ALBERT

Description: Author Posting. © Cambridge University Press, 2007. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 574 (2007): 465-493, doi:10.1017/S0022112006004216.

Description: Acoustic Doppler velocity profiler (ADVP) measurements of instantaneous three-dimensional velocity profiles over the entire turbulent boundary layer height, δ, of rough-bed open-channel flows at moderate Reynolds numbers show the presence of large scale coherent shear stress structures (called LC3S herein) in the zones of uniformly retarded streamwise momentum. LC3S events over streamwise distances of several boundary layer thicknesses dominate the mean shear dynamics. Polymodal histograms of short streamwise velocity samples confirm the subdivision of uniform streamwise momentum into three zones also observed by Adrian et al. (J. Fluid Mech., vol. 422, 2000, p. 1). The mean streamwise dimension of the zones varies between 1δ and 2.5δ. In the intermediate region (0.2〈z/δ〈0.75), the contribution of conditionally sampled u'w' events to the mean vertical turbulent kinetic energy (TKE) flux as a function of threshold level H is found to be generated by LC3S events above a critical threshold level Hmax for which the ascendant net momentum flux between LC3S of ejection and sweep types is maximal. The vertical profile of Hmax is nearly constant over the intermediate region, with a value of 5 independent of the flow conditions. Very good agreement is found for all flow conditions including the free-stream shear flows studied in Adrian et al. (2000). If normalized by the squared bed friction velocity, the ascendant net momentum flux containing 90% of the mean TKE flux is equal to 20% of the shear stress due to bed friction. In the intermediate region this value is nearly constant for all flow conditions investigated herein. It can be deduced that free-surface turbulence in open-channel flows originates from processes driven by LC3S, associated with the zonal organization of streamwise momentum. The good agreement with mean quadrant distribution results in the literature implies that LC3S identified in this study are common features in the outer region of shear flows.

Description: The study was supported by the Swiss National Foundation for Scientific Research for the experimental part (grant 2100 050739) and the French National Center for Scientific Research (CNRS) for the data analysis and interpretation.

Description: Author Posting. © Microscopy Society of America, 2007. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Microscopy and Microanalysis 13 Suppl. 2 (2007): 10-11, doi:10.1017/S1431927607075186.

Description: Differential interference contrast (DIC) microscopy is widely used to observe structure and motion in unstained, transparent living cells and isolated organelles, producing a monochromatic shadowcast image of optical phase gradient. Polarized light microscopy (Pol) reveals structural anisotropy due to form birefringence, intrinsic birefringence, stress birefringence, etc. DIC and Pol complement each other as, for example, in a live dividing cell, the DIC image will clearly show the chromosomes while the Pol image will depict the distribution of the birefringent microtubules in the spindle. Both methods, however, have the same shortcomings: they require the proper orientation of a specimen in relation to the optical system in order to achieve best results.

Description: Author Posting. © Cambridge University Press, 2007. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 593 (2007): 1-32, doi:10.1017/S0022112007008415.

Description: Results are presented from an experimental study of shallow flow in a channel partially obstructed by an array of circular cylinders. The cylinder array is a model for emergent vegetation in an open channel, but also represents a simple sparse porous medium. A shear layer with regular vortex structures forms at the edge of the array, evolving downstream to an equilibrium width and vortex size. The vortices induce nearly periodic oscillations with a frequency that matches the most unstable linear mode for a parallel shear flow. The shear layer is asymmetric about the array interface and has a two-layer structure. An inner region of maximum shear near the interface contains a velocity inflection point and establishes the penetration of momentum into the array. An outer region, resembling a boundary layer, forms in the main channel, and establishes the scale of the vortices. The vortex structure, educed by conditional sampling, shows strong crossflows with sweeps from the main channel and ejections from the array, which create significant momentum and mass fluxes across the interface. The sweeps maintain the coherent structures by enhancing shear and energy production at the interface. A linear stability analysis is consistent with the experimental results and demonstrates that the instability is excited by the differential drag between the channel and the array.

Description: This material is based upon work supported by the National Science Foundation under Grant 0125056.

Description: Using a panel data of S&P 500 Index firms covering 1998–2004, this paper compares the determinants of lobbying expenditures and campaign contributions and estimates the returns to lobbying as assessed by the financial market. Lobbying depends more on managerial incentives and protection needs beyond industry structures than contributions do. Lobbying also has a positive effect on the firm's equity returns relative to the market and, to a lesser degree, relative to its industry.

Description: Although scholars have begun to explore the determinants of public attitudes toward trade policy, we still do not know whether these attitudes have policy consequences. This paper presents the first systematic analysis of this question. I find that higher public support for free trade leads to lower tariffs, but only in democracies. I also find that democracy leads to lower tariffs only where public support for free trade is relatively high. Hence, although both public opinion and regime type are important, neither matters independently of the other. This finding suggests a need for further research on the conditional effects of both.

Description: Do neoliberal economic policies help or hinder human development? Many have argued that such policies promote economic stability and growth, which may have indirect positive effects on human welfare. Others claim that neoliberal policies retard human development. We argue that neoliberal economic policies may improve the human welfare in ways that are independent of their effects on economic performance. Specifically, this paper hypothesizes that open international trade policies, low-inflation macroeconomic environments, and market-oriented property rights regimes promote human development across the world. We test this argument by examining the impact of several measures of neoliberal policies on infant mortality rates across the world between 1960 and 1999. Results suggest that openness to imports, long-term membership in the GATT and WTO, low rates of inflation, and effective contract enforcement are each associated with lower rates of infant mortality across the world, even when controlling for countries' economic performance.

Description: In this paper we deconstruct the popular book by Thomas Friedman which argues that the world is integrated through the advent of a new form of globalization based on the Internet. We use the logic of international business strategy to demonstrate that Friedman's examples of worldwide integration are special cases which ignore the empirical realities of multinational enterprises (MNEs). We provide empirical evidence to demonstrate that the world's largest MNEs do not operate globally, but sell and produce the vast majority of their output within their home region of the triad. We develop a new analytical framework to explain the limited nature of Friedman's thinking, and we contrast this with the more robust frameworks available in international business. The latter frameworks, which take into account country level and regional level barriers to integration, are better at explaining the activities of MNEs. We conclude that, from the viewpoint of international business strategy, the prescriptive thinking from Friedman is misleading if it is believed that a global strategy is feasible. Instead, MNEs need to develop strategies to accommodate the realities of intra-regional integration and to overcome the liabilities of inter-regional expansion across the triad.

Description: The modernization of the banking sector, and particularly the big four state owned commercial banks, has a top priority on the Chinese reform agenda. Three of the four state banks found foreign strategic investors as minority shareholders and domestic banks now face more competition from global players since the country's WTO commitments came fully into effect at the end of 2006. A comprehensive approach to reform aims at pushing China's state banks into the league of global leading financial institutions within a few years time. But is this aim feasible despite prevalent state dominance? To shed light on the role and impact of the state in promoting sound risk management practices this paper focuses on the political economy of law implementation. Two main conclusions are drawn: (1) the direction of action is significantly different from reform outcomes due to weak incentives to enforce respective policies and as a consequence non-performing loan accumulation continues; and (2) on a more general level banking regulation in China illustrates that a normative approach based on international best practice is insufficient to address the issue of financial stability in many emerging and developing countries because it neglects the role of the institutional embeddedness of banking reform.

Description: While there is a strong theoretical foundation for the relationship between business sectors' political spending and the policy benefits that they receive, the empirical support for it is mixed. We use the logic of this exchange to examine a policy area that directly and significantly affects all businesses, and is thus a most likely case, taxation. Using principally firm-level tax rates of a large random sample of U.S. corporations for the 1998–2005 time period, we determine whether lobbying has measurable effects on firm-level tax rates. Contrary perhaps to popular belief, or at least anecdotal illustration, we find after controlling for firm size and industry-level tax rates, among other controls, that there is no discernible effect of political spending on firm-level taxation: firms that spend more in an effort to affect policy generally or tax policy specifically are no more likely to benefit from lower tax rates. We also examine the possibility that firms in the same industry coordinate efforts to affect tax rates. While we find limited evidence that firms occasionally coordinate within industries – or at least lobby simultaneously – to affect tax rates, perhaps more importantly, we determine that free-riding by smaller firms at the expense of the largest firms is rampant.

