ALBERT

Description: ... Pujol's book differs from the others in its purely theoretical approach to the generation and propagation of seismic waves. The author aims to fill a gap between the advanced books and the introductory ones, providing a complete derivation of the mathematical developments. ... One does not have to look for proofs elsewhere.

Description: Coral skeletal radiocarbon records reflect seawater ∆14C and are useful for reconstructing the history of water mass movement and ventilation in the tropical oceans. Here, we reconstructed the inter-annual variability in central equatorial Pacific surface water ∆14C from 1922–1956 using near-monthly 14C measurements in a Porites sp. coral skeleton (FI5A) from the windward side of Fanning Island (3°54′32′′N, 159°18'88′′W). The most pronounced feature in this record is a large, positive shift in the ∆14C between 1947 and 1956 that coincides with the switch of the Pacific Decadal Oscillation (PDO) from a positive to a negative phase in the mid-1940s. Although the absolute ∆14C values from 1950–1955 in FI5A differ from the ∆14C values of another coral core collected from the opposite side of the island, both records show a large, positive shift in their ∆14C records at that time. The relative increase in the ∆14C of each record is consistent with the premise that a common mechanism is controlling the ∆14C records within each coral record. Overall, the Fanning ∆14C data support the notion that a significant amount of subtropical seawater is arriving at the Equator, but does not allow us to determine the mechanism for its transport.

Description: The Russian Far East is characterized by widespread peat bogs with a sufficiently thick peat accumulation. A series of radiocarbon dates from the studied peat bogs (in Lower Amur) were obtained. Analysis of these dates shows that the total peat formation in this territory began in the Late Pleistocene–Holocene (11830 ± 820, TIG-157; 9975 ± 120, SOAN-4025). The rates of peat accumulation and the humidity index were counted. In addition, the botanical composition and degree of peat decomposition were defined. These data allow to study in more detail climate fluctuation and the 14C chronology of Holocene events in the region studied.

Description: Radiocarbon dating is universally used as an essential dating tool in the archaeological and earth (Quaternary) sciences. The technique has enjoyed considerable success with ongoing developments in both the sophistication of experimental practice and an ever-widening range of applications. Most recently (since the 1980s), a new generation of laboratories has been created, based on the exploitation of accelerator mass spectrometry (AMS) for the differentiation and measurement of carbon isotope abundances in natural materials. Worldwide, there are over 100 14C laboratories now operational in universities, research organizations, museums, and as commercial enterprises. There is an inevitable diversity of experimental approaches and applied priorities within these facilities. Some are well established, while others are relatively recent members of the international 14C community. Consequently, as a group, the laboratories reflect to varying extents the progress achieved over several decades of experience and methodological options. Furthermore, since progress in archaeology and related earth sciences cannot respect geographical and/or present political boundaries, there has been, and continues to be, an inevitable consequence that sample materials from specific cultural contexts are submitted to different laboratories and at different times. In this situation, the issue of comparability between results and amongst laboratories becomes paramount. Users of the results from 14C dating are also concerned with the comparability and quality of laboratory results and the quality assurance programs that laboratories undertake are thus important in ensuring user confidence. The harmonization of measurements and the traceability of results to internationally recognized standards are also major goals of the program of work described in this special issue.

Description: This paper examines the development of EU regulations in the car distribution sector. In the span of approximately fifteen years, the sector has shifted from being regarded by its critics as being one of the most protected havens of European industry to one faced with open competition. The paper claims that the inability of the car industry to resist liberalization in this sector is related to several factors. First, there was declining support from member states for their national producers, in part explained by global shifts in ownership and production which rendered concepts of “national producer” problematic. Second, technological changes combined with the impact of globalization on in the industry undermined the case for a link between sales and service of cars. Third, DG competition, led by Mario Monti, wished to push through the ability of consumers to make cross-border purchases of cars. Fourth, a more general logic embedded in the Single European Market programme (SEM) had led to several decisions to prosecute EU car producers for infringing SEM rules and thereby undermining the ability of EU member states to protect their “national producers.” This has implications more broadly: will increasing globalization of industrial ownership further undermine the state-firm nexus in the EU, thus reducing the propensity of national industries to resist liberalization? In this context, will member states be prepared to give the EU Commission a freer hand in forcing through liberalization in the remaining sectors that remain problematic?

Description: This paper outlines an approach for understanding the role of multinational corporations (MNCs) in global governance. We develop a typology of regime types with two dimensions, the goal of the regime, which can be market enabling or regulatory, and the location of authority, which can be national, regional, or international, with public and private elements. MNCs tend to support the creation of market enabling regimes at the international level, and prefer to keep social or environmental regulation under national or private authority. However, these are only generalizations and MNCs develop preferences based on their relative influence in various arenas, the costs of political participation, and competitive considerations. We argue that institutions of global governance represent the outcome of a series of negotiations among corporations, states, and non-state actors. The preferences and power of MNCs vary across issues and sectors, and from one negotiating forum to another, accounting for the uneven and fragmented nature of the resulting system. Our approach differs from the traditional FDI bargaining framework in that it recognizes the multi-party nature of negotiations and multiple sources of power. Moreover, the complexity and dynamic nature of the process results in a somewhat indeterminate process.

Description: This paper addresses the intersection of coalition formation, judicial strategies, and regulatory politics. Coalitions are a low-cost means for assembling minority interests into more powerful blocs. However, in most cases in regulatory politics, judicial strategies are high cost efforts. I argue that coalitions among interests form one basis for judicial participation, but that participation manifests in an array of coalition “microstructures.” For any one event, the microstructure of the interest group coalition varies, but across events the coalitions take on general forms. The paper offers evidence for a variety of coalition microstructures in interest group participation as amici curiae (“friends of the court”) in cases before the United States Supreme Court. The evidence is drawn from the case of the Group of Ten, a stable, long-term coalition of environmental interest groups that operated from 1981 to 1991.

Description: This paper considers whether highly concentrated industries are better represented in the political process, as Olson's Logic of Collective Action suggests, and, if they are, whether this is so for the reasons that the Logic claims. It begins with a review and critique of the quantitative literature that has largely tried and failed to substantiate Olson's view. The bulk of the paper consists of five longitudinal case studies of firms that dominate or have dominated industries: IBM, Intel, Microsoft, America Online, and Cisco. The cases suggest that there is merit to the Olsonian view, but that alone it does not constitute an adequate political theory of the concentrated industry or the dominant firm. Additional variables drawn from organizational and institutional theory need to be incorporated into such a theory, including variables that bear on the allocation of attention, threat perception, and information flow within dominant firms.

Description: The problems of rent seeking and state captured by business associations have been prominent among the concerns of economic development theory. This paper argues that firms and the state can make possible the building of new institutions that foster improvements in economic performance through arrangements that emphasize goal setting, problem solving, and continual evaluation of progress toward defined goals. The paper reviews key ideas on the learning-centered approach and builds on them to analyze the kinds of government–business relations that contribute to economic development. It uses case study material based on Chile's agro-industry business association FEPACH. It illustrates how innovative state policy coupled with private firms' efforts led to the discovery of group-based coordination that fostered rapid diffusion of new technology and production organization among Chilean enterprises. This work discusses the institutional reshaping of the business association and business–state relations to encourage learning and advance a process of development.

Description: This study of Japanese consumer electronic networks in North America challenges conventional wisdom on the pervasiveness of keiretsu ties in Japanese production networks abroad. The consumer electronics industry poses hard questions to current views on the relationship between keiretsu and FDI not only because of the more modest internationalization of subcontractors, but more interestingly, because Japanese electronic production networks overseas remained remarkably closed to outside suppliers even in the absence of keiretsu commitments that could constrain purchasing decisions. This article offers a comparison of domestic subcontracting practices in the Japanese automobile and consumer electronic industries, a discussion of the internationalization of electronic part makers, and an analysis of the sourcing strategies of Japanese firms in North America. The article highlights the impact of the non-market environment in Japanese FDI strategies since Japanese companies embarked on foreign production in North America as a direct response to export caps imposed by the American government and/or tighter regional integration rules adopted in NAFTA. Revealingly, Japanese automobile and electronic firms diverged in their reliance on subcontracting firms to meet the more stringent demands for regional production.

