutions of the shock-accelerated polygonal interfaces are then visualized by a high-speed schlieren system. Wave systems and interface structures can be clearly identified in experimental schlieren images, and agree well with the numerical ones. Quantitatively, the movement of the distorted interface, and the length and height of the interface structures are further compared and good agreements are achieved between experimental and numerical results. It is found that the evolution of these polygonal interfaces is closely related to their initial shapes. In the square interface, two vortices are generated shortly after the shock impact around the left corner and dominate the flow field at late stages. In the triangular and diamond cases, the most remarkable feature is the small 'SF〈inf〉6〈/inf〉 jet' which grows constantly with time and penetrates the downstream boundary of the interface, forming two independent vortices. These distinct morphologies of the three polygonal interfaces also lead to the different behaviours of the interface features including the length and height. It is also found that the velocities of the vortex pair predicted from the theory of Rudinger and Somers (J. Fluid Mech., vol.7, 1960, pp.161-176) agree with the experimental ones, especially for the square case. Typical free precursor irregular refraction phenomena and the transitions among them are observed and analysed, which gives direct experimental evidence for wave patterns and their transitions at a slow/fast interface. The velocities of triple points and shocks are experimentally measured. It is found that the transmitted shock near the interface boundary has weakened into an evanescent wave. © 2014 Cambridge University Press.

Description: This paper is concerned with a particular source of both broadband and tonal aeroengine noise, termed unsteady distortion noise. This noise arises from the interaction between turbulent eddies, which occur naturally in the atmosphere or are shed from the fuselage, and the rotor. This interaction produces broadband noise across a broad frequency spectrum. In cases in which there is strong streamtube contraction, which is especially true for open rotors at low-speed conditions (such as at take-off or for static testing), tonal noise at frequencies equal to multiples of the blade passing frequency are also produced, owing to the enhanced axial coherence caused by eddy stretching. In a previous paper (Majumdar & Peake, J. Fluid Mech., vol. 359, 1998, pp. 181-216), a model for unsteady distortion noise was developed in axisymmetric flow. However, asymmetric situations are also of much interest, and in this paper we consider two cases of asymmetric distortion: firstly that induced by the proximity of a second rotor, and secondly that caused by non-zero inclination to the flight direction, as found at take-off. This requires significant extension of the previous axisymmetric analysis. We find that the introduction of asymmetric flow features can have a significant decibel effect on the radiated sound power. For instance, in low-speed conditions we find that the tonal level is reduced significantly by the proximity of a second rotor, compared to the axisymmetric case, while the effect on the broadband levels is rather modest. © Cambridge University Press 2014.

Description: The stability of premixed flames in a duct is investigated using an asymptotic formulation, which is derived from first principles and based on high-activation-energy and low-Mach-number assumptions (Wu et al., J. Fluid Mech., vol. 497, 2003, pp. 23-53). The present approach takes into account the dynamic coupling between the flame and its spontaneous acoustic field, as well as the interactions between the hydrodynamic field and the flame. The focus is on the fundamental mechanisms of combustion instability. To this end, a linear stability analysis of some steady curved flames is undertaken. These steady flames are known to be stable when the spontaneous acoustic perturbations are ignored. However, we demonstrate that they are actually unstable when the latter effect is included. In order to corroborate this result, and also to provide a relatively simple model guiding active control, we derived an extended Michelson-Sivashinsky equation, which governs the linear and weakly nonlinear evolution of a perturbed flame under the influence of its spontaneous sound. Numerical solutions to the initial-value problem confirm the linear instability result, and show how the flame evolves nonlinearly with time. They also indicate that in certain parameter regimes the spontaneous sound can induce a strong secondary subharmonic parametric instability. This behaviour is explained and justified mathematically by resorting to Floquet theory. Finally we compare our theoretical results with experimental observations, showing that our model captures some of the observed behaviour of propagating flames. © Cambridge University Press 2014.

Description: We present wall-modelled large-eddy simulations (WLES) of oblique shock waves interacting with the turbulent boundary layers (TBLs) (nominal$def xmlpi #1{}def mathsfbi #1{ oldsymbol {mathsf {#1}}}let le =leqslant let leq =leqslant let ge =geqslant let geq =geqslant def Pr {mathit {Pr}}def Fr {mathit {Fr}}def Rey {mathit {Re}}delta _{99}=5.4 mathrm{mm}$and${mathit{Re}}_{heta }approx 1.4imes 10^4$) developed inside a duct with an almost-square cross-section ($45 mathrm{mm}imes 47.5 mathrm{mm}$) to investigate three-dimensional effects imposed by the lateral confinement of the flow. Three increasing strengths of the incident shock are considered, for a constant Mach number of the incoming air stream$Mapprox 2$, by varying the height (1.1, 3 and 5 mm) of a compression wedge located at a constant streamwise location that spans the top wall of the duct at a 20° angle. Simulation results are first validated with particle image velocimetry (PIV) experimental data obtained at several vertical planes (one near the centre of the duct and three near one of the sidewalls) for the 1.1 and 3 mm-high wedge cases. The instantaneous and time-averaged structure of the flow for the stronger-interaction case (5 mm-high wedge), which shows mean flow reversal, is then investigated. Additional spanwise-periodic simulations are performed to elucidate the influence of the sidewalls, and it is found that the structure and location of the shock system, as well as the size of the separation bubble, are significantly modified by the lateral confinement. A Mach stem at the first reflected interaction is present in the simulation with sidewalls, whereas a regular shock intersection results for the spanwise-periodic case. Low-frequency unsteadiness is observed in all interactions, being stronger for the secondary shock reflections of the shock train developed inside the duct. The downstream evolution of secondary turbulent flows developed near the corners of the duct as they traverse the shock system is also studied.