Description: The main aim is to question why we don't see more firms petitioning for import relief. It is well accepted that petitioning itself can restrain imports, lead to higher prices and hence higher profits (in the short run). What prevents more firms from filing for protection? It may be that petitioning reflects cost inefficiency on the part of the petitioning firm, and concerns about revealing this information might act as a deterrent for firms to come forward with their complaints. However, in a declining industry where a large number of firms are contemplating exit, petitioning could be a signal that the firm expects to remain in the market for the near future. The signaling hypothesis is tested by comparing the stock market response of an antidumping petition for petitioning firms and non-petitioning firms producing the same product.

Description: To ascertain whether youth bulges are related to violent conflict and whether violent conflict falls off when youth bulges are followed by busts, we analyzed data from 1998–2005 covering 127 nations. Controlling for variables representing such factors as socio-development, macroeconomics, technology advancement, government capacity, and geo-politics, we find that youth bulges are related to violent conflict, but when youth bulges are followed by busts violent conflict grows rather than diminishes contrary to the prediction we make. From this analysis, we draw implications for further research and analysis with regard to doing business in violence-prone nations.

Description: Analyses of central bank independence (CBI) have generated two sets of apparently contradictory results - CBI appears to be both inversely related to inflation and positively related to the rise in unemployment and slowdown in economic growth during disinflations. I suggest that these results may issue from autonomous central banks being associated with sharper, more aggressive disinflations. To test the proposition I use two measures of policy stance, one of which contains more information concerning policymaker's expectations than has heretofore been the case. The results suggest a need to qualify yet further the optimality of CBI.

Description: In the Angkor monuments of Cambodia, pieces of wood remain (as head frames of doorways, crossbeams, ceiling boards, etc.) in the following 8 monuments: Bakong, Lolei, Baksei Chamkrong, North Khleang, Angkor Wat, Banteay Kdei, Bayon, and Gates of Angkor Thorn. Accelerator mass spectrometry (AMS) radiocarbon dating carried out on 15 wood samples collected from the above 8 monuments revealed that most of the wood samples are original, except for the head frame of a doorway in Baksei Chamkrong, the ceiling boards in the northwest tower, and a crossbeam with pivot hole in the southwest tower of the Inner Gallery of Angkor Wat. The 14C age for the head frame of a doorway in the inner wall under the central tower of North Khleang supports the hypothesis that the inner walls are additions from a later period.

Description: Chemical and structural similarities between poorly preserved charcoal and its contaminants, as well as low radiocarbon concentrations in old samples, complicate 14C age determinations. Here, we characterize 4 fossil charcoal samples from the late Middle Paleolithic and early Upper Paleolithic strata of Kebara Cave, Israel, with respect to the structural and chemical changes that occur when they are subjected to the acid-base-acid (ABA) treatment. Differential thermal analysis and TEM show that acid treatment disrupts the structure, whereas alkali treatment results in the reformation of molecular aggregates. The major changes are ascribed to the formation of salt bridges at high pH and the disruption of the graphite-like crystallites at low pH. Weight losses during the treatments are consistently greater for older samples, implying that they are less well preserved. Based on the changes observed in vitro due to pH fluctuations, various methods for removing contamination, as well as a mechanism for preferential preservation of charcoal in nature, are proposed.

Description: Bayesian analysis of 6 radiocarbon and 2 luminescence determinations from Punta de Chimino's acropolis provides subcentury chronometric accuracy for a Protoclassic hiatus and a more decisive, incipient Early Classic abandonment. For the latter event, sensitivity tests and a redundant modal value pattern reduce the period of historical interest from a few centuries to several decades. The findings aid in selecting between 2 historical scenarios and demonstrate that improved chronological accuracy is attainable for sites and contexts lacking calendrical dates.

Description: We report radiocarbon ages on cellulose isolated from the gut contents of a Diprotodon found at Lake Callabonna, South Australia. The maximum age obtained corresponds to a minimum age of 〉53,400 BP for this extinct giant marsupial. This is older than, and hence consistent with, the generally accepted Australian megafauna extinction window. We argue that dichromate and other strong oxidants are less selective than chlorite for lignin destruction in wood, and our results suggest that ages approaching laboratory background can be obtained using a repeated pretreatment sequence of chlorite-alkali-acid and measurement of the sometimes discarded 330°C combustion fraction.

Description: Accelerator mass spectrometry (AMS) radiocarbon dates were obtained for 18 mollusk shells collected alive along the Buenos Aires province coast, Argentina, over the period AD 1914–1935. Reservoir ages were estimated for all samples on the basis of the tree-ring calibration curve for the Southern Hemisphere (SHCal04, McCormac et al. 2004) and the marine δR values calculated as the difference between the conventional 14C age and the age deduced from the marine, mixed-layer model calculation (Marine04, Hughen et al. 2004). For most coastal locations, a great δR scatter was observed, ranging from 191 to 2482 yr, which is explained by the input of varying content of dissolved carbonate by rivers and groundwater (“hardwater effect”) and indicates a serious limitation for shell-based 14C chronologies. Within the interior of Bahía Blanca estuary, δR values ranged from −40 to 50 ± 46 as a consequence of the local geological particularities of the environment. This suggests that, with some restrictions, the marine calibration curve with standard parameters (δR = 0) could be used at this location.

Description: A variety of physical and chemical techniques are used to fractionate soil organic matter, but detailed comparisons of the different approaches and tests of how separation methods influence the properties of isolated organic matter pools are lacking. In this case study based on A horizon samples of 2 California coniferous forests soils, we 1) evaluate the effects of root removal and ultrasonic dispersion on the properties of the

Description: We have developed sample pretreatments for silk for radiocarbon dating. Characteristics of silk under different types of pretreatment were investigated, as well as the behavior of dye and possible contaminants. We found that dye could be removed completely, together with all other foreign materials bigger than 1.2 μm, using a glass microfiber filter after decomposition with 6N HCl. The decomposed proteins were concentrated using Centriprep® ultrafiltration concentrators with 3 different molecular weight cut-offs. By taking a molecular weight fraction—which selects for secondary structures of silk protein—14C dating of silk samples can be made more reliable. This study confirms that uniformly fractured polypeptide chains of silk provide an appropriate fraction for 14C age dating to select silk protein against dye particles and undecomposed foreign contaminants.

Description: This study presents the results of archaeological samples submitted for dating at the recently constructed University of Tennessee Center for Archaeometry and Geochronology (UTCAG) radiocarbon dating laboratory (Knoxville, Tennessee, USA). The samples selected for this initial study were obtained from excavations at the McCrosky Island site (40SV43) in Sevier County, Tennessee, USA. Three of the samples dated were split between the UTCAG laboratory and another laboratory to assess the UTCAG laboratory protocols. In an effort to further validate the laboratory methods employed, several other samples were submitted without prior knowledge of contextual data. The dates obtained for these samples were then compared to their association with recovered artifacts and/or archaeological context.

Description: We investigated sample dilution as a technique for accelerator mass spectrometry (AMS) radiocarbon analysis of very small samples (down to 30 μg). By diluting such samples up to a total weight of 200 μg, we can still perform reliable AMS measurements and improve the success rate significantly for targets that are difficult to measure. A disadvantage of this dilution technique is a loss of measurement precision. In addition, calculations of the 14C/12C isotope ratios and the uncertainties therein are not straightforward because of peculiarities in isotope fractionation processes in the AMS system. Therefore, to make sample dilution a routine method in our laboratory, we did extensive theoretical and experimental research to find the optimum conditions for all relevant parameters. Here, we report on the first detailed study dealing with all aspects of sample dilution. Our results can be applied in general. As an illustrative test case, we analyze 14C data for CO2 extracted from an ice core, from which samples of 35 μg C or less are available.

Description: We present the first marine reservoir age and δR determination for the island of St. Helena using marine mollusk radiocarbon dates obtained from an historical context of known age. This represents the first marine reservoir age and δR determination in the southern Atlantic Ocean within thousands of kilometers of the island. The depletion of 14C in the shells indicates a rather larger reservoir age for that portion of the surface Atlantic than models indicate. The implication is that upwelling old water along the Namibian coast is transported for a considerable distance, although it is likely to be variable on a decadal timescale. An artilleryman's button, together with other artifacts found in a midden, demonstrate association of the mollusk shells with a narrow historic period of AD 1815-1835.