Description: The increasing trend towards the internationalization of the world economy coupled with the liberalizing agenda of international institutions and Western governments has profound implications for the delivery of health and other welfare services. As governments pursue policies which extend the scope for the involvement of private companies in the delivery of welfare services, processes of internationalization are likely to become increasingly important to such services as multinational providers emerge. This article begins the process of developing a systematic understanding of the relationships between the structure of welfare states, the social and economic policies of governments and international institutions, and the strategies and interests of private companies. It is argued that it is the particular mix of direct state provision, tax/subsidy, and regulation in the welfare state formation that provides the opportunities for, or barriers to, the expansion of internationalizing private providers of healthcare. This argument is illustrated through a case study of the current process of reform in the British healthcare system, where a relative shift away from direct state provision towards subsidizing and regulating private providers is facilitating a process of internationalization.

Description: The key objective of this paper is to highlight the interconnectedness between China's political and economic system and its weak enforcement of accounting and auditing standards. The institutional analysis shows that the prevailing political and economic priorities constituting China's “socialist market economy” create a framework, that basically relies on state-led enforcement with weak supplementary private safeguard mechanisms. The resulting policy-mix is characterized by a mismatch of incentives and available devices to effectively enhance enforcement. While the state bureaucracy has little incentive to effectively fight financial misreporting because of both blurred policy–economy boundaries and the coexistence of multiple and even non-economic goals, shareholders and creditors do not have sufficient and effective private safeguard mechanisms at hand. Findings lead to the conclusion that China's recent harmonization move of accounting and auditing standards urgently needs to be backed up by stronger efforts to create effective enforcement mechanisms. Sound reforms would have to center on a rigorous upgrading and restructuring of the responsible bodies supervising auditing quality and financial disclosure. Parallel to these measures, the increasing integration into the global economy may provide incentives and competitive pressure to comply with globally accepted standards.

Description: State Supreme Courts have grown in importance during the last thirty years in the formation of public policy. Their judgements determine many aspects of constitutional law, tort reform, judicial selection, and campaign finance reform, among others. A vast body of literature has been developed that analyzes State Supreme Court decision making, which emphasizes the conditioning effects of the legal and institutional environment. This article expands on this previous work by incorporating the interaction of the judiciary with other government institutions, and applies the Positive Political Theory approach to law and legal institutions to the State Supreme Court. In addition, the neo-institutionalist literature of the selection process is incorporated to defend a systematic approach towards decision making. Towards that end, this article explores how judicial decisions are conditioned by institutional rules, resulting in a formal modeling of how the State Supreme Courts interact with political actors to form constitutional interpretation. This model includes the judicial selection process'retention or competitive reelection—and is extended to constitutional amendment rules, explaining how these two interact rather than acting independently. Finally, the hypothesis is tested that when State Supreme Court judges face retention elections and political preferences are homogeneous, the probability increases of observing constitutional amendment prosposals.

Description: Kauri wood, a sub-fossil wood from New Zealand (which had previously been used in an IAEA exercise, IAEA-C4, in 1990), was considered to be an important sample to include in FIRI because it provided a link to previous exercises, was available in sufficient quantity, and was a “close to background” organic sample. IAEA-C4 had previously been criticized since it was believed that in its milling, some contamination had been introduced, so that a replacement sample would prove useful. The Kauri wood has a very low 14C activity and, as such, is very sensitive to even small amounts of contaminant carbon. Such low-activity samples give a true test for the laboratory procedures since pretreatment and laboratory background definition become critical.

Description: The design of FIRI is such that for each laboratory, we have some basic, though limited, information on the laboratory procedures, including the method of pretreatment applied to the samples, the modern standard, and the background material used. These can be considered as factors in the experiment and through statistical analysis, we can investigate whether they offer a statistically significant explanation of the observed variation. The different levels of the factors are described in Table 4.1. In addition, the laboratory type is also considered as a further factor (with 3 levels of LSC, GPC, and AMS).

Description: The design of FIRI included 3 pairs of duplicate samples: A and B (Kauri wood) near background, D and F (Belfast wood) around 50 pMC, and G and J (barley mash) at 111 pMC. Why include duplicates? Duplicates by their nature allow us to explore the within-lab variability and to assess whether the quoted errors are representative. We can also explore the differences as a function of the sample activity. In this section, we explore the differences between the duplicates. We also consider some different graphical presentations. First, we summarize the differences, then graphically explore the boxplot (to consider the distribution of differences), then a scatterplot of the duplicate pair (to show correlation and reproducibility), and finally, a measure of agreement plot (Bland and Altman 1999). The horizontal axis in this final plot is the mean of the duplicate pair and the vertical axis is the difference in the duplicate pair. Agreement between the pairs would result in the points being randomly scattered around the horizontal zero line.

Description: As part of the FIRI program, it was recognized that providing samples in sufficient quantity for laboratory procedures is close to ideal and does not represent “typical” conditions. Therefore, laboratories were asked to consider 2 optional studies: investigating the effects of sample size on results and achieving high precision. The sample size study was focused on Sample E, humic acid, which had been chosen because of the rigorous pretreatment it had undergone in the solution stage, and which would ensure sample homogeneity. The precision study was focused on Sample D, the Belfast dendro-dated wood sample, given its importance in the master calibration.

Description: The issue of comparability of measurements (and thus bias, accuracy, and precision of measurement) from diverse laboratories is one which has been the focus of some attention both within the radiocarbon community and the wider user communities. As a result, the 14C community has undertaken a widescale, far-reaching, and evolving program of intercomparisons, to the benefit of laboratories and users alike. The benefit to the users is, however, indirect, since the 14C intercomparisons have not been used to generate “league tables” of performance, but rather to allow individual laboratories to check procedures and modify them as required.The historical progression of 14C laboratory intercomparisons from the Third (TIRI, completed in 1995, Gulliksen and Scott 1995) and Fourth (FIRI, completed in 2000, Scott 2003; Boaretto et al. 2000; Bryant et al. 2002) suggests that a Fifth (VIRI) should also be expected. We describe the plans for VIRI.

Description: It is common practice to estimate the age of undated material extracted from a sediment core from radiocarbon or other radiometric dates of samples taken above and below the extracted material. This paper presents a simple expression for the variance of this estimated age. This variance accounts for both 14C dating error and error due to bioturbation.

Description: Carmi (2002) is a response to our study published in Radiocarbon 43(1) by Rasmussen et al. (2001). We noted widespread possible exposure to castor oil of the Dead Sea Scrolls (DSS) in the Rockefeller Museum in the 1950s and reported experiments showing that the AAA pretreatment used in the first 2 series of radiocarbon datings of the DSS (Bonani et al. [1992] and Jull et al. [1995]), “cannot be guaranteed to have removed all of the modern carbon in any samples if they had been contaminated with castor oil and hence could have produced some 14C dates that were younger than the texts' true ages.” Carmi, a coauthor of the Bonani et al. (1992) study, criticizes our analysis on 4 grounds:

Description: Pachacamac, covering an area of about 600 hectares (ha) near the Pacific shore, is one of the largest and most important archaeological sites in Peru. Most of the monumental adobe-made buildings of the later pre-Inca period (or Late Intermediate Period, about 10th–15th century AD) are so-called pyramids with ramps (the role of the ramps has been interpreted in different ways). Precise dating of the pyramids appears as a crucial step in defining the functions of Pachacamac in pre-Inca times. In this paper, we present the results obtained from 3 field campaigns at Pyramid III, one of the biggest buildings of the site. A total of 24 radiocarbon datasets from 4 different laboratories will help us to place the various steps of development of Pyramid III on a timescale, defined on the basis of the excavations. More absolute dates are available from another pyramid with ramps, which allow us to make comparisons and propose a new model of interpretation for the Pachacamac site during the Late Intermediate Period (LIP).

Description: A significant and substantial effort has been made by the 14C community in quality assurance (QA) procedures, of which participation in FIRI is only one part but one that provides an independent and blind check on laboratory performance. The overwhelming willingness to participate is a testament to the importance which laboratories place on quality.

Description: TIRI was officially launched at the 14th International Radiocarbon Conference in Arizona in 1991. Prior to the conference, 150 laboratories received a letter describing the general intention to organize an intercomparison and over 90 laboratories from around the world responded positively to the invitation to participate. Simply stated, the aims of this intercomparison were: 1.To function as the third arm of the quality assurance (QA) procedure.2.To provide an objective measure of the maintenance and improvement in analytical quality.3.To assist in the development of a “self-help” scheme for participating laboratories.