Description: An experimental investigation into the fluctuating pressure acting on sediment particles on the bed of an open-channel flow was carried out in a large laboratory flume for a range of flow depths and bed slopes. The pressure measurements were made using 23 spherical particles instrumented with differential pressure sensors. These measurements were complemented with simultaneous measurements of the velocity field using high-resolution stereoscopic particle image velocimetry. The pressure statistics show that the standard deviations of the drag and lift fluctuations vary from 2.0 to 2.6 and from 2.5 to 3.4 times the wall shear stress, respectively, and are dependent on relative submergence and flow Reynolds number. The skewness is positive for the drag fluctuations and negative for the lift fluctuations. The kurtosis values of both drag and lift fluctuations increase with particle submergence. The two-particle correlation between drag and lift fluctuations is found to be relatively weak compared to the two-point drag-drag and lift-lift correlations. The pressure cross-correlations between particles separated in the longitudinal direction exhibit maxima at certain time delays corresponding to the convection velocities varying from 0.64 to 0.72 times the bulk flow velocity, being very close to the near-bed eddy convection velocities. The temporal autocorrelation of drag fluctuations decays much faster than that for the lift fluctuations; as a result, the temporal scales of lift fluctuations are 3-6 times that of drag fluctuations. The spatial and temporal scales of both drag and lift fluctuations show dependence on flow depth and bed slope. The spectral behaviour of both drag and lift fluctuations is also assessed. A f-11/3 slope is observed for the spectra of the drag fluctuations over the majority of the frequency range, whereas the lift spectra suggest two scaling ranges, following a f-11/3 slope at high frequencies and f-5/3 behaviour at lower frequencies. © Cambridge University Press 2014.

Description: We describe an experimental study of the forces acting on a square cylinder (of width b) which occupies 10-40% of a channel (of width w), fixed in a free-surface channel flow. The force experienced by the obstacle depends critically on the Froude number upstream of the obstacle, Fr〈inf〉1〈/inf〉 (depth h〈inf〉1〈/inf〉), which sets the downstream Froude number, Fr〈inf〉2〈/inf〉 (depth h〈inf〉2〈/inf〉). When Fr〈inf〉1〈/inf〉 〈 Fr〈inf〉1c〈/inf〉, where Fr〈inf〉1c〈/inf〉 is a critical Froude number, the flow is subcritical upstream and downstream of the obstacle. The drag effect tends to decrease or increase the water depth downstream or upstream of the obstacle, respectively. The force is form drag caused by an attached wake and scales as F〈inf〉D〈/inf〉¯ ≃ C〈inf〉D〈/inf〉ρbu2〈inf〉1〈/inf〉h〈inf〉1〈/inf〉/2, where C〈inf〉D〈/inf〉 is a drag coefficient and u〈inf〉1〈/inf〉 is the upstream flow speed. The empirically determined drag coefficient is strongly influenced by blocking, and its variation follows the trend C〈inf〉D〈/inf〉 = C〈inf〉D0〈/inf〉(1 + C〈inf〉D0〈/inf〉b/2w)2, where C〈inf〉D0〈/inf〉 = 1.9 corresponds to the drag coefficient of a square cylinder in an unblocked turbulent flow. The r.m.s. lift force is approximately 10-40% of the mean drag force and is generated by vortex shedding from the obstacle. When Fr〈inf〉1〈/inf〉 = Fr〈inf〉1c〈/inf〉 (〈 1), the flow is choked and adjusts by generating a hydraulic jump downstream of the obstacle. The drag force scales as F¯〈inf〉D〈/inf〉 ≃ C〈inf〉K〈/inf〉ρbg(h2〈inf〉1〈/inf〉 - h2〈inf〉2〈/inf〉)/2, where experimentally we find C〈inf〉K〈/inf〉 ≃ 1. The r.m.s. lift force is significantly smaller than the mean drag force. A consistent model is developed to explain the transitional behaviour by using a semi-empirical form of the drag force that combines form and hydrostatic components. The mean drag force scales as F〈inf〉D〈/inf〉¯ ≃ λρbg1/3u4/3〈inf〉1〈/inf〉 h4/3〈inf〉1〈/inf〉, where λ is a function of b/w and Fr〈inf〉1〈/inf〉. For a choked flow, λ=λ〈inf〉c〈/inf〉 is a function of blocking (b/w). For small blocking fractions, λc = C〈inf〉D0〈/inf〉/2. In the choked flow regime, the largest contribution to the total drag force comes from the form-drag component. © 2014 Cambridge University Press.