Description: For at least 100,000 yr, marine shell beads have been important ornamental and symbolic artifacts intimately associated with the behavior of anatomically modern humans. In California, giant rock scallop (Hinnites multirugosus) beads were once thought to have been used only for the last 1000 yr, where they were considered to be markers of high social status among the Chumash Indians of the Santa Barbara Channel region. Direct accelerator mass spectrometry (AMS) radiocarbon dating of 1 giant rock scallop ornament and 2 beads from San Miguel Island extends the use of this shell for personal adornment to at least 8000 cal BP. Our study emphasizes the importance of direct AMS 14C dating of artifacts to enhance cultural chronologies and clarify the antiquity of various technologies and associated behaviors. Our results also caution archaeologists when equating artifact rarity with sociopolitical complexity.

Description: We measured radiocarbon ages of 22 decadal replications and 1 bulk group from 5 tree-ring specimens using acid-base-acid pretreatment and accelerator mass spectrometry (AMS). The study has the goal of refining the precision and resolution of a segment of the conventional Bronze Age chronology in the Eurasian steppe attributed to the multicultural community known as Andronovo. The archaeological timbers were gathered from 3 cemeteries at the Lisakovsky cluster of sites in Kazakhstan, where there is a prominent Andronovo occurrence that appears to show evidence of overlapping Alakul and Fedorovo cultures in the southern margin of the Eurasian steppe. The new set of Andronovo calendar dates derived from 14C wiggles and a composite floating tree-ring chronology places the cultural overlap from 1780 to 1660 cal BC. Results indicate older ages of artifacts from the Lisakovsky site than were previously determined by the typological chronology, shifting them from the Late Bronze Age to also include the transition between the Middle and Late Bronze Age. The chronological order of the Lisakovsky cemeteries provides strong evidence of contemporaneity of the Alakul and Fedorovo cultures in the Tobol River Valley for a portion of the 120-yr period of occupation. We discuss an application of the dated Alakul-Fedorovo overlap to the relationship and origin of different groups of the Andronovo community in the Ural region. Our results demonstrate the substantial power that tree rings from Bronze Age timbers provide for developing a precise and highly resolved calendar chronology of prehistoric human occupation in the Eurasian steppe during the 2nd millennium BC.

Description: When ancient hearths at open archaeological sites do not yield carbonized annual plant remains or other high-quality samples, wood charcoal is commonly used for radiocarbon dating. Sagebrush (Artemisia tridentata Nutt.), a shrub frequently used for fuel across much of the western United States, seems a potentially better candidate for 14C dating than tree wood since the possibility for significant age discrepancy might be less. A comparison of multiple assays from single features reveals that sagebrush can overestimate age more than even tree wood charcoal. A plausible cause of this appears to be persistence of the shrub on the ground surface for an extended interval after death, such that use as fuel almost invariably occurs hundreds of years after fixation of carbon. The potential for age discrepancy may decrease as population density increases because the demand for fuel wood would have resulted in a more rapid turnover of the fuel biomass. This is not true for Archaic period foragers of western North America when population levels were likely quite low and residential mobility quite high.

Description: The open-air archaeological site at Krems-Hundssteig is a well-known Upper Paleolithic site located in Lower Austria. The site was discovered in the late 19th/early 20th centuries when a large number of archaeological remains were collected during the course of loess quarrying. Although no systematic excavation has ever been performed, Krems-Hundssteig has been described since its discovery as typical of the Aurignacian period in this region based on the numerous archaeological finds; accordingly, the culture has been named Kremsien by some authors. Surprisingly, the artifacts found in a recent excavation adjacent to this location showed solely Gravettian features, calling into question the original assignment to the Aurignacian. Although the earlier assignment was supported by a radiocarbon date of ∼35 kyr BP (Hahn 1977), new accelerator mass spectrometry (AMS) 14C dates proved that the recently excavated cultural layer originates from the Gravettian period. Older paleosols were also detected by sondage drillings at some depth below it.The new results indicate that a large Aurignacian level and a substantial complex of Gravettian layers are present in this area. Therefore, it must be assumed that more than 1 cultural level was affected and destroyed by the historic loess quarrying, and that the assemblage of Krems-Hundssteig artifacts, traditionally ascribed to the Aurignacian, might be interspersed with Gravettian pieces.

Description: Grant Kocharov was a man whose life mirrored all the complexity and controversy of the fate of Russia in the second part of the 20th century. Kocharov was a bright, colorful, and ambitious person. He was born in Georgia, and his childhood and youth were not sunny and cloudless. His father died early and it was very difficult for his mother to feed their large family.

Description: The reliability of radiocarbon ages based on soil organic matter (SOM) from Holocene buried soils in Middle Park, Colorado, is assessed by comparison with ages of charcoal. On average, 14C ages of SOM from buried surface horizons are 880 ± 230 14C yr younger than charcoal ages from the same horizon. Humic acid (HA) and low-temperature (400 °) combustion residue (LT) fractions are 390 ± 230 and 1290 ± 230 14C yr younger than charcoal ages, respectively, and HA ages are on average 860 ± 140 14C yr older than LT fractions. We interpret the offsets between 14C ages of charcoal and SOM fractions and the consistent offsets between the HA and LT fractions to reflect the duration of pedogenesis and different residence times of the SOM fractions examined here. The stratigraphic coherence of charcoal 14C ages suggests short residence time on the landscape, with little subsequent reworking. 14C ages of HA and LT fractions are complimentary to charcoal, and HA ages are interpreted to represent minimum ages for the onset of pedogenesis and LT ages are considered maximum ages for burial. The 14C chronology from buried soils indicates an episode of hillslope erosion in Middle Park during the early Holocene, followed by a long period of land surface stability and soil formation between 9000–4500 BP. Two episodes of late Holocene hillslope erosion between 3500–2500 and 1000–500 BP correspond with warming recognized in the Colorado Front Range, while surface stability and soil formation between 2500–1000 BP is contemporaneous with evidence for cooling at higher elevations.

Description: In order to estimate the modern reservoir age of the seawater (R) and the corresponding local offset from the global marine radiocarbon calibration curve (δR) for coastal sites of Senegal and Mauritania, we analyzed pre-bomb mollusk shells collected between AD 1837 and 1945. In total, 27 shell samples were measured, including 19 from Senegal and 8 from Mauritania. The results for Senegal for the weighted mean of R is 511 ± 50 BP and δR is 176 ± 15 BP; for Mauritania, R is 421 ± 15 BP and δR is 71 ± 13 BP. While these values indicate a significant difference from the global mean value of R for Senegal, the R value for coastal Mauritania is close to the average ocean value R of ~400 yr (Stuiver and Braziunas 1993).

Description: We present a new method developed for measuring radiocarbon of methane (14CH4) in ancient air samples extracted from glacial ice and dating 11,000–15,000 calendar years before present. The small size (∼20 μg CH4 carbon), low CH4 concentrations ([CH4], 400–800 parts per billion [ppb]), high carbon monoxide concentrations ([CO]), and low 14C activity of the samples created unusually high risks of contamination by extraneous carbon. Up to 2500 ppb CO in the air samples was quantitatively removed using the Sofnocat reagent. 14C procedural blanks were greatly reduced through the construction of a new CH4 conversion line utilizing platinized quartz wool for CH4 combustion and the use of an ultra-high-purity iron catalyst for graphitization. The amount and 14C activity of extraneous carbon added in the new CH4 conversion line were determined to be 0.23 ± 0.16 μg and 23.57 ± 16.22 pMC, respectively. The amount of modern (100 pMC) carbon added during the graphitization step has been reduced to 0.03 μg. The overall procedural blank for all stages of sample handling was 0.75 ± 0.38 pMC for ∼20-μg, 14C-free air samples with [CH4] of 500 ppb. Duration of the graphitization reactions for small (

Description: This paper provides a comprehensive review of the empirical literature in transaction cost economics (TCE) across multiple social science disciplines and business fields. We show how TCE has branched out from its economic roots to examine empirical phenomena in several other areas. We find TCE is increasingly being applied not only to business-related fields such as accounting, finance, marketing, and organizational theory, but also to areas outside of business including political science, law, public policy, and agriculture and health. With few exceptions, however, the use of TCE reasoning to inform empirical research in these areas is piecemeal. We find that there is considerable support of many of the central tenets of TCE, but we also observe a number of lingering theoretical and empirical issues that need to be addressed. We conclude by discussing the implications of these issues and outlining directions for future theoretical and empirical work.