Description: The sets of core samples were distributed to over 120 laboratories that had returned an original questionnaire seeking expressions of interest in participation. A reporting format for the results was also agreed and distributed to the laboratories at the same time. This is shown in Table 2.1. Laboratories were originally given 1 yr (i.e., to August 2000) to complete the analyses and return the results, but this was later extended to December 2000. In this section, we briefly describe the laboratory characteristics and the overall response rate of the participating laboratories.

Description: After the first and main phase of FIRI, which focused on routinely measured materials, an optional series of samples were also made available to participating laboratories. This second list included archaeological samples, mammoth tusks, and modern cellulose. Not all samples were available in sufficient quantity for radiometric measurement (in particular, the mammoth tusks). The samples are briefly described in Table 9.1 below.

Description: In this section, we present the exploratory analysis of the results submitted by the extended deadline of December 2000. We first deal with Samples C.J, before considering the near-background samples A and B (Kauri wood). The aims of the exploratory analysis are to discover the range of results reported for each sample and the initial evaluation of the effects of any factors that might be a source of variation in the results. For each sample, in turn, we consider the main summary statistics.the number of results reported (N), their mean or average, median, the standard deviation (StDev), the standard error of the mean (Sem), the quartiles (25th [Q1] and 75th [Q3] percentiles), and the minimum (Min) and maximum (Max)—before graphically studying the overall distribution of results in the form of a boxplot, with a view to identifying any extreme or outlying observations. The summary statistics and distribution of results for each laboratory type are also shown. Further details on the statistical methods used are contained in Appendix 3.

Description: The radiocarbon of the local reservoir effect (RE) was observed in many sectors along the Argentinean Patagonic coast. Results show variations in the 14C offsets and differences between marine and continental species growing within the same locality, ranging from about 80–1100 yr BP. It is postulated that such variations are mainly due to local factors, including the coast morphology and the contribution of continental waters. The relevance of these kinds of studies for the interpretation of age in archaeological samples is highlighted in this paper.

Description: The date of a Chinese ink rubbing was determined using radiocarbon accelerator mass spectrometry (AMS) to be in the range from AD 1480 to AD 1670 (95.4% confidence limit). Together with a scanning electron miscroscope (SEM) analysis of the ink and a comparative study of the Chinese characters, it was determined that the ink rubbing must have been performed before Emperor Kang Hsi (AD 1662–1722), who ruled at the beginning of the Chin Dynasty. On the other hand, the stone stele, from which the ink rubbing was produced, was carved in AD 531, which is consistent with an analysis of some erased characters. Such analysis seems to be useful to help clarify possible forgeries of these art objects.

Description: Recent years have seen a recognition of the importance of government action to business and a rapidly developing path of research on business and politics, but this research has focused overwhelmingly on the legislative and executive branches and too often ignored the judiciary.1 A failure to consider a role for the courts is a substantial lacuna in the research. The judicial branch plays a substantial role in politics and governance. In most cases, the passage of a statute or even the promulgation of a regulation has legal effect only through the courts. A business's success (or failure) in lobbying the legislative or executive branches for a particular policy program may be entirely counteracted in the courts. At the extreme, such an action might be declared unconstitutional, making it legally null and ineffective, and perhaps eliminating the possibility of any future attempt to revive the action.

Description: Although the pluralist theory of politics predicts that the focus of organizational activity should shift to the judicial arena whenever the expectations of government as regulator and the demands of regulated interests fail to converge, there has been little systematic research focusing on the question of business litigation as a specific form of interest mobilization. This article develops an integrated organizational choice model of interest mobilization to explain corporate litigation against the United States government. I argue that a company's decision to proceed with litigation is predicated upon the company's (1) resource capacity, (2) constraints of the regulatory environment, and (3) perception of procedural unfairness of the government in the administrative process. The argument is tested with data from a survey of top U.S. business executives whose companies unsuccessfully petitioned the government for administered protection between 1990 and 1995. The argument receives strong empirical support, and suggests that U.S. corporations facing import competition consider litigation an important component of their overall political strategy for obtaining nonmarket benefits.

Description: In recent years a range of public policy (Howlett 2000) and international relations (Cutler et al., 1999; Hurd, 1999; Haufler, 2001) scholars have devoted attention to the emergence of voluntary (Kernaghan 1999; Prakash 1999), market-based, and “private” regulatory regimes that have emerged to address matters of concern to global civil society that previously were largely addressed through state-centered public policy instruments and processes.

Description: This paper discusses the problems in the effective implementation of tort reform policy, focusing on several different areas that seek to review both the fundamental problems associated with punitive damages as well as the legal arguments in favor of tort reform. The limitations against the creation of a truly efficient system lie in the fact that strategic actors have the ability to anticipate the effects of reforms, and act to create feedback loops that diffuse the impact of the reform attempt. To implement effective tort reform policy one must understand how these strategic actors behave within the civil justice system, as well as how feedback loops limit the overall effectiveness of the tort reform policy. The findings suggest that the system of “decoupling” liability is the most efficient of all the current reform attempts or proposals, while the system can also be improved by adopting policies that isolate the incentive structures of plaintiff's attorneys.

Description: We present the results of an experimental study on the solidification of aqueous solutions of potassium nitrate and sodium nitrate cooled from below. Upon cooling, two distinct mushy layers form, primary and cotectic, separated by an approximately planar horizontal interface. A density reversal between the two mushes causes the residual liquid in the upper, primary mush to be more buoyant than the melt overlying it, while the cotectic mush is compositionally stable. The unstable concentration gradient between the melt and primary mush causes convection that keeps the melt well-mixed and reduces the concentration gradient to zero after a finite time. At this point, the cotectic mush overtakes the primary mush and a transition from a convective regime to a diffusive regime occurs. Our measurements show that this transition is rapid and alters the growth rate of the single (cotectic) mush layer that remains. Concentration measurements taken from within the melt during convection and from within the mush during the diffusive regime show good agreement with the concentration evolution predicted by use of the equilibrium ternary phase diagram. We describe a global conservation model for solidification of a ternary alloy in this regime. Predictions from our model forced with empirical data for the heat and solute fluxes are in good agreement with the measured data for the interface positions of the two mushy layers. We also discuss how solid fractions vary with different melt concentrations in a non-convecting alloy and examine the influence of vertical solute transport in the convecting case. The identification of a density reversal in the solidification of a ternary alloy begins to address the complexities in solidification processes of multi-component alloys.

Description: The axisymmetric capillary pinch-off of a viscous fluid thread of viscosity λμ and surface tension γ immersed in a surrounding fluid of viscosity μ is studied. Similarity variables are introduced (with lengthscales decreasing like τ, the time to pinch-off, in a rapidly translating frame) and the self-similar shape is determined directly by a combination of modified Newton iteration and a standard boundary-integral method. A large range of viscosity ratios is studied (0.002 ≤ λ ≤ 500) and asymmetric profiles are observed for all λ, with conical shapes far from the pinching point, in agreement with previous time-dependent studies. The stability of the steady solutions is investigated and oscillatory instability is found for λ ≥ 32. For λ ≪ 1 an asymptotic scaling of λ1/2 is suggested for the slopes of the far-field conical shapes. These compare well with the quantitative predictions of a one-dimensional theory based on Taylor's (1964) analysis of a slender bubble.

Description: The steady shape of a drop of dilute polymer solution falling through a quiescent viscous Newtonian fluid is considered. Experimentally, we find that an immiscible drop of 0.16% xanthan gum in 80:20 glycerol/water falling through 9.8 P polydimethylsiloxane oil may exhibit a stable dimple at its trailing edge. At higher volumes the dimple extends far into the interior of the drop, and pinches off via a Rayleigh-type instability, injecting oil droplets into the polymer drop. At even larger volumes, a toroidal shape develops. We show that the dimpled shape can be reproduced mathematically with axisymmetric solutions for Stokes flow past a non-Newtonian drop, using the constitutive equation for a Simple Fluid of Order Three.

Description: Faraday waves are standing waves which arise through a parametric instability on the surface of a vertically oscillated fluid layer. They can emerge with various symmetries, simply square to N-fold rotationally symmetric, which for N 〉 3 are quasi-crystalline. In an experiment with a very large aspect ratio we determine the boundaries of the stability regions of waves with different rotational symmetries in the driving frequency-amplitude parameter plane. We find a remarkable agreement with a recent theory by Chen & Viñals (1999) who predict the stability boundaries at the onset amplitude. We argue why such agreement can only be observed in a very large experiment. The main nonlinear damping mechanism of the waves is a three-wave resonance. We devise a simple model that captures this mechanism and that can explain quantitatively the change of the symmetry of the waves with fluid depth. Detailed information about the surface is obtained by scanning the wave field and measuring the phase of subharmonic and harmonic components. Also the results of these measurements compare very favourably to the theoretical predictions.