Description: Density fronts are common features of ocean and atmosphere boundary layers. Field observations and numerical simulations have shown that the sharpening of frontal gradients, or frontogenesis, can spontaneously generate inertia-gravity waves (IGWs). Although significant progress has been made in describing frontogenesis using approximations such as quasi-geostrophy (Stone, J. Atmos. Sci., vol. 23, 1966, pp. 455-565, Williams & Plotkin J. Atmos. Sci., vol. 25, 1968, pp. 201-206) semi-geostrophy (Hoskins, Annu. Rev. Fluid Mech., vol. 14, 1982, pp.131-151), these models omit waves. Here, we further develop the analytical model of Shakespeare & Taylor (J. Fluid Mech., vol. 736, 2013, pp.366-413) to describe the spontaneous emission of IGWs from an initially geostrophically balanced front subjected to a time-varying horizontal strain. The model uses the idealised configuration of an infinitely long, straight front and uniform potential vorticity (PV) fluid, with a uniform imposed convergent strain across the front, similar to Hoskins & Bretherton (J. Atmos. Sci., vol. 29, 1972, pp.11-37). Inertia-gravity waves are generated via two distinct mechanisms: acceleration of the large-scale flow and frontal collapse. Wave emission via frontal collapse is predicted to be exponentially small for small values of strain but significant for larger strains. Time-varying strain can also generate finite-amplitude waves by accelerating the cross-front flow and disrupting geostrophic balance. In both cases waves are trapped by the oncoming strain flow and can only propagate away from the frontal zone when the strain field weakens sufficiently, leading to wave emission that is strongly localised in both time and space. © 2014 Cambridge University Press.

Description: A laminar water jet issuing at high speed from a short circular nozzle into air exhibits various instability features at different distances from the nozzle exit. Near the exit, the effects of gaseous friction and pressure are relatively weak. Deformation of the jet surface in this region is mainly due to the instability of a thin liquid shear layer flow, which relaxes from the velocity profile produced by the nozzle wall. In this paper, a model for this type of instability based on linear stability analysis is investigated to describe the process initiating the formation of liquid ligaments disintegrating into fine droplets near the nozzle exit. The modelling comprises identifying unstable waves excitable in the liquid shear layer and exploring a self-destabilizing mechanism by which unstable waves responsible for the formation of liquid ligaments are naturally reproduced from the upstream-propagating capillary waves produced by the growth of the unstable waves themselves. An expression for the location of ligament formation onset is derived that can be compared with experiments. The model also explains changes in jet instability features away from the nozzle exit and for very short nozzles.

Description: We investigate the fluctuations of thermodynamic state variables in compressible aerodynamic wall turbulence, using results of direct numerical simulation (DNS) of compressible turbulent plane channel flow. The basic transport equations governing the behaviour of thermodynamic variables (density, pressure, temperature and entropy) are reviewed and used to derive the exact transport equations for the variances and fluxes (transport by the fluctuating velocity field) of the thermodynamic fluctuations. The scaling with Reynolds and Mach number of compressible turbulent plane channel flow is discussed. Statistics and correlation coefficients of the thermodynamic fluctuations are examined. Finally, detailed budgets of the transport equations for the variances and fluxes of the thermodynamic variables are analysed. The implications of these results, leading both to the understanding of the thermodynamic interactions in compressible wall turbulence and to possible improvements in statistical modelling, are assessed. Finally, the required extension of existing DNS data to fully characterise this canonical flow is discussed. © 2014 Cambridge University Press.

Description: Porous geological formations are commonly interspersed with thin, roughly horizontal, low-permeability layers. Statistically steady convection at high Rayleigh number Ra is investigated numerically in a two-dimensional porous medium that is heated at the lower boundary and cooled at the upper, and contains a thin, horizontal, low-permeability interior layer. In the limit that both the dimensionless thickness h and permeability II of the low-permeability layer are small, the flow is described solely by the impedance of the layer ω h=II and by Ra. In the limit ω→ (i.e. h→o), the system reduces to a homogeneous Rayleigh-Darcy (porous Rayleigh-Bénard) cell. Two notable features are observed as ω is increased: the dominant horizontal length scale of the flow increases; and the heat flux, as measured by the Nusselt number ωu, can increase. For larger values of , ωu always decreases. The dependence of the flow on Ra is explored, over the range 2500≤Ra≤2×104. Simple one-dimensional models are developed to describe some of the observed features of the relationship Nuω. © © 2014 Cambridge University Press.