Description: This paper makes two new propositions regarding the modelling of rarefied (non-equilibrium) isothermal gas flows at the microscale. The first is a new test case for benchmarking high-order, or extended, hydrodynamic models for these flows. This standing time-varying shear-wave problem does not require boundary conditions to be specified at a solid surface, so is useful for assessing whether fluid models can capture rarefaction effects in the bulk flow. We assess a number of different proposed extended hydrodynamic models, and we find the R13 equations perform the best in this case. Our second proposition is a simple technique for introducing non-equilibrium effects caused by the presence of solid surfaces into the computational fluid dynamics framework. By combining a new model for slip boundary conditions with a near-wall scaling of the Navier-Stokes constitutive relations, we obtain a model that is much more accurate at higher Knudsen numbers than the conventional second-order slip model. We show that this provides good results for combined Couette/Poiseuille flow, and that the model can predict the stress/strain-rate inversion that is evident from molecular simulations. The model's generality to non-planar geometries is demonstrated by examining low-speed flow around a micro-sphere. It shows a marked improvement over conventional predictions of the drag on the sphere, although there are some questions regarding its stability at the highest Knudsen numbers. © 2008 Cambridge University Press.

Description: The deformation of an elastic micro-capsule in an infinite shear flow is studied numerically using a spectral method. The shape of the capsule and the hydrodynamic flow field are expanded into smooth basis functions. Analytic expressions for the derivative of the basis functions permit the evaluation of elastic and hydrodynamic stresses and bending forces at specified grid points in the membrane. Compared to methods employing a triangulation scheme, this method has the advantage that the resulting capsule shapes are automatically smooth, and few modes are needed to describe the deformation accurately. Computations are performed for capsules with both spherical and ellipsoidal unstressed reference shape. Results for small deformations of initially spherical capsules coincide with analytic predictions. For initially ellipsoidal capsules, recent approximate theories predict stable oscillations of the tank-treading inclination angle, and a transition to tumbling at low shear rate. Both phenomena have also been observed experimentally. Using our numerical approach we can reproduce both the oscillations and the transition to tumbling. The full phase diagram for varying shear rate and viscosity ratio is explored. While the numerically obtained phase diagram qualitatively agrees with the theory, intermittent behaviour could not be observed within our simulation time. Our results suggest that initial tumbling motion is only transient in this region of the phase diagram. © 2008 Cambridge University Press.

Description: Numerical simulations of laser energy deposition in air are conducted. Local thermodynamic equilibrium conditions are assumed to apply. Variation of the thermodynamic and transport properties with temperature and pressure are accounted for. The flow field is classified into three phases: shock formation; shock propagation; and subsequent collapse of the plasma core. Each phase is studied in detail. Vorticity generation in the flow is described for short and long times. At short times, vorticity is found to be generated by baroclinic means. At longer times, a reverse flow is found to be generated along the plasma axis resulting in the rolling up of the flow field near the plasma core and enhancement of the vorticity field. Scaling analysis is performed for different amounts of laser energy deposited and different Reynolds numbers of the flow. Simulations are conducted using three different models for air based on different levels of physical complexity. The impact of these models on the evolution of the flow field is discussed. © 2008 Cambridge University Press.

Description: Direct numerical simulation (DNS) of vortex shedding behind a tapered plate with the taper ratio 20 placed normal to the inflow has been performed. The Reynolds numbers based on the uniform inflow velocity and the width of the plate at the wide and narrow ends were 1000 and 250, respectively. For the first time ever cellular vortex shedding was observed behind a tapered plate in a numerical experiment (DNS). Multiple cells of constant shedding frequency were found along the span of the plate. This is in contrast to apparent lack of cellular vortex shedding found in the high-Reynolds-number experiments by Gaster & Ponsford (Aero. J., vol. 88, 1984, p. 206). However, the present DNS data is in good qualitative agreement with similar high-Reynolds-number experimental data produced by Castro & Watson ( Exp. Fluids, vol. 37, 2004, p. 159). It was observed that a tapered plate creates longer formation length coupled with higher base pressure as compared to non-tapered (i.e. uniform) plates. The three-dimensional recirculation bubble was nearly conical in shape. A significant base pressure reduction towards the narrow end of the plate, which results in a corresponding increase in Strouhal number, was noticed. This observation is consistent with the experimental data of Castro & Rogers (Exp. Fluids, vol. 33, 2002, p. 66). Pressure-driven spanwise secondary motion was observed, both in the front stagnation zone and also in the wake, thereby reflecting the three-dimensionality induced by the tapering. © 2008 Cambridge University Press.

Description: We consider levitation of an axisymmetric drop of molten glass above a spherical porous mould through which air is injected at a constant velocity. Owing to the viscosity contrast, the float height for a given shape is established on a much shorter time scale than the subsequent deformation of the drop under gravity, surface tension and the underlying lubrication pressure. Equilibrium shapes, in which an internal hydrostatic pressure is coupled to the external lubrication pressure through the total curvature and the Young-Laplace equation, are determined using a numerical continuation scheme. The set of solution branches is surprisingly complicated and shows a rich bifurcation structure in the parameter space ( Bo =ρg V2/3/γ, Ca = μav/γ), where Bo is bond number and Ca is capillary number, ρ and V are the drop density and volume, γ the surface tension, μa the air viscosity and v the injection velocity. The linear stability of equilibria is determined using a boundary-integral representation for drop deformation that factors out the rapid vertical adjustment of the float height. The results give good agreement with time-dependent simulations. For sufficiently large Ca there are intervals of Bo for which there are no stable solutions and, as Ca increases, these intervals grow and merge. The region of stability decreases as the mould radius aM increases with an approximate scaling Ca∼aM-5, which imposes practical limitations on the use of this geometry for the manufacture of lenses. © 2008 Cambridge University Press 2008.

Description: Two-dimensional Lagrangian acceleration statistics of inertial particles in a turbulent boundary layer with free-stream turbulence are determined by means of a particle tracking technique using a high-speed camera moving along the side of the wind tunnel at the mean flow speed. The boundary layer is formed above a flat plate placed horizontally in the tunnel, and water droplets are fed into the flow using two different methods: sprays placed downstream from an active grid, and tubes fed into the boundary layer from humidifiers. For the flow conditions studied, the sprays produce Stokes numbers varying from 0.47 to 1.2, and the humidifiers produce Stokes numbers varying from 0.035 to 0.25, where the low and high values refer to the outer boundary layer edge and the near-wall region, respectively. The Froude number is approximately 1.0 for the sprays and 0.25 for the humidifiers, with a small variation within the boundary layer. The free-stream turbulence is varied by operating the grid in the active mode as well as a passive mode (the latter behaves as a conventional grid). The boundary layer momentum-thickness Reynolds numbers are 840 and 725 for the active and passive grid respectively. At the outer edge of the boundary layer, where the shear is weak, the acceleration probability density functions are similar to those previously observed in isotropic turbulence for inertial particles. As the boundary layer plate is approached, the tails of the probability density functions narrow, become negatively skewed, and their peak occurs at negative accelerations (decelerations in the streamwise direction). The mean deceleration and its root mean square (r.m.s.) increase to large values close to the plate. These effects are more pronounced at higher Stokes number. In the vertical direction, there is a slight downward mean deceleration and its r.m.s., which is lower in magnitude than that of the streamwise component, peaks in the buffer region. Although there are free-stream turbulence effects, and the complex boundary layer structure plays an important role, a simple model suggests that the acceleration behaviour is dominated by shear, gravity and inertia. The results are contrasted with inertial particles in isotropic turbulence and with fluid particle acceleration statistics in a boundary layer. The background velocity field is documented by means of hot-wire anemometry and laser Doppler velocimetry measurements. These appear to be the first Lagrangian acceleration measurements of inertial particles in a shear flow. © 2008 Cambridge University Press.