Description: By truncating the range of van der Waals forces in Our molecular dynamics model we reduce the lengthscale and timescale gap between the outer (wedge) and inner (precursor) regions in droplet spreading simulations. This results in a molecular model which combines atomic-scale resolution with the ability to capture large-scale behaviour as manifested by the Tanner spreading law. Our results show that Tanner's law can be recovered, even if van der Waals effects and the resulting precursor film are limited to distances of the order of three atomic diameters from the substrate. In other words, removal of the singularity is not necessary up to a few atomic diameters from the contact line. The very good quantitative agreement with theory and experiments suggests that the original precursor theory of de Gennes can be generalized to precursors of molecular thickness in which flow is not characterized by the continuum (Stokes) model. Gravity current simulations are also in excellent agreement with the theory of Huppert and recent experimental results showing lubrication scalings at small capillary numbers.

Description: Low-momentum releases of buoyant material from area sources are investigated in the context of the model of Morton, Taylor and Turner (1956) (MTT). The general solution of the model equations is shown to include the case of a converging-diverging flow which we have used to model plumes from the area sources. These solutions have as asymptotes certain power solutions in terms of height, i.e. the MTT solution at large heights and a non-entraining solution near the source. The new solutions exhibit distinct and interesting flow features such as a neck (point of minimum cross-section) and a velocity peak somewhat above. The new results have been compared with the few known experimental data sources and reasonable agreement is demonstrated. In the process we have also examined the importance of the Boussinesq approximation and find results recently published not to be valid except in one special case.

Description: It has been observed in experiments that significant levels of sound may be produced when a curved flame propagates downwards along a tube in a gravity field. In this paper, we present a mathematical description of this acoustic amplification process, which represents a simple form of combustion instability. First, based on the large-activation-energy and small-Mach-number assumptions, a general asymptotic formulation is derived, in which the nature of flame-sound coupling is brought out explicitly. This framework is then employed to study the weakly nonlinear coupling between a Darrieus-Landau (D-L) instability mode of the flame and an acoustic mode of the tube, which is the main mechanism for sound generation in the experiments. In order to provide a somewhat unified description, the linear coupling via the direct pressure effect has also been included in our analysis. A set of coupled equations which govern the evolution of the acoustic and D-L modes was derived. The solutions show that the nonlinear coupling leads to very rapid amplification of sound. After reaching an appreciable level, the sound inhibits the flame, causing the latter to flatten. The sound then saturates at an almost constant level, or continues to grow at a smaller rate owing to the pressure effect. The above theoretical predictions are in good qualitative agreement with experiments. The present study also considered the influence of weak vortical disturbances in the oncoming flow. It is shown that certain components in these perturbations may form resonant triads with the acoustic and D-L modes, thereby providing an additional coupling mechanism.

Description: In this study we consider the separated flow of an inviscid fluid around a moving flat plate. The motion of the plate, which is initially started from rest, is prescribed and unconstrained and we set ourselves the task of fully characterizing the resulting motion in the surrounding fluid. To do this we use a boundary integral representation for the complex-conjugate velocity field φ(z, t) and require that the force and torque on the plate be determined as part of the solution. The flow solution is assumed to consist of a bound vortex sheet coincident with the plate and two free vortex sheets that emanate from each of the plate's two sharp edges. The time evolution of these vortex sheets is then considered in general. For physical reasons, the flow solution is required to satisfy the unsteady Kutta condition, which states that φ(z, t) must be bounded everywhere, and the rigorous imposition of this condition then yields two types of additional constraint. The first governs the rate at which circulation is shed from the plate's edges and the second ensures that the free vortex sheets are shed tangentially. In fact, all the familiar flow characteristics associated with the imposition of the steady Kutta condition are rigorously shown to have exact parallels in the unsteady case. In addition, explicit expressions for the normal force and torque on the plate are derived. An asymptotic solution to the full system of evolution equations is developed for small times t 〉 O and a simplified version of this solution is used as an initial condition for a desingularized numerical treatment of the full problem. A fast numerical algorithm is proposed and implemented and the results of several example calculations are presented. The featured examples are limited to high effective angles of attack due to the occurrence of a specific type of event that prevents further time-integration of the evolution equations using the current numerical method. The event corresponds physically to a situation in which a Lagrangian point placed at one of the plate's edges moves onto instead of away from the edge.

Description: We investigate experimentally and numerically the filling of a collapsible tube, motivated by venous hemodynamics in the lower limbs. The experiments are performed by filling an initially collapsed flexible tube, applying pressure through a hydraulic circuit. The tube law and the tube tension have been previously measured. The tube shape, the flow rate and the pressure at the two ends of the tube are measured continuously. The filling occurs in three stages: a rapid equilibration of the pressure near the tube entry with atmospheric pressure, a quasi-steady filling of the tube with a linearly rising pressure, and a final stage of tube inflation. Our numerical model is the classical one-dimensional collapsible tube equations. Excellent quantitative agreement is found between computations and experimental data. We show experimentally observed shapes near the tube end that indicate possible three-dimensional effects; however these effects do not impair significantly the ability of the one-dimensional model to describe the experiment. Travelling waves of large amplitude are observed in the simulations and the experiments.

Description: Following the study of the spectral properties of linearized swept Hiemenz flow (see Part 1, Obrist & Schmid 2003) we investigate the potential of swept Hiemenz flow to support transiently growing perturbations owing to the non-normal nature of the underlying linear stability operator. Transient amplification of perturbation energy is found for polynomial orders higher than zero, and a catalytic role of the continuous modes in increasing transient growth is demonstrated. The adjoint stability equations are derived and used in a numerical receptivity experiment to illustrate the scattering of vortical free-stream disturbances into the least stable boundary layer mode.

Description: The structure of thermal convection in horizontal plane Couette flow is investigated. Numerical experiments show that transformation of the structure takes place in the linear stage of perturbation growth. In the non-rotating or slowly rotating case, the transformation from cellular to parallel roll convection occurs. In the rapidly rotating case, on the other hand, the transformation from cellular to parallel roll convection occurs via transverse roll convection. As a result, transverse roll convection of finite amplitude can be formed in the rapidly rotating frame of reference. The formation mechanism of the transverse roll is investigated by linear analysis. In both the non-rotating and rotating cases, the horizontal velocity shear temporarily accelerates the growth rate of the transverse mode for a relatively short period. In the non-rotating or slowly rotating case, however, the net effect of this horizontal velocity shear is small. In the rapidly rotating case, on the other hand, the shearing of the perturbation by the background flow results in greatly enhancing potential energy conversion of the transverse mode. As a result, the net effect becomes large enough to make the transverse mode dominate over the parallel mode. Although the transverse roll convection of finite amplitude appears for a relatively short period of time just after its onset, the present result might explain some aspects of observed transverse rolls, such as in the Jovian atmosphere.

Description: This paper considers wave-driven rip currents from a circulation-vorticity point of view. A highly simplified description of rip currents using continuous generation of point vortices at fixed locations is found to have a wide range of applicability around the rip neck. Rip scaling becomes straightforward, and is seen to collapse to a single form. Numerical experiments with this simplified system have the ability to predict well startup transients including previously unexplained peaks, and frequency-dependent effects of wave groups on rip currents. Quantitative mean currents in the rip neck are represented moderately well by this theory.

Description: Laboratory experiments by earlier authors have shown that the near-surface velocity of an otherwise uniform current is reduced by following waves, but is increased by opposing waves. By a boundary-layer analysis with depth-dependent eddy viscosities, we show analytically that this is the consequence of second-order effects of wave-current interaction. Physical effects of waves on the current profile due to the moving free surface, wave attenuation and convective inertia are discussed. Comparisons with available experiments for smooth and rough seabeds are discussed. New predictions of the longitudinal variations along the current are made.

Description: Both lighter- and hydrophobic heavier-than-liquid particles will float on liquid-air surfaces. Capillary forces cause the particles to cluster in typical situations identified here. This kind of clustering causes particles to segregate into islands and bands of high concentrations in thin liquid films rimming the inside of a slowly rotating cylinder partially filled with liquid. A second regime of particle segregation, driven by secondary motions induced by off-centre gas bubbles in a more rapidly rotating cylinder at higher filling levels, is identified. A third regime of segregation of bidisperse suspensions is found in which two layers of heavier-than-liquid particles that stratify when there is no rotation, segregate into alternate bands of particles when there is rotation.