Description: Experiments have been performed on the disturbance of a high-Reynolds-number turbulent boundary layer by three forward steps with sizes close to 3.8, 15 and 60 % of the boundary layer thickness. Particular attention is focused on the impact of the steps on the fluctuating surface pressure field. Measurements were made from 5 boundary layer thicknesses upstream to 22 boundary layer thicknesses downstream of the step, a distance equivalent to over 600 step heights for the smallest step size. Flow speeds of 30 and 60 m s-1 were studied, corresponding to boundary layer momentum thickness Reynolds numbers of 15 500 and 26 600 and step size Reynolds numbers from 6640 to 213 000. The steps produce a disturbance to the boundary layer pressure spectrum that scales on step size and decays remarkably slowly with distance downstream. When normalized on step height and free-stream velocity, the disturbance is self-similar and appears to develop almost independently of the enveloping boundary layer. The disturbance is still clearly visible at 150 step heights downstream of the mid-size step. Pressure correlations show the disturbance to be characterized by organized quasiperiodic motions that become visible well downstream of reattachment. The coherence and scale of these motions, as seen in the wall pressure correlations, scales on the step height and thus their visibility relative to the boundary layer grows rapidly as the step size is increased. © 2014 Cambridge University Press.

Description: The very near wake of a flat plate with a circular trailing edge, exhibiting pronounced shedding of wake vortices, is investigated with data from direct numerical simulations (DNSs). Computations were performed for two cases. In the first case the Reynolds numbers based on plate length and thickness were 1.255 × 106 and 1.0 × 104, respectively. In the second case the two Reynolds numbers were 3.025 × 105 and 5.0 × 103, respectively. The separating boundary layers are turbulent and statistically identical thus resulting in a wake that is symmetric in the mean. The focus here is on the instability of the detached shear layers and the evolution of rib-vortex-induced localized regions of reverse flow. These regions detach from the main body of reverse flow in the trailing edge region and are convected downstream. The detached shear layers intermittently exhibit unstable behaviour, sometimes resulting in the development of shear-layer vortices as seen in earlier cylinder flow investigations with laminar separating boundary layers. Only a small fraction of the separated turbulent boundary layer experiences this instability, and also rolls up into the initial shed vortices. The instability causes a broadband peak in pressure spectra computed within the shear layers. Phase-averaged intensity and shear stress distributions of the randomly fluctuating component of velocity in the very near wake are also provided here and compared with those obtained in the near wake. The distributions of the production terms in the transport equations for the turbulent stresses are also provided. © © Cambridge University Press 2014. This is a work of the U.S. Government and is not subject to copyright protection in the United States..

Description: A new model to account for the presence of the test-section wall in wind-turbine or propeller measurements is proposed. The test section, here assumed to be cylindrical, is modelled by means of axisymmetric source panels, while the wind turbine (or the propeller) is modelled with a simplified vortex model (Segalini & Alfredsson, J. Fluid Mech., vol. 725, 2013, pp. 91-116). Combining both models in an iterative scheme allows the simulation of the effect of the test-section wall on the flow field around the rotor. Based on this novel approach, an analysis of the flow modification due to blockage is conducted together with a comparison of actuator-disk theory results. Glauert's concept of equivalent unconfined turbine is reviewed and extended to account for the angular velocity of the rotor. It is shown that Glauert's equivalent free-stream velocity concept is beneficial and can correct most of the systematic error introduced by the presence of the test-section wall, although some discrepancies remain, especially in the power coefficient. The effect of the confinement on the wake structure is also discussed in terms of wake expansion/contraction, pitch of the tip vortices and forces at the rotor. © 2014 Cambridge University Press.

Description: Air curtains are used to reduce the heat and mass exchange across open doorways. Their sealing ability is assessed in terms of the effectiveness E, the fraction of the exchange flow prevented by the air curtain compared to an unobstructed open door. Previous work has studied air-curtain effectiveness when the doorway is the only means of ventilating a space. In this paper, we examine the effects of additional displacement ventilation on the dynamics of the air curtain and the resulting changes in its effectiveness. The main controlling parameter is the deflection modulus Dm, which is the ratio between the momentum flux of the air curtain and the transverse forces due to the displacement ventilation. For a relatively warm interior, we find that, for small values of Dm, the air curtain is drawn inside the space by the ventilation flow. For large values of Dm, the flow through the doorway is controlled by the air curtain. A smooth transition occurs between these two regimes, and we estimate the Dm value for the onset of this transition. Our model provides a quantitative prediction of E.Dm/ in the ventilation-driven regime, and gives a qualitative description of the other two regimes. Laboratory experiments were conducted to test the proposed model. The experimental data were compared to theoretical predictions, and good agreement was found. © 2014 Cambridge University Press.