Description: The dynamics of receding contact lines is investigated experimentally through controlled perturbations of a meniscus in a dip-coating experiment. We first describe stationary menisci and their breakdown at the coating transition. Above this transition where liquid is deposited, it is found that the dynamics of the interface can be interpreted as a quasi-steady succession of stationary states. This provides the first experimental access to the entire bifurcation diagram of dynamical wetting, confirming the hydrodynamic theory developed in Part 1. In contrast to quasi-static theories based on a dynamic contact angle, we demonstrate that the transition strongly depends on the large-scale flow geometry. We then establish the dispersion relation for large wavenumbers, for which we find a decay rate σ proportional to wavenumber q . The speed dependence of σ is described well by hydrodynamic theory, in particular the absence of diverging time scales at the critical point. Finally, we highlight some open problems related to contact angle hysteresis that lead beyond the current description. © 2008 Cambridge University Press.

Description: A novel modification of the classical Langhaar linearization of the mutually coupled momentum equations for developing two-phase flows in circular ducts is presented. This modification enables us to treat: (i) flows developing from spatially periodic initial velocity distributions without the presence of droplets, and (ii) two-phase flows in which monosize, non-evaporating and evaporating droplets suspended in a developing gas flow of an initially uniform velocity distribution exchange momentum with the host-gas flow. New solutions are presented for the downstream evolution in the velocity profiles which develop from spatially periodic initial velocity distributions that eventually reach the fully developed Poiseuille velocity profile. These solutions are validated by employing known numerical procedures, providing strong support for the physical underpinnings of the present modified linearization. New solutions are also presented for the evolution in drop velocities and vapour spatial distributions for evaporating droplets suspended in an initially uniform velocity profile of the host gas. Asymptotic solutions are presented for the flow region which lies very close to the inlet of the tube, where the relative velocity between the droplets and the host gas is high, and thus the velocity fields of the two phases are mutually coupled. These solutions provide new explicit formulae for the droplet velocity field as a function of the initial conditions and droplet diameter (relative to the tube diameter) for non-evaporating drops, and also as a function of evaporation rate for evaporating drops. © 2008 Cambridge University Press.

Description: The Kelvin wave is the lowest eigenmode of Laplace's tidal equation and is widely observed in both the ocean and the atmosphere. In this work, we neglect mean currents and instead include the full effects of the Earth's sphericity and the wave dispersion it induces. Through a mix of perturbation theory and numerical computations using a Fourier/Newton iteration/continuation method, we show that for sufficiently small amplitude, there are Kelvin travelling waves (cnoidal waves). As the amplitude increases, the branch of travelling waves terminates in a so-called corner wave with a discontinuous first derivative. All waves larger than the corner wave evolve to fronts and break. The singularity is a point singularity in which only the longitudinal derivative is discontinuous. As we solve the nonlinear shallow water equations on the sphere, with increasing ∈ ('Lamb's parameter'), dispersion weakens, the amplitude of the corner wave decreases rapidly, and the longitudinal profile of the corner wave narrows dramatically. © Cambridge University Press 2008.

Description: The capillary instability of a liquid thread containing a regular array of spherical particles along the centreline is considered with reference to microencapsulation. The thread interface may be clean or occupied by an insoluble surfactant. The main goal of the analysis is to illustrate the effect of the particle spacing on the growth rate of axisymmetric perturbations and identify the structure of the most unstable modes. A normal-mode linear stability analysis based on Fourier expansions for Stokes flow reveals that, at small particle separations, the interfacial profiles are nearly pure sinusoidal waves whose growth rate is nearly equal to that of a pure thread devoid of particles. Higher harmonics suddenly enter the normal modes for moderate and large particle separations, elevating the growth rates and yielding a stability diagram that consists of a sequence of superposed pure-thread lobes. A complementary numerical stability analysis based on the boundary integral formulation for Stokes flow reveals the strong stabilizing effect of particles whose radius is comparable to the thread radius. Numerical simulations of the finite-amplitude motion based on the boundary integral method demonstrate that thread breakup leads to particles coated with annular layers of different thicknesses. © 2008 Cambridge University Press 2008.

Description: We examine steady longitudinal freezing of a two-dimensional single-component free liquid film. In the liquid, there are thermocapillary and volume-change flows as a result of temperature gradients along the film and density change upon solidification. We examine these flows, heat transfer, and interfacial shapes using an asymptotic analysis which is valid for thin films with small aspect ratios. These solutions depend sensitively on contact conditions at the tri-junctions. In particular, when the sum of the angles formed in the solid and liquid phases falls below a critical value, the existence of steady solutions is lost and the liquid film cannot be continuous, suggesting breakage of the film owing to freezing. The solutions are relevant to the freezing of foams of metals or ceramics, materials unaffected by surface active agents. © 2008 Cambridge University Press 2008.

Description: A computational fluid dynamics cavitation model based on the Eulerian-Lagrangian approach and suitable for hole-type diesel injector nozzles is presented and discussed. The model accounts for a number of primary physical processes pertinent to cavitation bubbles, which are integrated into the stochastic framework of the model. Its predictive capability has been assessed through comparison of the calculated onset and development of cavitation inside diesel nozzle holes against experimental data obtained in real-size and enlarged models of single- and multi-hole nozzles. For the real-size nozzle geometry, high-speed cavitation images obtained under realistic injection pressures are compared against model predictions, whereas for the large-scale nozzle, validation data include images from a charge-coupled device (CCD) camera, computed tomography (CT) measurements of the liquid volume fraction and laser Doppler velocimetry (LDV) measurements of the liquid mean and root mean square (r.m.s.) velocities at different cavitation numbers (CN) and two needle lifts, corresponding to different cavitation regimes inside the injection hole. Overall, and on the basis of this validation exercise, it can be argued that cavitation modelling has reached a stage of maturity, where it can usefully identify many of the cavitation structures present in internal nozzle flows and their dependence on nozzle design and flow conditions. © 2008 Cambridge University Press.

Description: We consider the stability of small perturbations to a uniform inviscid compressible flow within a cylindrical linear-elastic thin shell. The thin shell is modelled using Flügge's equations, and is forced from the inside by the fluid, and from the outside by damping and spring forces. In addition to acoustic waves within the fluid, the system supports surface waves, which are strongly coupled to the thin shell. Stability is analysed using the Briggs - Bers criterion, and the system is found to be either stable or absolutely unstable, with absolute instability occurring for sufficiently small shell thicknesses. This is significantly different from the stability of a thin shell containing incompressible fluid, even for parameters for which the fluid would otherwise be expected to behave incompressibly (for example, water within a steel thin shell). Asymptotic expressions are derived for the shell thickness separating stable and unstable behaviour. We then consider the scattering of waves by a sudden change in the duct boundary from rigid to thin shell, using the Wiener - Hopf technique. For the scattering of an inbound acoustic wave in the rigid-wall section, the surface waves are found to play an important role close to the sudden boundary change. The solution is given analytically as a sum of duct modes. The results in this paper add to the understanding of the stability of surface waves in models of acoustic linings in aeroengine ducts. The oft-used mass - spring - damper model is regularized by the shell bending terms, and even when these terms are very small, the stability and scattering results are quite different from what has been claimed for the mass - spring - damper model. The scattering results derived here are exact, unique and causal, without the need to apply a Kutta-like condition or to include an instability wave. A movie is available with the online version of the paper. © 2008 Cambridge University Press.

Description: A mathematical model is presented for steady fluid flow across microvessel walls through a serial pathway consisting of the endothelial surface glycocalyx and the intercellular cleft between adjacent endothelial cells, with junction strands and their discontinuous gaps. The three-dimensional flow through the pathway from the vessel lumen to the tissue space has been computed numerically based on a Brinkman equation with appropriate values of the Darcy permeability. The predicted values of the hydraulic conductivity Lp, defined as the ratio of the flow rate per unit surface area of the vessel wall to the pressure drop across it, are close to experimental measurements for rat mesentery microvessels. If the values of the Darcy permeability for the surface glycocalyx are determined based on the regular arrangements of fibres with 6 nm radius and 8 nm spacing proposed recently from the detailed structural measurements, then the present study suggests that the surface glycocalyx could be much less resistant to flow compared to previous estimates by the one-dimensional flow analyses, and the intercellular cleft could be a major determinant of the hydraulic conductivity of the microvessel wall. © 2008 Cambridge University Press.