Description: Random motions of irrotational gravity water surface waves on deep water are formulated using the so-called Wiener-Hermite functional series expansion, based on the 'ideal random process', i.e. the white noise. Such a procedure is known to differ fundamentally from moment expansions such as Gram-Charlier or Edgeworth series. The applications concern 'free waves' which are homogeneous in the horizontal plane and stationary in time. Starting from the basic hydrodynamic equation and boundary conditions, the general procedure for obtaining the equations for the deterministic kernels is described. First, the expansion is carried out with no approximation of the hydrodynamic equations but the expansion is limited to the first order. This defines the Gaussian part of the wave field. As expected, the nonlinearity of the hydrodynamic equations has effects on the dispersion relation through explicit frequency and acceleration terms whose physical interpretations are discussed. No attempt is made to solve the highly complicated coupled nonlinear integral kernels equations. Instead, Dirac kernel functions are chosen à priori as an approach to a narrowband random wave field. In this case, the nonlinearity is found to be characterized by a 'statistical wave steepness' having an upper limit value of order 0.42. As a second example, a non-Gaussian field is determined on the basis of the hydrodynamic equations truncated at second order in the wave amplitude. In the case of Dirac first-order kernels, the second-order nonlinear effect results in the generation of the second harmonic of the fundamental wave component. The ratio between the energy levels of these two components is found to compare well with standard results from laboratory experiments.

Description: Understanding the rates of cooling and solidification in laminar flows down sloping channels is central to predicting the advance of lava flows. The mechanisms involved include thermal convection and a competition between shear strain rate and the rate of formation of solid at the chilled surface of the flow. We report experiments in which polyethylene glycol wax flows in a laminar fashion down an inclined, open channel of rectangular cross-section under cold water. Two distinctly different flow regimes are recognized: 'tube' flow in which solidification of the flow surface creates a stationary roof while melt continues to flow through a relatively well-insulated 'tube' beneath, and a 'mobile crust' regime in which a solid surface crust develops only in the centre of the channel. In the latter regime the crust is carried down the channel, separated from the walls by crust-free shear regions in which cooling produces only dispersed fragments of solid owing to the effects of shearing. This flow structure is quasi-invariant over a large distance downstream. We show that thermal convection takes place in organized rolls that have axes aligned with the shear flow, and conclude that transition between the two flow regimes occurs at a critical value of the combined parameter ν = Ψ(Ra/R0)1/3, where Ψ = U0ts/Ho is the ratio of a surface solidification timescale ts to a shearing timescale H0/U0, H0 and U0 are the flow depth and centreline surface velocity in the absence of solidification, Ra is a Rayleigh number and R0 is a constant.

Description: A series of scale-model experiments investigated the scouring mechanisms associated with a tsunami impinging on a coastal cylindrical structure. Since scaling effects are significant in sediment transport, a large-scale sediment tank was used. Video images from inside the cylinder elucidated the vortex structures and the time development of scour around the cylinder. The scour development and mechanisms differed according to the sediment substrate - sand or gravel. For gravel, the most rapid scour coincided with the greatest flow velocities. On the other hand, for the sand substrate, the most rapid scour occurred at the end of drawdown - after flow velocities had subsided and shear stresses were presumed to have decreased. This behaviour can be explained in terms of pore pressure gradients. As the water level and velocity subside, the pressure on the sediment bed decreases, creating a vertical pressure gradient within the sand and decreasing the effective stress within the sand. Gravel is too porous to sustain this pressure gradient. During drawdown, the surface pressure decreases approximately linearly from a sustained peak at ΔP to zero over time ΔT. The critical fraction Λ of the buoyant weight of sediment supported by the pore pressure gradient can be estimated as Λ = 2/√π ΔP/γb√cvΔT, in which γb is the buoyant specific weight of the saturated sediment and cv is the coefficient of consolidation. Much deeper scour was observed where Λ exceeded one-half.

Description: At high Reynolds number, the flow of an incompressible viscous fluid over a lifting surface is a rich blend of fluid dynamic phenomena. Here, boundary layers formed at the leading edge develop over both the suction and pressure sides of the lifting surface, transition to turbulence, separate near the foil's trailing edge, combine in the near wake, and eventually form a turbulent far-field wake. The individual elements of this process have been the subject of much prior work. However, controlled experimental investigations of these flow phenomena and their interaction on a lifting surface at Reynolds numbers typical of heavy-lift aircraft wings or full-size ship propellers (chord-based Reynolds numbers, Rec ∼ 107-108) are largely unavilable. This paper presents results from an experimental effort to identify and measure the dominant features of the flow over a two-dimensional hydrofoil at nominal Rec values from near one million to more than 50 million. The experiments were conducted in the US Navy's William B. Morgan Large Cavitation Channel with a solid-bronze hydrofoil (2.1 m chord, 3.0 m span, 17 cm maximum thickness) at flow speeds from 0.25 to 19.3 m s-1. The foil section, a modified NACA 16 with a pressure side that is nearly flat and a suction side that terminates in a blunt trailing-edge bevel, approximates the cross-section of a generic naval propeller blade. Time-averaged flow-field measurements drawn from laser-Doppler velocimetry, particle-imaging velocimetry, and static pressure taps were made for two trailing-edge bevel angles (44° and 56°). These velocity and pressure measurements were concentrated in the trailing-edge and near-wake regions, but also include flow conditions upstream and far downstream of the foil, as well as static pressure distributions on the foil surface and test section walls. Observed Reynolds-number variations in the time-averaged flow over the foil are traced to changes in suction-side boundary-layer transition and separation. Observed Reynolds-number variations in the time-averaged near wake suggest significant changes occur in the dynamic flow in the range of Rec investigated.

Description: Active feedback control was applied to suppress oscillations in thermocapillary convection in a half-zone liquid bridge. The experiment is on a unit-aspect-ratio liquid bridge where the most unstable azimuthal mode has wavenumber 2 when control is absent. Active control was realized by locally modifying the surface temperature using the local temperature measured at different locations fed back through a simple control law. The performance of the control process was quantified by analysing local temperature signals, and the flow structure was simultaneously identified by flow visualization. With optimal placement of sensors and heaters, proportional control can raise the critical Marangoni number by more than 40%. The amplitude of the oscillation can be suppressed to less than 30% of the initial value for a wide range of Marangoni number, up to 90% of the critical value. The proportional control was tested for a period-doubling state and it stabilized the oscillation to a periodic state. Weakly nonlinear control was applied by adding a cubic term to the control law to improve the performance of the control and alter the bifurcation characteristics.

Description: We analyse the density evolution of fluid within a confined ventilated space resulting from the action of a dense turbulent plume originating at the top of the space with finite source volume flux, Q0, and initial source buoyancy flux, B0. The space is ventilated through upper and lower openings of areas Au and Al respectively, which are separated by a vertical distance H. We show that if Q30 〈 2B0Hc2lA2l (where cl is an empirically determined discharge coefficient) then a two-layer steady stratification becomes established in the room, with outflow through the lower opening and inflow through the upper opening. The interface location depends not only on the geometry of the openings, but also the source conditions. We show that as Q0 increases for fixed B0, the height of the interface, which equals the depth of the lower layer of relatively dense fluid, increases. Eventually, when the source volume flux has a value greater than Qm = (cl Al)2/3 (2B0H)1/3, the natural exchange flow becomes blocked and a steady outflow through both of the openings develops. As a result, the density of the fluid throughout the room gradually evolves towards the density of the incoming dense fluid. We compare our theoretical predictions with a series of laboratory experiments, and discuss the implications of our model for the design of ventilation systems.

Description: Finite-amplitude capillary waves, which can accompany the axisymmetric flow of a thin viscous film over a rotating disk, are considered. A system of approximate evolution equations for the film thickness and volumetric flow rates in the radial and azimuthal directions is derived, which contains two similarity parameters. In order to inspire confidence in this model, its steady solutions and their linear stability characteristics are compared to those of the full Navier-Stokes equations. Localized equations, which account for the presence of inertial, capillary, centrifugal and Coriolis forces, are obtained via truncation of the approximate system. Periodic solutions of these equations are then determined and found to be similar to those observed experimentally. Our results suggest that the steady quasi-periodic waves with largest amplitude compare well with experimentally observed wave profiles.