Description: Understanding the non-local pressure contributions and viscous effects on the small-scale statistics remains one of the central challenges in the study of homogeneous isotropic turbulence. Here we address this issue by studying the impact of the pressure Hessian as well as viscous diffusion on the statistics of the velocity gradient tensor in the framework of an exact statistical evolution equation. This evolution equation shares similarities with earlier phenomenological models for the Lagrangian velocity gradient tensor evolution, yet constitutes the starting point for a systematic study of the unclosed pressure Hessian and viscous diffusion terms. Based on the assumption of incompressible Gaussian velocity fields, closed expressions are obtained as the results of an evaluation of the characteristic functionals. The benefits and shortcomings of this Gaussian closure are discussed, and a generalization is proposed based on results from direct numerical simulations. This enhanced Gaussian closure yields, for example, insights on how the pressure Hessian prevents the finite-time singularity induced by the local self-amplification and how its interaction with viscous effects leads to the characteristic strain skewness phenomenon. © 2014 Cambridge University Press.

Description: In this study we undertook various calculations of the turbulent flow around a building in close proximity to neighbouring obstacles, with the aim of gaining an understanding of the velocity and the surface-pressure variations with respect to the azimuth angle of wind direction and the gap distance between the obstacles. This paper presents the effects of flow interference among consecutive cubes for azimuth angles of θ= 0, 15, 30, and 45° and gap distances of G D 0:5h; 1:0h; 1:5h, and ∞ (i.e. a single cube), where h is the cube height, placed in a turbulent boundary layer. A transient detached eddy simulation (DES) was carried out to calculate the highly complicated flow domain around the three wall-mounted cubes to observe the fluctuating pressure, which substantially contributes to the suction pressure when there is separation and reattachment around the leading and trailing edges of the cubes. In addition, the results indicate that an increasing azimuth angle increases the pressure variation on the centre cube of the three parallel-aligned cubes. The mean pressure variation can even change from negative to positive on the side face. Owing to interference effects, the mean pressure coefficient of the centre cube of the three parallel-aligned cubes was generally lower than the coefficient of the single cube and tended to increase depending on the gap distance. Furthermore, when the three consecutive cubes are in a tandem arrangement, the gap distance has little influence on the first cube but results in significant interference effects on the second and third cubes. © 2014 Cambridge University Press.

Description: We study the turbulent Ekman layer at moderately high Reynolds number, 1600 〈 Re = δ〈inf〉E〈/inf〉G/nu 〈 3000, using direct numerical simulations (DNS). Here, δ〈inf〉E〈/inf〉 = √2v/f is the laminar Ekman layer thickness, G the geostrophic wind, ν the kinematic viscosity and f is the Coriolis parameter. We present results for both neutrally, moderately and strongly stably stratified conditions. For unstratified cases, large-scale roll-like structures extending from the outer region down to the wall are observed. These structures have a clear dominant frequency and could be related to periodic oscillations or instabilities developing near the low-level jet. We discuss the effect of stratification and Re on one-point and two-point statistics. In the strongly stratified Ekman layer we observe stable co-existing large-scale laminar and turbulent patches appearing in the form of inclined bands, similar to other wall-bounded flows. For weaker stratification, continuously sustained turbulence strongly affected by buoyancy is produced. We discuss the scaling of turbulent length scales, height of the Ekman layer, friction velocity, veering angle at the wall and heat flux. The boundary-layer thickness, the friction velocity and the veering angle depend on Lf/uτ, where u〈inf〉τ〈/inf〉 is the friction velocity and L the Obukhov length scale, whereas the heat fluxes appear to scale with L+=Lu〈inf〉τ〈/inf〉/ν. © © 2014 Cambridge University Press.

Description: We report our systematic development of a general and exact theory for diagnosis of total force and moment exerted on a generic body moving and deforming in a calorically perfect gas. The total force and moment consist of a longitudinal part (L-force) due to compressibility and irreversible thermodynamics, and a transverse part (T-force) due to shearing. The latter exists in incompressible flow but is now modulated by the former. The theory represents a full extension of a unified incompressible diagnosis theory of the same type developed by J. Z. Wu and coworkers to compressible flow, with Mach number ranging from low-subsonic to moderate-supersonic flows. Combined with computational fluid dynamics (CFD) simulation, the theory permits quantitative identification of various complex flow structures and processes responsible for the forces, and thereby enables rational optimal configuration design and flow control. The theory is confirmed by a numerical simulation of circular-cylinder flow in the range of free-stream Mach number M1 between 0.2 and 2.0. The L-drag and T-drag of the cylinder vary with M1 in different ways, the underlying physical mechanisms of which are analysed. Moreover, each L-force and T-force integrand contains a universal factor of local Mach number M. Our preliminary tests suggest that the possibility of finding new similarity rules for each force constituent could be quite promising. © 2014 Cambridge University Press.