Description: The deformation of a Newtonian/viscoelastic drop suspended in a viscoelastic fluid is investigated using a three-dimensional front-tracking finite-difference method. The viscoelasticity is modelled using the Oldroyd-B constitutive equation. Matrix viscoelasticity affects the drop deformation and the inclination angle with the flow direction. Numerical predictions of these quantities are compared with previous experimental measurements using Boger fluids. The elastic and viscous stresses at the interface, polymer orientation, and the elastic and viscous forces in the domain are carefully investigated as they affect the drop response. Significant change in the drop inclination with increasing viscoelasticity is observed; this is explained in terms of the first normal stress difference. A non-monotonic change - a decrease followed by an increase - in the steady-state drop deformation is observed with increasing Deborah number (De) and explained in terms of the competition between increased localized polymer stretching at the drop tips and the decreased viscous stretching due to change in drop orientation angle. The transient drop orientation angle is found to evolve on the polymer relaxation time scale for high De. The breakup of a viscous drop in a viscoelastic matrix is inhibited for small De, and promoted at higher De. Polymeric to total viscosity ratio β was seen to affect the result through the combined parameter β De indicating a dominant role of the first normal stress difference. A viscoelastic drop in a viscoelastic matrix with matched relaxation time experiences less deformation compared to the case when one of the phases is viscous; but the inclination angle assumes an intermediate value between two extreme cases. Increased drop phase viscoelasticity compared to matrix phase leads to decreased deformation. © 2008 Cambridge University Press.

Description: We study the mixing properties of two systems: (i) a half-filled quasi-two-dimensional circular drum whose rotation rate is switched between two values and which can be analysed in terms of the existing mathematical formalism of linked twist maps; and (ii) a half-filled three-dimensional spherical tumbler rotated about two orthogonal axes bisecting the equator and with a rotational protocol switching between two rates on each axis, a system which we call a three-dimensional linked twist map, and for which there is no existing mathematical formalism. The mathematics of the three-dimensional case is considerably more involved. Moreover, as opposed to the two-dimensional case where the mathematical foundations are firm, most of the necessary mathematical results for the case of three-dimensional linked twist maps remain to be developed though some analytical results, some expressible as theorems, are possible and are presented in this work. Companion experiments in two-dimensional and three-dimensional systems are presented to demonstrate the validity of the flow used to construct the maps. In the quasi-two-dimensional circular drum, bidisperse (size-varying or density-varying) mixtures segregate to form lobes of small or dense particles that coincide with the locations of islands in computational Poincaré sections generated from the flow model. In the 3d spherical tumbler, patterns formed by tracer particles reveal the dynamics predicted by the flow model. © 2008 Cambridge University Press.

Description: Motivated by the propulsion mechanisms adopted by gastropods, annelids and other invertebrates, we consider shape optimization of a flexible sheet that moves by propagating deformation waves along its body. The self-propelled sheet is separated from a rigid substrate by a thin layer of viscous Newtonian fluid. We use a lubrication approximation to model the dynamics and derive the relevant Euler-Lagrange equations to simultaneously optimize swimming speed, efficiency and fluid loss. We find that as the parameters controlling these quantities approach critical values, the optimal solutions become singular in a self-similar fashion and sometimes leave the realm of validity of the lubrication model. We explore these singular limits by computing higher-order corrections to the zeroth order theory and find that wave profiles that develop cusp-like singularities are appropriately penalized, yielding non-singular optimal solutions. These corrections are themselves validated by comparison with finite element solutions of the full Stokes equations, and, to the extent possible, using recent rigorous a priori error bounds. © 2008 Cambridge University Press.

Description: Two different approaches have been used to calculate turbulent flow along a long thin cylinder where the flow is aligned with the cylinder. A boundary-layer code is used to predict the mean flow for very long cylinders (length to radius ratio of up to O (106)), with the effects of the turbulence estimated through a turbulence model. Detailed comparison with experimental results shows that the mean properties of the flow are predicted within experimental accuracy. The boundary-layer model predicts that, sufficiently far downstream, the surface shear stress will be (almost) constant. This is consistent with experimental results from long cylinders in the form of sonar arrays. A periodic Navier-Stokes problem is formulated, and solutions generated for Reynolds number from 300 to 5 × 104. The results are in agreement with those from the boundary-layer model and experiments. Strongly turbulent flow occurs only near the surface of the cylinder, with relatively weak turbulence over most of the boundary layer. For a thick boundary layer with the boundary-layer thickness much larger than the cylinder radius, the mean flow is effectively constant near the surface, in both temporal and spatial frameworks, while the outer flow continues to develop in time or space. Calculations of the circumferentially averaged surface pressure spectrum show that, in physical terms, as the radius of the cylinder decreases, the surface noise from the turbulence increases, with the maximum noise at a Reynolds number of O (103). An increase in noise with a decrease in radius (Reynolds number) is consistent with experimental results. © 2008 Cambridge University Press.

Description: Accurate numerical computations of the onset of thermal convection in wide rotating spherical shells are presented. Low-Prandtl-number (E) fluids, and non-slip boundary conditions are considered. It is shown that at small Ekman numbers (E), and very low σ values, the well-known equatorially trapped patterns of convection are superseded by multicellular outer-equatorially-attached modes. As a result, the convection spreads to higher latitudes affecting the body of the fluid, and increasing the internal viscous dissipation. Then, from E 〈 10-5, the critical Rayleigh number (Rc) fulfils a power-law dependence Rc ∼ E-4/3, as happens for moderate and high Prandtl numbers. However, the critical precession frequency ( ωc ) and the critical azimuthal wavenumber (mc) increase discontinuously, jumping when there is a change of the radial and latitudinal structure of the preferred eigenfunction. In addition, the transition between spiralling columnar (SC), and outer-equatorially-attached (OEA) modes in the (σ, E)-space is studied. The evolution of the instability mechanisms with the parameters prevents multicellular modes being selected from σ ≳0.023. As a result, and in agreement with other authors, the spiralling columnar patterns of convection are already preferred at the Prandtl number of the liquid metals. It is also found that, out of the rapidly rotating limit, the prograde antisymmetric (with respect to the equator) modes of small mc can be preferred at the onset of the primary instability. © 2008 Cambridge University Press.

Description: The formation of soap films by vertical withdrawal from a bath is typically described by Frankel's law, which assumes rigid film 'walls' and shear-like dynamics. Since most soap films have interfaces that are not rigid, and as the flow in the withdrawal of thin free films is typically extensional, we reconsider the theory of soap film formation. By assuming extensional flow dominated by surface viscous stresses we find that the film thickness scales as the two-thirds power of the withdrawal speed U. This speed dependence is also predicted by Frankel's law; the difference lies in the origin of the viscous resistance which sets the pre-factor. When bulk viscous stresses are important the speed dependence can vary between U2/3 and U2. © 2008 Cambridge University Press.

Description: An experimental investigation of an idealized rapidly sheared granular flow was performed to test the predictions of a model based on the kinetic theory of dry granular media. Glass ballotini beads were placed in an annular shear cell and the lower boundary rotated to induce a shearing motion in the bed. A single particle was tracked using the positron emission particle tracking (PEPT) technique, a method that determines the location of a particle through the triangulation of gamma photons emitted by a radioactive tracer particle. The packing fraction and velocity fields within the three-dimensional flow were measured and compared to the predictions of a model developed using the conservation and balance equations applicable to dissipative systems, and solved incorporating constitutive relations derived from kinetic theory. The comparison showed that kinetic theory is able to capture the general features of a rapid shear flow reasonably well over a wide range of shear rates and confining pressures. © 2008 Cambridge University Press.

Description: A study of streamwise oriented vortical structures embedded in turbulent boundary layers is performed by investigating an experimental database acquired by stereoscopic particle image velocimetry (SPIV) in a plane normal both to the mean flow and the wall. The characteristics of the experimental data allow us to focus on the spatial organization within the logarithmic region for Reynolds numbers Reθ up to 15000. On the basis of the now accepted hairpin model, relationships and interaction between streamwise vortices are first investigated via computation of two-point spatial correlations and the use of linear stochastic estimation (LSE). These analyses confirm that the shape of the most probable coherent structures corresponds to an asymmetric one-legged hairpin vortex. Moreover, two regions of different dynamics can be distinguished: the near-wall region below y+=150, densely populated with strongly interacting vortices; and the region above y+=150 where interactions between eddies happen less frequently. Characteristics of the detected eddies, such as probability density functions of their radius and intensity, are then studied. It appears that Reynolds number as well as wall-normal independences of these quantities are achieved when scaling with the local Kolmogorov scales. The most probable size of the detected vortices is found to be about 10 times the Kolmogorov length scale. These results lead us to revisit the equation for the mean square vorticity fluctuations, and to propose a new balance of this equation in the near-wall region. This analysis and the above results allow us to propose a new description of the near-wall region, leading to a new scaling which seems to have a good universality in the Reynolds-number range investigated. The possibility of reaching a universal scaling at high enough Reynolds number, based on the external velocity and the Kolmogorov length scale is suggested. © 2008 Cambridge University Press.