Description: Direct numerical simulations of the motion of 27 three-dimensional deformable buoyant bubbles in periodic domains are presented. The full Navier-Stokes equations are solved by a parallelized finite-difference/front-tracking method that allows a deformable interface between the bubbles and the suspending fluid and the inclusion of surface tension. The Eötvös number is taken as equal to 5, so that the bubbles are ellipsoidal, and the Galileo number is 900, so that the rise Reynolds number of a single bubble in an unbounded flow is about 26. Three values of the void fraction have been investigated: 2%, 6% and 12%. At 6%, a change in the behaviour of the bubbles is observed. The bubbles are initially dispersed homogeneously throughout the flow field and their average rise Reynolds number is 23. After the bubbles have risen by about 90 bubble diameters, they form a vertical stream and accelerate. The microstructure of the bubble suspension is analysed and an explanation is proposed for the formation of these streams. The results for the ellipsoidal bubbles are compared to the results for nearly spherical bubbles, for which the Eötvös number is 1 and the Galileo number is 900. The dispersion of the bubbles and the velocity fluctuations in the liquid phase are analysed.

Description: Sound transmission through ducts of constant cross-section with a uniform inviscid mean flow and a constant acoustic lining (impedance wall) is classically described by a modal expansion, where the modes are eigenfunctions of the corresponding Laplace eigenvalue problem along a duct cross-section. A natural extension for ducts with cross-section and wall impedance that are varying slowly (compared to a typical acoustic wavelength and a typical duct radius) in the axial direction is a multiple-scales solution. This has been done for the simpler problem of circular ducts with homentropic irrotational flow. In the present paper, this solution is generalized to the problem of ducts of arbitrary cross-section. It is shown that the multiple-scales problem allows an exact solution, given the cross-sectional Laplace eigensolutions. The formulation includes both hollow and annular geometries. In addition, the turning point analysis is given for a single hard-wall cut-on, cut-off transition. This appears to yield the same reflection and transmission coefficients as in the circular duct problem.

Description: Two- and three-dimensional numerical simulations are performed to study interfacial waves in a periodic domain by imposing a source term in the horizontal momentum equation. Removing the source term before breaking generates a stable interfacial wave. Continued forcing results in a two-dimensional shear instability for waves with thinner interfaces, and a convective instability for waves with thick interfaces. The subsequent three-dimensional dynamics and mixing is dominated by secondary cross-stream convective rolls which account for roughly half of the total dissipation of wave energy. Dissipation and mixing are maximized when the interface thickness is roughly the same size as the amplitude of the wave, while the mixing efficiency is a weak function of the interface thickness. The maximum instantaneous mixing efficiency is found to be 0.36 ± 0.02.

Description: Turbulent channel flow simulations are performed using second- and fourth-order finite difference codes. A systematic comparison of the large-eddy simulation (LES) results for different grid resolutions, finite difference schemes, and several turbulence closure models is performed. The use of explicit filtering to reduce numerical errors is compared to results from the traditional LES approach. Filter functions that are smooth in spectral space are used, as the findings of this investigation are intended for application of LES to complex domains. Explicit filtering introduces resolved subfilter-scale (RSFS) as well as subgrid-scale (SGS) turbulence terms. The former can be theoretically reconstructed; the latter must be modelled. The dynamic Smagorinsky model, the dynamic mixed model, and the new dynamic reconstruction model are all studied. It is found that for explicit filtering, increasing the reconstruction levels for the RSFS stress improves the mean velocity as well as the turbulence intensities. When compared to LES without explicit filtering, the difference in the mean velocity profiles is not large; however the turbulence intensities are improved for the explicit filtering case.

Description: We study the problem of body-force-driven shear flows in a plane channel of width ℓ with free-slip boundaries. A mini-max variational problem for upper bounds on the bulk time-averaged energy dissipation rate ε is derived from the incompressible Navier-Stokes equations with no secondary assumptions. This produces rigorous limits on the power consumption that are valid for laminar or turbulent solutions. The mini-max problem is solved exactly at high Reynolds numbers Re = Uℓ/ν, where U is the r.m.s. velocity and ν is the kinematic viscosity, yielding an explicit bound on the dimensionless asymptotic dissipation factor β = εℓ/U3 that depends only on the 'shape' of the shearing body force. For a simple half-cosine force profile, for example, the high Reynolds number bound is β ≤ π2/√216 = 0.6715.... We also report extensive direct numerical simulations for this particular force shape up to Re ≈ 400; the observed dissipation rates are about a factor 3 below the rigorous high-Re bound. Interestingly, the high-Re optimal solution of the variational problem bears some qualitative resemblance to the observed mean flow profiles in the simulations. These results extend and refine the recent analysis for body-forced turbulence in Doering & Foias (2002).

Description: We present experimental measurements of the normal stresses in sheared Stokesian suspensions. Though the suspending fluid is Newtonian, dispersing rigid non-Brownian particles in it yields a suspension that is non-Newtonian, as it exhibits normal stress differences and an excess isotropic pressure in viscometric flows. At small to moderate concentrations, the normal stresses are very small in magnitude, and hence difficult to measure. This difficulty is compounded by the presence of noise due to unavoidable experimental artifacts. Owing to these limitations, most measurements reported earlier were carried out at relatively high particle concentrations, and some at shear rates large enough that the effects of particle and fluid inertia may have been significant. In our study, we have used a novel technique to measure the small stress levels. This was achieved by applying a sinusoidally varying shear rate with a fixed (low) frequency superimposed on a constant shear rate, and using a lock-in amplifier to measure the Fourier component of the same frequency in the stress signal. We have measured normal stresses in cylindrical-Couette and parallel-plate geometries, and combined these measurements to determine the two normal stress differences for particle volume fractions in the range 0.3-0.45. While the normal stresses are very small at low concentrations, they rise rapidly with increasing concentration. The normal stresses vary linearly with the magnitude of the shear rate, and are independent of its sign. In contrast to polymeric solutions, both normal stress differences are negative, and the first normal stress difference is significantly smaller in magnitude. We compare our data with the results or earlier studies, and observe good agreement.

Description: Existing results on the linearized water-wave problem for a homogeneous fluid are extended to the case of a two-layer fluid. In particular, the appropriate form of Maz'ya's identity is presented and used to obtain results on the uniqueness of the solutions to forcing problems for a structure in a two-layer fluid. Further, examples of geometries are constructed for which trapped modes occur; such modes are finite-energy solutions of the unforced problem and provide examples of non-uniqueness.

Description: The early phase of high-speed liquid droplet impact on a rigid wall is characterized by compressibility effects through the creation of a shock wave attached to the contact area periphery. Initially, the area of compressed liquid is assumed to be bounded by the shock envelope, which propagates both laterally and upwardly into the bulk of the liquid. In this paper, an analytical model accounting for the lateral liquid motion in the compressed area is developed and compared to the axisymmetric numerical solution of the inviscid (Euler) flow equations. It is shown that the often employed assumption that the compressed area is separated from the liquid bulk by a single shock wave attached to the contact line breaks down and results in an anomaly. This anomaly emerges prior to the time when the shock wave departs from the contact line, initiating lateral liquid jetting. In order to remove this anomaly, the analytical model presented in this paper proposes the transition from a single to a multiple wave structure in the contact line region, prior to jetting eruption. The occurrence of this more complex multiple wave structure is also supported by the numerical results.

Description: A three-dimensional boundary-layer model of shallow-water flows assuming hydrostatic pressure with negligible numerical diffusion and wave damping has been extended to turbulent flow. A standard two-layer mixing-length model determines vertical length scales. The horizontal mixing length is made a multiple β of the vertical value and β is determined from comparison with experiment. Eddy viscosity is of a general three-dimensional form where, for example, the horizontal mixing length and associated strain rates determine the magnitude of eddy viscosity and hence vertical mixing (and vice versa). Direct comparison is made with previous experiments for subcritical flow around a conical island of small side slope which exhibits the transition from a vigorous vortex-shedding wake to a steady recirculating wake as the stability parameter, St, is increased. The value of β influences wake structure, particularly for stability parameters close to the critical (the value at which the wake becomes steady or stable). The critical value in the experiments was 0.4 and this was reproduced in the model with β = 6. Vortex shedding patterns with St = 0.26 and 0.36 were qualitatively reproduced. The flows were subcritical with an onset Froude number of about 0.2, with values approaching 0.6-0.7 in areas where depth-averaged vorticity magnitude was also greatest, at a small distance from the wet/dry intersection. At this intersection, depth-averaged vorticity approached zero while potential vorticity (depth-averaged vorticity/depth) was at a maximum, indicating the importance of the intersection as an origin for vorticity.