Description: Helicity, which is defined as the scalar product of velocity and vorticity, H=u · ω, is an inviscidly conserved quantity in a barotropic fluid. Mean helicity is zero in flows that are parity invariant. System rotation breaks parity invariance and has therefore the potential of giving rise to non-zero mean helicity. In this paper we study the helicity dynamics in the incompressible Ekman boundary layer. Evolution equations for the mean field helicity and the mean turbulent helicity are derived and it is shown that pressure flux injects helicity at a rate 2ΩG2 over the total depth of the Ekman layer, where G is the geostrophic wind far from the wall and Ω = Ωe〈inf〉y〈/inf〉 is the rotation vector and ey is the wall-normal unit vector. Thus right-handed/left-handed helicity will be injected if Ω is positive/negative. We also show that in the uppermost part of the boundary layer there is a net helicity injection with opposite sign as compared with the totally integrated injection. Isotropic relations for the helicity dissipation and the helicity spectrum are derived and it is shown that it is sufficient to measure two transverse velocity components and use Taylor's hypothesis in the mean flow direction in order to measure the isotropic helicity spectrum. We compare the theoretical predictions with a direct numerical simulation of an Ekman boundary layer and confirm that there is a preference for right-handed helicity in the lower part of the Ekman layer and left-handed helicity in the uppermost part when Ω 〉 0. In the logarithmic range, the helicity dissipation conforms to isotropic relations. On the other hand, spectra show significant departures from isotropic conditions, suggesting that the Reynolds number considered in the study is not sufficiently large for isotropy to be valid in a wide range of scales. Our analytical and numerical results strongly suggest that there is a turbulent helicity cascade of right-handed helicity in the logarithmic range of the atmospheric boundary layer when Ω 〉 0, consistent with recent measurements by Koprov, Koprov, Ponomarev & Chkhetiani (Dokl. Phys., vol. 50, 2005, pp. 419'422). The isotropic relations which are derived may facilitate future measurements of the helicity spectrum in the atmospheric boundary layer as well as in controlled wind tunnel experiments. © 2014 Cambridge University Press.

Description: We examine the effect of large bulk viscosity on the classical problem of two-dimensional shock-boundary-layer interaction. The flow is taken to be steady and supersonic over a flat adiabatic plate. The boundary layer is taken to be laminar and the fluid is modelled as a perfect gas with a bulk viscosity that is large compared with its shear viscosity. The flow details are computed using a fifth-order weighted essentially non-oscillatory finite difference scheme and a third-order Runge-Kutta scheme for the spatial and temporal discretizations. The primary result of interest is the suppression of separation when the ratio of bulk to shear viscosity is sufficiently large. © 2014 Cambridge University Press.

Description: We present a simple two-step method by which one-dimensional spectra of horizontal velocity and buoyancy measured along a ship track can be decomposed into a wave component consisting of inertia-gravity waves and a vortex component consisting of a horizontal flow in geostrophic balance. The method requires certain assumptions for the data regarding stationarity, homogeneity, and horizontal isotropy. In the first step an exact Helmholtz decomposition of the horizontal velocity spectra into rotational and divergent components is performed and in the second step an energy equipartition property of hydrostatic inertia-gravity waves is exploited that allows a diagnosis of the wave energy spectrum solely from the observed horizontal velocities. The observed buoyancy spectrum can then be used to compute the residual vortex energy spectrum. Further wave-vortex decompositions of the observed fields are possible if additional information about the frequency content of the waves is available. We illustrate the method on two recent oceanic data sets from the North Pacific and the Gulf Stream. Notably, both steps in our new method might be of broader use in the theoretical and observational study of atmosphere and ocean fluid dynamics. © 2014 Cambridge University Press.

Description: Thrust-generating flapping foils are known to produce jets inclined to the free stream at high Strouhal numbers St = fA/U〈inf〉∞〈/inf〉, where f is the frequency and A is the amplitude of flapping and U〈inf〉∞〈/inf〉 is the free-stream velocity. Our experiments, in the limiting case of St → ∞ (zero free-stream speed), show that a purely oscillatory pitching motion of a chordwise flexible foil produces a coherent jet composed of a reverse Bénard-Kármán vortex street along the centreline, albeit over a specific range of effective flap stiffnesses. We obtain flexibility by attaching a thin flap to the trailing edge of a rigid NACA0015 foil; length of flap is 0.79 c where c is rigid foil chord length. It is the time-varying deflections of the flexible flap that suppress the meandering found in the jets produced by a pitching rigid foil for zero free-stream condition. Recent experiments (Marais et al., J. Fluid Mech., vol. 710, 2012, p. 659) have also shown that the flexibility increases the St at which non-deflected jets are obtained. Analysing the near-wake vortex dynamics from flow visualization and particle image velocimetry (PIV) measurements, we identify the mechanisms by which flexibility suppresses jet deflection and meandering. A convenient characterization of flap deformation, caused by fluid-flap interaction, is through a non-dimensional 'effective stiffness', EI∗ = 8 EI/(ρV〈inf〉TEmax〈/inf〉2 sf c〈inf〉f〈/inf〉3/2), representing the inverse of the flap deflection due to the fluid-dynamic loading; here, EI is the bending stiffness of flap, ρ is fluid density, V〈inf〉TEmax〈/inf〉 is the maximum velocity of rigid foil trailing edge, sf is span and c〈inf〉f〈/inf〉 is chord length of the flexible flap. By varying the amplitude and frequency of pitching, we obtain a variation in EI∗ over nearly two orders of magnitude and show that only moderate EI∗ (0.1 ≲ EI∗ ≲ 1) generates a sustained, coherent, orderly jet. Relatively 'stiff' flaps (EI∗ ≳ 1), including the extreme case of no flap, produce meandering jets, whereas highly 'flexible' flaps (EI∗ ≲ 0.1) produce spread-out jets. Obtained from the measured mean velocity fields, we present values of thrust coefficients for the cases for which orderly jets are observed. © 2014 Cambridge University Press.