Description: We examine the natural ventilation flows which develop when a low-level heat source interacts with a distributed zone of cooling at high level in an enclosed space. We develop some new analogue laboratory experiments in which we use a saline plume to model a localized heat source and a heated plate to model a distributed source of cooling. The experiments show that in a building with a low-level point source of heating, a two-layer steady stratification develops in which the depth of the lower layer decreases as the intensity of the cooling at the ceiling increases. We develop a theoretical model which accounts for the penetrative entrainment across the interface associated with the convection in the upper layer. We show that this becomes more dominant as the cooling increases and eventually the room becomes well-mixed. We discuss the role of such distributed cooling on the design of natural ventilation and its ability to provide sufficient flow and adequate temperature control. © 2008 Cambridge University Press.

Description: It is shown that the Euler hydrodynamics for vortical flows of an ideal fluid is equivalent to the equations of motion of a charged compressible fluid moving due to a self-consistent electromagnetic field. The velocity of new auxiliary fluid coincides with the velocity component normal to the vorticity line for the primitive equations. Therefore this new hydrodynamics represents hydrodynamics of vortex lines. Their compressibility reveals a new mechanism for three-dimensional incompressible vortical flows connected with breaking (or overturning) of vortex lines which can be considered as one of the variants of collapses. Transition to the Lagrangian description in the new hydrodynamics corresponds, for the original Euler equations, to a mixed Lagrangian-Eulerian description-the vortex line representation (VLR). The Jacobian of this mapping defines the density of vortex lines. It is shown also that application of VLR to the Navier-Stokes equations results in an equation of diffusive type for the Cauchy invariant. The diffusion tensor for this equation is defined by the VLR metric. © 2008 Cambridge University Press.

Description: Gaseous detonation propagation in a bifurcated tube was experimentally and numerically studied for stoichiometric hydrogen and oxygen mixtures diluted with argon. Pressure detection, smoked foil recording and schlieren visualization were used in the experiments. Numerical simulation was carried out at low initial pressure (8.00 kPa), based on the reactive Navier-Stokes equations in conjunction with a detailed chemical reaction model. The results show that the detonation wave is strongly disturbed by the wall geometry of the bifurcated tube and undergoes a successive process of attenuation, failure, re-initiation and the transition from regular reflection to Mach reflection. Detonation failure is attributed to the rarefaction waves from the left-hand corner by decoupling leading shock and reaction zones. Re-initiation is induced by the inert leading shock reflection on the right-hand wall in the vertical branch. The branched wall geometry has only a local effect on the detonation propagation. In the horizontal branch, the disturbed detonation wave recovers to a self-sustaining one earlier than that in the vertical branch. A critical case was found in the experiments where the disturbed detonation wave can be recovered to be self-sustaining downstream of the horizontal branch, but fails in the vertical branch, as the initial pressure drops to 2.00 kPa. Numerical simulation also shows that complex vortex structures can be observed during detonation diffraction. The reflected shock breaks the vortices into pieces and its interaction with the unreacted recirculation region induces an embedded jet. In the vertical branch, owing to the strength difference at any point and the effect of chemical reactions, the Mach stem cannot be approximated as an arc. This is different from the case in non-reactive steady flow. Generally, numerical simulation qualitatively reproduces detonation attenuation, failure, re-initiation and the transition from regular reflection to Mach reflection observed in experiments. © 2008 Cambridge University Press.

Description: The general equations necessary for a basic theoretical interpretation of the physics of turbulence in ferrofluids are presented. The equations are examined and show multiple novel turbulence aspects that arise in ferrofluids. For example, two new modes of turbulent kinetic energy and turbulent kinetic energy dissipation rate occur, and unique modes of energy conversion (rotational to/from translational kinetic energy and magnetic energy to/from turbulent kinetic energy) are exhibited in turbulent ferrofluid flows. Furthermore, it is shown that potential models for turbulence in ferrofluids are complicated by additional closure requirements from the five additional nonlinear terms in the governing equations. The equations are applied to turbulence of a ferrofluid in the presence of a steady magnetic field (as well as the case of no magnetic field) in order to identify the importance of the new terms. Results are presented for the enhanced anisotropy in the presence of a magnetic field, and results show how turbulence properties (both classical ones and new ones) vary with the strength of the magnetic field. Three different equations for the magnetization are examined and lead to different results at large magnitudes of the applied magnetic field. © 2008 Cambridge University Press.

Description: Temporal and spatio-temporal instabilities of binary liquid films flowing down an inclined uniformly heated plate with Soret effect are investigated by using the Chebyshev collocation method to solve the full system of linear stability equations. Seven dimensionless parameters, i.e. the Kapitza, Galileo, Prandtl, Lewis, Soret, Marangoni, and Biot numbers (Ka, G, Pr, L, χ, M, B), as well as the inclination angle (β) are used to control the flow system. In the case of pure spanwise perturbations, thermocapillary S- and P-modes are obtained. It is found that the most dangerous modes are stationary for positive Soret numbers (χ ≥ 0), and oscillatory for χ 〈 0. Moreover, the P-mode which is short-wave unstable for χ = 0 remains so for χ 〈 0, but becomes long-wave unstable for χ 〉 0 and even merges with the long-wave S-mode. In the case of streamwise perturbations, a long-wave surface mode (H-mode) is also obtained. From the neutral curves, it is found that larger Soret numbers make the film flow more unstable as do larger Marangoni numbers. The increase of these parameters leads to the merging of the long-wave H- and S-modes, making the situation long-wave unstable for any Galileo number. It also strongly influences the short-wave P-mode which becomes the most critical for large enough Galileo numbers. Furthermore, from the boundary curves between absolute and convective instabilities (AI/CI) calculated for both the long-wave instability (S- and H-modes) and the short-wave instability (P-mode), it is shown that for small Galileo numbers the AI/CI boundary curves are determined by the long-wave instability, while for large Galileo numbers they are determined by the short-wave instability. © 2008 Cambridge University Press.

Description: A swimming micro-organism is modelled as a squirming sphere with prescribed tangential surface velocity and referred to as a squirmer. The centre of mass of the sphere may be displaced from the geometric centre, and the effects of inertia and Brownian motion are neglected. The well-known Stokesian dynamics method is modified in order to simulate squirmer motions in a concentrated suspension. The movement of 216 identical squirmers in a concentrated suspension without any imposed flow is simulated in a cubic domain with periodic boundary conditions, and the coherent structures within the suspension are investigated. The results show that (a) a weak aggregation of cells appears as a result of the hydrodynamic interaction between cells; (b) the cells generate collective motions by the hydrodynamic interaction between themselves; and (c) the range and duration of the collective motions depend on the volume fraction and the squirmers' stresslet strengths. These tendencies show good qualitative agreement with previous experiments. © 2008 Cambridge University Press.

Description: An air-water coupled model is developed to investigate wind-wave generation processes at low wind speed where the surface wind stress is about 0.089 dyn cm-2 and the associated surface friction velocities of the air and the water are ua* ∼ 8.6 cm s-1 and uw* ∼ 0.3 cm s-1, respectively. The air-water coupled model satisfies continuity of velocity and stress at the interface simultaneously, and hence can capture the interaction between air and water motions. Our simulations show that the wavelength of the fastest growing waves agrees with laboratory measurements (λ ∼ 8-12 cm) and the wave growth consists of linear and exponential growth stages as suggested by theoretical and experimental studies. Constrained by the linearization of the interfacial boundary conditions, we perform simulations only for a short time period, about 70s; the maximum wave slope of our simulated waves is ak ∼ 0.01 and the associated wave age is c/ua * ∼ 5, which is a slow-moving wave. The effects of waves on turbulence statistics above and below the interface are examined. Sensitivity tests are carried out to investigate the effects of turbulence in the water, surface tension, and the numerical depth of the air domain. The growth rates of the simulated waves are compared to a previous theory for linear growth and to experimental data and previous simulations that used a prescribed wavy surface for exponential growth. In the exponential growth stage, some of the simulated wave growth rates are comparable to previous studies, but some are about 2-3 times larger than previous studies. In the linear growth stage, the simulated wave growth rates for these four simulation runs are about 1-2 times larger than previously predicted. In qualitative agreement with previous theories for slow-moving waves, the mechanisms for the energy transfer from wind to waves in our simulations are mainly from turbulence-induced pressure fluctuations in the linear growth stage and due to the in-phase relationship between wave slope and wave-induced pressure fluctuations in the exponential growth stage. © 2008 Cambridge University Press.