Description: The unsteady separated flow produced by a finite-core vortex on a plane shear layer is studied here as a vortex-induced instability. The mechanism of such an interaction, where the distance between the wall and the vortex is many times the local boundary layer thickness, is shown here by flow visualization and the solution of the unsteady Navier-Stokes equation. A new theory is proposed here, which is generic to the Navier-Stokes equation without any assumptions, that is based on growth of disturbance energy in time. A dynamical systems approach based on the proper orthogonal decomposition technique is used to provide a quantitative measure.

Description: Double-diffusive plumes, injected into surroundings of nearly the same density, are observed to separate near the source and to produce both upward and downward convection, which is enhanced as layers form at the top and bottom of the experimental tank. This process has been quantified in this paper for both sugar plumes in homogeneous salt solution and salt plumes in sugar solution, over a range of small density differences on either side of zero. The tank was fitted with a partition at mid-depth, which could be closed at the end of a known period of input, so that the concentration changes above and below the source could be deduced. The density of the input and tank fluids, and that of the upper and lower layers, was measured in each case, as well as a second property, conductivity for the salt and optical rotation for the sugar inputs. These measurements were motivated by, and shed light on, the experimental results of Turner & Veronis (2000). There are large differences between the upward and downward transports produced by the two types of plume, because of the different rates of diffusion of salt and sugar in and out of the plumes and the subsequent transports through the interfaces that form as the plumes spread out along the top and bottom boundaries. One result is that at a density ratio close to 1 a salt plume produces equal upward and downward transports of salt, whereas at the same density ratio a sugar plume leads to a much larger downward flux of sugar. This is consistent with the 'diffusive' final state observed by Turner & Veronis (2000), and this conclusion is supported by a more detailed analysis of the redistribution of the tank fluid.

Description: The temporal stability of swept attachment-line boundary layer flow based on a swept Hiemenz flow model is studied. Starting from the global stability problem and motivated by analytical free-stream solutions, a Hermite expansion is employed in the chordwise coordinate direction which results in coupled local stability problems. A complete study of the temporal spectrum is presented and the discrete and continuous modes are classified according to their symmetry, chordwise polynomial order and asymptotic decay. Uniform, Görtler-Hämmerlin and higher-order modes are described in detail. Estimates are given for the location of the continuous spectrum, and bounds are derived for the validity of the linear approximation.

Description: Inertial waves in a homogeneous rotating fluid travel along rays that are inclined with respect to the rotation axis. The angle of inclination depends solely on the ratio of the wave frequency and twice the angular frequency. Because of this fixed angle, the waves can become focused when reflected at a sloping wall. In an infinitely long channel with a sloping wall, the repeated action of focusing may lead to the approach to a limit cycle, the so-called wave attractor, where the energy is concentrated. This effect is studied in the laboratory in a rectangular tank with one sloping wall, placed excentrically on a rotating table. The waves are excited by modulation of the background rotation. Several frequency ratios are used to study different wave attractors and one standing wave. The observations consist mainly of particle image velocimetry data in horizontal and vertical cross-sections in one half of the basin. The attractors are observed in the vertical cross-sections. They show continuous phase propagation, which distinguishes them from the standing wave where the phase changes at the same time over the whole cross-section. However, particle motion of inertial waves is three-dimensional and the actual basin is not an ideal two-dimensional channel but is of finite length. This implies that the waves must adapt to the vertical endwalls, although a prediction of the nature of these adaptations and the structure of the three-dimensional wave field is at present lacking. For critical waves, whose rays are parallel to the slope, clear three-dimensional behaviour is observed. The location of most intense motion along this critical slope attractor changes in the horizontal direction and horizontal phase propagation is observed, with a wavelength between 1/5 and 1/4 of the basin length. For the other attractors there is little evidence of phase propagation in the horizontal direction. The motion along the attractor is however stronger near the vertical endwalls for attractors with wave rays of slopes close to 1 or larger. The standing wave and the other attractors are more clearly visible near 1/5 of the tank length.

Description: In this paper, numerical simulations are presented of the nonlinear critical-layer evolution of a forced gravity wave packet in a stratified shear flow. The wave packet, localized in the horizontal direction, is forced at the lower boundary of a two-dimensional domain and propagates vertically towards the critical layer. The wave-mean-flow interactions in the critical layer are investigated numerically and contrasted with the results obtained using a spatially periodic monochromatic forcing. With the horizontally localized forcing, the net absorption of the disturbance at the critical layer continues for large time and the onset of the nonlinear breakdown is delayed compared with the case of monochromatic forcing. There is an outward flux of momentum in the horizontal direction so that the horizontal extent of the packet increases with time. The extent to which this happens depends on a number of factors including the amplitude and horizontal length of the forcing. It is also seen that the prolonged absorption of the disturbance stabilizes the solution to the extent that it is always convectively stable; the local Richardson number remains positive well into the nonlinear regime. In this respect, our results for the localized forcing differ from those in the case of monochromatic forcing where significant regions with negative Richardson number appear.

Description: This paper reports an experimental investigation of simple shear flow penetrating a model of a fibrous porous medium. The flow field is established between a stationary inner cylinder and a concentric outer cylinder rotating at a constant speed. The model medium is a regular array of rods which are oriented across the flow and which fill a fraction of the annular space between the cylinders. Rods with circular, square and triangular cross-sections are investigated, and the solid volume fraction of the arrays ranges from 0.01 to 0.16. With a viscous oil as the working fluid, the Reynolds number is much less than unity. Velocity measurements made using particle image velocimetry focus on the region around the edge of each array tested. The measurements reveal that eddies form between the two outermost circles of rods, for solid volume fractions above a minimum value which depends on rod shape. The velocity data are used to find the interfacial slip velocity and the average velocity at the interface between the porous medium and the outer shear flow. The data demonstrate that the slip velocity decays with increasing solid volume fraction, as expected, but the velocity is found to be nearly independent of rod shape and of the number of circles of rods comprising an array. It is also found that the slip velocity is only 24-30% of the value predicted from the Brinkman equation.

Description: We consider a thin layer of a viscous fluid flowing down a uniformly heated planar wall. The heating generates a temperature distribution on the free surface which in turn induces surface tension gradients. We model this thermocapillary flow by using the Shkadov integral-boundary-layer (IBL) approximation of the Navier Stokes/energy equations and associated free-surface boundary conditions. Our linear stability analysis of the flat-film solution is in good agreement with the Goussis and Kelly (1991) stability results from the Orr Sommerfeld eigenvalue problem of the full Navier Stokes/energy equations. We numerically construct nonlinear solutions of the solitary wave type for the IBL approximation and the Benney-type equation developed by Joo et al. (1991) using the usual long-wave approximation. The two approaches give similar solitary wave solutions up to an O(1) Reynolds number above which the solitary wave solution branch obtained by the Joo et al. equation is unrealistic, with branch multiplicity and limit points. The IBL approximation on the other hand has no limit points and predicts the existence of solitary waves for all Reynolds numbers. Finally, in the region of small film thicknesses where the Marangoni forces dominate inertia forces, our IBL system reduces to a single equation for the film thickness that contains only one parameter. When this parameter tends to zero, both the solitary wave speed and the maximum amplitude tend to infinity.

Description: We report experimental results on highly supercritical thermal convection in a rapidly rotating hemispherical shell with parabolic gravity. Using silicone oil as the working fluid and an Ekman number Ek = 4.7 × 10-6 we reach Rayleigh numbers up to 1.2 × 1010, over 600 times critical. In-situ temperature measurements show that, at these highly supercritical states where convective heat transfer becomes dominant, the time-averaged temperature in the fluid becomes nearly uniform except in a thin thermal boundary layer near the inner spherical boundary. Heat transfer measurements show that Nusselt number Nu increases with Rayleigh number Ra as Nu ∝ Ra0.4. The measured amplitudes of temperature fluctuations scale well with a model of geostrophic convective turbulence. We also examine convection in a two-layer fluid in the same geometry, using layers of water and silicone oil to produce a stable density stratification. We determine the dependence of heat transfer on the thickness ratio of the layers.