Description: Interestingly, the Chapman-Jouguet detonation velocity (Dcj) based on a one-dimensional and steady model compares well with the measured data. For the spinning detonation, in particular, this agreement is particularly notable, since the flow is highly three-dimensional and unsteady; perpendicular to the leading shock front, a transverse detonation wave (TDW) spins periodically. In the wake of this TDW, a secondary flow, called here the cross-current, appears which is orthogonal to the leading shock. Despite the presence of these cross-currents, the DCJ agreement remains remarkably satisfactory, and we investigate the reason for this, for spinning detonation in a tube. First, we focus on the origin of the cross-current. The cross-current, driven by the shock pressure, arises initially across a warped shock frontal surface, and both its sign and magnitude depend on the local slopes of the shock surface. The cross-current undergoes further pressure-driven transitions, with its magnitude eventually diminishing downstream and reducing the flow to a quasi-one-dimensional one. Second, regarding the unsteadiness, under the assumptions that the TDW spins at constant angular wave speed and the flow is steady in the frame rotating with it, the unsteady energy equation becomes integrable, resulting in the invariance of the so-called rothalpy. Also, in the integral forms of the mass and momentum balance, the unsteady terms drop out. Taken together, in the far field the governing equations are reduced to being one-dimensional and steady. From these the (Dcj) follows immediately, which appears to be the reason for the enduring usefulness of the (Dcj). The results of the analysis are confirmed with computational fluid dynamics (CFD). Additionally, the area-averaged flow profiles are found to display more than a passing resemblance to the Zeldovitch-Von Neumann-Doering (ZND) model. © © 2014 Cambridge University Press.

Description: An investigation into the influence of seemingly analogous kinematics (plunge versus tow) for rapidly accelerating, low-aspect-ratio plates has been performed. The instantaneous forces and velocity fields were obtained simultaneously using a six-component force/moment sensor together with a three-dimensional particle tracking velocimetry (3D-PTV) system. Despite identical effective shear-layer velocities and effective angles of attack, the force histories are found to vary between the two aforementioned cases (plunge versus tow) once the impulsive motion is complete, as originally reported on by Kriegseis etA al.A (J. Fluid Mech., vol. 736, 2013, pp.A 91-106). In order to uncover the cause for this curious discrepancy between the two analogous cases a vortex force decomposition is implemented. It is shown that the interplay between growth and orientation of the vortical structures significantly affects vortical hydrodynamic impulse and vortex force, and thus the net lift on the body. © © 2014 Cambridge University Press.

Description: The realizability condition for statistical models of turbulence is augmented to ensure that not only is the Reynolds stress tensor positive semi-definite, but the process of its evolution is physically attainable as well. The mathematical constraints due to this process realizability requirement on the rapid pressure strain correlation are derived. The resulting constraints reveal important limits on the inter-component energy transfer and the consequent flow stability characteristics, as a function of the mean flow. For planar mean flows, the realizability constraints are most stringent for the case of purely sheared flows rather than elliptic flows. The relationship between the constraints and flow stability is explained. Process realizability leads to closure model guidance not only at the two-component (2C) limit of turbulence (as in the classical realizability approach) but throughout the anisotropy space. Consequently, the domain of validity and applicability of current models can be clearly identified for different mean flows. A simple framework for incorporating these process realizability constraints in model formulation is outlined. © 2014 Cambridge University Press.