Description: The multiplicity, stability and bifurcations of low-Prandtl-number steady natural convection in a two-dimensional rectangular cavity with partially and symmetrically heated vertical walls are studied numerically. The problem represents a simple model of a set-up in which the height of the heating element is less than the height of the molten zone. The calculations are carried out by the global spectral Galerkin method. Linear stability analysis with respect to two-dimensional perturbations, a weakly nonlinear approximation of slightly supercritical states and the arclength path-continuation technique are implemented. The symmetry-breaking and Hopf bifurcations of the flow are studied for aspect ratio (height/length) varying from 1 to 6. It is found that, with increasing Grashof number, the flow undergoes a series of turning-point bifurcations. Folding of the Solution branches leads to a multiplicity of steady (and, possibly, oscillatory) states that sometimes reaches more than a dozen distinct steady solutions. The stability of each branch is studied separately. Stability and bifurcation diagrams, patterns of steady and oscillatory flows, and patterns of the most dangerous perturbations are reported. Separated stable steady-state branches are found at certain values of the governing parameters. The appearance of the complicated multiplicity is explained by the development of the stably and unstably stratified regions, where the damping and the Rayleigh Bénard instability mechanisms compete with the primary buoyancy force localized near the heated parts of the vertical boundaries. The study is carried out for a low-Prandtl-number fluid with Pr = 0.021. It is shown that the observed phenomena also occur at larger Prandtl numbers, which is illustrated for Pr = 10. Similar three-dimensional instabilities that occur in a cylinder with a partially heated sidewall are discussed.

Description: Using slender-body hydrodynamics in the inertialess limit, we examine the motion of Purcell's Swimmer, a planar, fore-aft-symmetric three-link flagellum or propulsive mechanism that translates by alternately moving its front and rear segments. Purcell (1976) concluded via symmetry arguments that the net displacement of such a swimmer must follow a straight line, but the direction and other details of the motion have never been investigated. Numerical results indicate that the direction of net translation and the speed of Purcell's swimmer depend on the angular amplitude of the swimming strokes as well as on the relative length of the links. Analytical results are presented for small rotations about the straightened configuration, and physical arguments are given to qualitatively explain the propulsive dynamics. The optimal swimmer configurations under the conditions of constant forcing and of minimum mechanical work are determined. We use a definition of efficiency based on the straightened configuration as a reference state to compare Purcell's swimmer with the previously treated swimming motions of an undulating rod and a rotating helix. Finally, we demonstrate the importance of the anisotropy in the local hydrodynamic slender-body drag to swimming motions at low Reynolds number by showing that, in general, any inextensible swimmer in an otherwise quiescent fluid cannot alter its average position under conditions of locally isotropic drag.

Description: It is well known that the drag in a turbulent flow of a polymer solution is significantly reduced compared to Newtonian flow. Here we consider this phenomenon by means of a direct numerical simulation of a turbulent channel flow. The polymers are modelled as elastic dumbbells using the FENE-P model. In the computations the polymer model is solved simultaneously with the flow equations, i.e. the polymers are deformed by the flow and in their turn influence the flow structures by exerting a polymer stress. We have studied the results of varying the polymer parameters, such as the maximum extension, the elasticity and the concentration. For the case of highly extensible polymers the results of our simulations are very close to the maximum drag reduction or Virk (1975) asymptote. Our simulation results show that at approximately maximum drag reduction the slope of the mean velocity profile is increased compared to the standard logarithmic profile in turbulent wall flows. For the r.m.s. of the streamwise velocity fluctuations we find initially an increase in magnitude which near maximum drag reduction changes to a decrease. For the velocity fluctuations in the spanwise and wall-normal directions we find a continuous decrease as a function of drag reduction. The Reynolds shear stress is strongly reduced, especially near the wall, and this is compensated by a polymer stress, which at maximum drag reduction amounts to about 40% of the total stress. These results have been compared with LDV experiments of Ptasinski et al. (2001) and the agreement, both qualitatively and quantitatively, is in most cases very good. In addition we have performed an analysis of the turbulent kinetic energy budgets. The main result is a reduction of energy transfer from the streamwise direction, where the production of turbulent kinetic energy takes place, to the other directions. A substantial part of the energy production by the mean flow is transferred directly into elastic energy of the polymers. The turbulent velocity fluctuations also contribute energy to the polymers. The elastic energy of the polymers is subsequently dissipated by polymer relaxation. We have also computed the various contributions to the pressure fluctuations and identified how these change as a function of drag reduction. Finally, we discuss some cross-correlations and various length scales. These simulation results are explained here by two mechanisms. First, as suggested by Lumley (1969) the polymers damp the cross-stream or wall-normal velocity fluctuations and suppress the bursting in the buffer layer. Secondly, the 'shear sheltering' mechanism acts to amplify the streamwise fluctuations in the thickened buffer layer, while reducing and decoupling the motions within and above this layer. The expression for the substantial reduction in the wall drag derived by considering the long time scales of the nonlinear fluctuations of this damped shear layer, is shown to be consistent with the experimental data of Virk et al. (1967) and Virk (1975).

Description: The stability of a separating boundary-layer flow at the rear of a two-dimensional bump mounted on a flat plate is numerically investigated. Above a critical Reynolds number, the flow field is shown to undergo self-sustained two-dimensional low-frequency fluctuations in the upstream region of the separation bubble, evolving into aperiodic vortex shedding further downstream. The computed steady flow states below the critical Reynolds number are shown to be convectively unstable. On extrapolating the flow field to Reynolds numbers above criticality, some evidence is found that the onset of the oscillatory behaviour coincides with topological flow changes near the reattachment point leading to the rupture of the (elongated) recirculation bubble. The structural changes near reattachment are shown to trigger an abrupt local transition from convective to absolute instability, at low frequencies. On preventing the separation bubble from bursting by reaccelerating the flow by means of a second bump further downstream, the separated flow remains steady for increasing Reynolds numbers, until a local region of absolute instability in the upper part of the geometrically controlled recirculation bubble is produced. The resulting global instability consists of self-sustained nonlinear saturated perturbations oscillating at a well-defined frequency, very distinct from the the low-frequency motion of the elongated recirculation bubble in the single-bump geometry. A frequency selection criterion based on local absolute frequencies, which has been successfully applied to wake flows, is shown to accurately predict the global frequency.

Description: Conditions determining the existence of localized steadily translating two-layer vortices (modons) of arbitrary symmetric form on the β-plane are considered. A numerical method for direct construction of modon solutions is suggested and its accuracy is analysed in relation to the parameters of the computational procedure and the geometrical and physical parameters of the modon sought. Using this method, several non-circular baroclinic solutions are constructed marked by nonlinearity of the dependence of the potential vorticity (PV) on the streamfunction in the trapped-fluid area of the modon, i.e. where the streamlines are closed. The linearity of this dependence and the circularity of the trapped-fluid area are shown to be equivalent properties of a modon. Special attention is given to elliptical modons - extended both in the direction of the modon propagation and in the orthogonal direction, the baroclinic PV component being assumed continous. The differences between the two types of elliptical modons are discussed. The simplest vortical couples and shielded modons are considered. In the context of the continuity of the baroclinic PV field, the stability modons is discussed based on numerical simulations.

Description: The paper is the second in a series concerned with the development of the quasi-mode concept in the context of boundary layers. The evolution of localized two-dimensional perturbations in boundary layers without inflection points is considered within the framework of linear inviscid theory. Making use of the results of Part 1 (Shrira and Sazonov 2001) for monochromatic perturbations it is shown that arbitrary broadband initial perturbations tend to a universal asymptotic regime at large times t. We refer to the phenomenon of the emergence of the asymptotic regime as 'adjustment'. The regime itself corresponds to a slow dynamics of long-wave triple-deck-type perturbations and is described well as the evolution of a single quasi-mode, which allows dramatic simplification of its description. At the asymptotic stage the spatio-temporal structure of the perturbation is explicitly described in terms of Fresnel's functions with coefficients specified by certain integrals of the initial distribution. Asymptotically the perturbation represents a sharply localized group of decaying oscillations which propagate with celerity approaching the mean flow velocity at the surface. For generic perturbations, the decay, in terms of streamwise velocity, is t1/2. The envelope of the group is formed by the Landau damping intrinsic to the quasi-modes, and the length of the group and the number of oscillations in the group grow with time as t2/3 and t1/6, respectively. The evolution of the nonquasi-modal part is also investigated. The vorticity perturbation is found to form a vortex patch shaped like a comet tail and advected by the mean flow. The picture of evolution established for generic perturbations is found to hold for several classes of non-generic but physically relevant initial distributions; the corresponding solutions are presented and discussed. The analytical results have been confirmed by the direct numerical simulation of the linearized primitive equations.