Description: By characterising the hydrodynamic stresses generated by statistically homogeneous and isotropic turbulence in rigid aggregates, we estimate theoretically the rate of turbulent breakup of colloidal aggregates and the size distribution of the formed fragments. The adopted method combines direct numerical simulation of the turbulent field with a discrete element method based on Stokesian dynamics. In this way, not only is the mechanics of the aggregate modelled in detail, but the internal stresses are evaluated while the aggregate is moving in the turbulent flow. We examine doublets and cluster-cluster isostatic aggregates, where the failure of a single contact leads to the rupture of the aggregate and breakup occurs when the tensile force at a contact exceeds the cohesive strength of the bond. Owing to the different role of the internal stresses, the functional relationship between breakup frequency and turbulence dissipation rate is very different in the two cases. In the limit of very small and very large values, the frequency of breakup scales exponentially with the turbulence dissipation rate for doublets, while it follows a power law for cluster-cluster aggregates. For the case of large isostatic aggregates, it is confirmed that the proper scaling length for maximum stress and breakup is the radius of gyration. The cumulative fragment distribution function is nearly independent of the mean turbulence dissipation rate and can be approximated by the sum of a small erosive component and a term that is quadratic with respect to fragment size. © Cambridge University Press 2014.

Description: The linear instability of several rotating, stably stratified, interior vertical shear flows U.z/ is calculated in Boussinesq equations. Two types of baroclinic, ageostrophic instability, AI1 and AI2, are found in odd-symmetric U.z/ for intermediate Rossby number (Ro). AI1 has zero frequency; it appears in a continuous transformation of the unstable mode properties between classic baroclinic instability (BCI) and centrifugal instability (CI). It begins to occur at intermediate Ro values and horizontal wavenumbers (k; l) that are far from lD0 or k D0, where the growth rate of BCI or CI is the strongest. AI1 grows by drawing kinetic energy from the mean flow, and the perturbation converts kinetic energy to potential energy. The instability AI2 has inertia critical layers (ICL); hence it is associated with inertia-gravity waves. For an unstable AI2 mode, the coupling is either between an interior balanced shear wave and an inertia-gravity wave (BG), or between two inertia-gravity waves (GG). The main energy source for an unstable BG mode is the mean kinetic energy, while the main energy source for an unstable GG mode is the mean available potential energy. AI1 and BG type AI2 occur in the neighbourhood of ASD0 (a sign change in the difference between absolute vertical vorticity and horizontal strain rate in isentropic coordinates; see McWilliams et al., Phys. Fluids, vol. 10, 1998, pp. 3178-3184), while GG type AI2 arises beyond this condition. Both AI1 and AI2 are unbalanced instabilities; they serve as an initiation of a possible local route for the loss of balance in 3D interior flows, leading to an efficient energy transfer to small scales. © 2014 Cambridge University Press.

Description: We investigate the shock-induced turbulent mixing between a light and a heavy gas, where a Richtmyer-Meshkov instability (RMI) is initiated by a shock wave with Mach number Ma = 1.5. The prescribed initial conditions define a deterministic multimode interface perturbation between the gases, which can be imposed exactly for different simulation codes and resolutions to allow for quantitative comparison. Wellresolved large-eddy simulations are performed using two different and independently developed numerical methods with the objective of assessing turbulence structures, prediction uncertainties and convergence behaviour. The two numerical methods differ fundamentally with respect to the employed subgrid-scale regularisation, each representing state-of-the-art approaches to RMI. Unlike previous studies, the focus of the present investigation is to quantify the uncertainties introduced by the numerical method, as there is strong evidence that subgrid-scale regularisation and truncation errors may have a significant effect on the linear and nonlinear stages of the RMI evolution. Fourier diagnostics reveal that the larger energy-containing scales converge rapidly with increasing mesh resolution and thus are in excellent agreement for the two numerical methods. Spectra of gradient-dependent quantities, such as enstrophy and scalar dissipation rate, show stronger dependences on the small-scale flow field structures as a consequence of truncation error effects, which for one numerical method are dominantly dissipative and for the other dominantly dispersive. Additionally, the study reveals details of various stages of RMI, as the flow transitions from large-scale nonlinear entrainment to fully developed turbulent mixing. The growth rates of the mixing zone widths as obtained by the two numerical methods are ~t7/12 before re-shock and ~(t - t0)2/7 long after re-shock. The decay rate of turbulence kinetic energy is consistently ~(t-t0)-10/7 at late times, where the molecular mixing fraction approaches an asymptotic limit ≈ 0.85. The anisotropy measure.

Description: The problem of near-trapping of linear water waves in the time domain for rigid bodies or variations in bathymetry is considered. The singularity expansion method (SEM) is used to give an approximation of the solution as a projection onto a basis of modes. This requires a modification of the method so that the modes, which grow towards infinity, can be correctly normalized. A time-dependent solution, which allows for possible trapped modes, is introduced through the generalized eigenfunction method. The expression for the trapped mode and the expression for the near-trapped mode given by the SEM are shown to be closely connected. A numerical method that allows the SEM to be implemented is also presented. This method combines the boundary element method with an eigenfunction expansion, which allows the solution to be extended analytically to complex frequencies. The technique is illustrated by numerical simulations for geometries that support near-trapping. © 2014 Cambridge University Press.