Description: The effect of confining a gas bubble between two parallel walls was investigated for the inertia-dominated regime characterized by high Reynolds and low Weber numbers. Single bubble experiments were performed with non-polar liquids such that the bubble surface could be considered clean; hence, shear free. The drag coefficient was found to be the result of two main effects: the Reynolds number and the confinement. The total drag could be written as the product of the corresponding unconfined drag, which depended mainly on the Reynolds number, and a function F(s) = 1 + κs3. The confinement parameter s was defined as the ratio of the bubble radius to the gap width. The value of the constant κ depended on the way in which the bubbles moved within the gap, which was found to be either in a rectilinear (κ ≈ 8) or oscillatory trajectory (κ ≈ 80). For Re 〈 70, and a range of values of the confinement parameter, the bubbles followed a rectilinear path. For this regime, numerical simulations were performed to obtain the drag force on the bubble directly; a reasonable agreement was found with experiments. Moreover, a comparison of these results with a potential-flow-based model indicated that the vorticity produced at the walls induced a significant part of the drag. For Re 〉 70, oscillations were observed in the bubble trajectory. In all cases, the oscillation occurred in a zigzag manner. Near the transition the bubbles oscillated but did not reach the walls; for larger Reynolds numbers, the bubbles collided repeatedly with the walls as they ascended. The instability, which is different from the well-known unconfined path instability, resulted from the reversal of sign of the wall-induced lift force: for low Reynolds number, the walls have a stabilizing effect because of the repulsive nature of the lift force between the walls and the bubble, while for high Reynolds number the lift is attractive and trajectories become unstable. Considering a model for the lift force of a bubble moving near a wall, the conditions for the transition were identified. A reasonable agreement between the model and experiments was found. © 2008 Cambridge University Press.

Description: A steady theory is presented for gravity currents propagating with constant speed into a stratified fluid with a general density profile. Solution curves for front speed versus height have an energy-conserving upper bound (the conjugate state) and a lower bound marked by the onset of upstream influence. The conjugate state is the largest-amplitude nonlinear internal wave supported by the ambient stratification, and in the limit of weak stratification approaches Benjamin's energy-conserving gravity current solution. When the front speed becomes critical with respect to linear long waves generated above the current, steady solutions cannot be calculated, implying upstream influence. For non-uniform stratification, the critical long-wave speed exceeds the ambient long-wave speed, and the critical-Froude-number condition appropriate for uniform stratification must be generalized. The theoretical results demonstrate a clear connection between internal waves and gravity currents. The steady theory is also compared with non-hydrostatic numerical solutions of the full lock release initial-value problem. Some solutions resemble classic gravity currents with no upstream disturbance, but others show long internal waves propagating ahead of the gravity current. Wave generation generally occurs when the stratification and current speed are such that the steady gravity current theory fails. Thus the steady theory is consistent with the occurrence of either wave-generating or steady gravity solutions to the dam-break problem. When the available potential energy of the dam is large enough, the numerical simulations approach the energy-conserving conjugate state. Existing laboratory experiments for intrusions and gravity currents produced by full-depth lock exchange flows over a range of stratification profiles show excellent agreement with the conjugate state solutions. © 2008 Cambridge University Press.

Description: Steady inlet flow through a circular tube with an axisymmetric blockage of varying size is studied both numerically and experimentally. The geometry consists of a long, straight tube and a blockage, semicircular in cross-section, serving as a simplified model of an arterial stenosis. The stenosis is characterized by a single parameter, the aim being to highlight fundamental behaviours of constricted flows, in terms of the total blockage. The Reynolds number is varied between 50 and 2500 and the stenosis degree by area between 0.20 and 0.95. Numerically, a spectral-element code is used to obtain the axisymmetric base flow fields, while experimentally, results are obtained for a similar set of geometries, using water as the working fluid. At low Reynolds numbers, the flow is steady and characterized by a jet flow emanating from the contraction, surrounded by an axisymmetric recirculation zone. The effect of a variation in blockage size on the onset and mode of instability is investigated. Linear stability analysis is performed on the simulated axisymmetric base flows, in addition to an analysis of the instability, seemingly convective in nature, observed in the experimental flows. This transition at higher Reynolds numbers to a time-dependent state, characterized by unsteadiness downstream of the blockage, is studied in conjunction with an investigation of the response of steady lower Reynolds number flows to periodic forcing. © 2008 Cambridge University Press.

Description: A general theoretical formalism is developed to assess how base-flow modifications may alter the stability properties of flows studied in a global approach of linear stability theory. It also comprises a systematic approach to the passive control of globally unstable flows by the use of small control devices. This formalism is based on a sensitivity analysis of any global eigenvalue to base-flow modifications. The base-flow modifications investigated are either arbitrary or specific ones induced by a steady force. This leads to a definition of the so-called sensitivity to base-flow modifications and sensitivity to a steady force. These sensitivity analyses are applied to the unstable global modes responsible for the onset of vortex shedding in the wake of a cylinder for Reynolds numbers in the range 47 ≤ Re ≤ 80. First, it is demonstrated how the sensitivity to arbitrary base-flow modifications may be used to identify regions and properties of the base flow that contribute to the onset of vortex shedding. Secondly, the sensitivity to a steady force determines the regions of the flow where a steady force acting on the base flow stabilizes the unstable global modes. Upon modelling the presence of a control device by a steady force acting on the base flow, these predictions are then extensively compared with the experimental results of Strykowski & Sreenivasan (J. Fluid Mech., vol. 218, 1990, p. 71). A physical interpretation of the suppression of vortex shedding by use of a control cylinder is proposed in the light of the sensitivity analysis. © 2008 Cambridge University Press.

Description: The primary objective of this investigation is to determine experimentally the sources of jet mixing noise. In the present study, four different approaches are used. It is reasonable to assume that the characteristics of the noise sources are imprinted on their radiation fields. Under this assumption, it becomes possible to analyse the characteristics of the far-field sound and then infer back to the characteristics of the sources. The first approach is to make use of the spectral and directional information measured by a single microphone in the far field. A detailed analysis of a large collection of far-field noise data has been carried out. The purpose is to identify special characteristics that can be linked directly to those of the sources. The second approach is to measure the coherence of the sound field using two microphones. The autocorrelations and cross-correlations of these measurements offer not only valuable information on the spatial structure of the noise field in the radial and polar angle directions, but also on the sources inside the jet. The third approach involves measuring the correlation between turbulence fluctuations inside a jet and the radiated noise in the far field. This is the most direct and unambiguous way of identifying the sources of jet noise. In the fourth approach, a mirror microphone is used to measure the noise source distribution along the lengths of high-speed jets. Features and trends observed in noise source strength distributions are expected to shed light on the source mechanisms. It will be shown that all four types of data indicate clearly the existence of two distinct noise sources in jets. One source of noise is the fine-scale turbulence and the other source is the large turbulence structures of the jet flow. Some of the salient features of the sound field associated with the two noise sources are reported in this paper. © 2008 Cambridge University Press.

Description: To understand the fluid dynamics of a biologically inspired unsteady low-aspect-ratio propulsor, unsteady pressure distributions were measured and compared with time-averaged thrust performance and wake visualizations. The experiments were performed on rigid rectangular panels with different aspect ratios, pitching in a uniform flow. Panel aspect ratio and pitching amplitude were shown to affect the magnitude and time dependence of the pressure distribution on the panel surface, the vorticity generation on the panel, and thrust production. A new scaling is proposed that includes these parameters and collapses the oscillating pressure magnitude and the thrust coefficient. © 2008 Cambridge University Press.

Description: The results of an experimental investigation to determine the influence of two physiologically relevant inlet conditions on the flow physics downstream of an idealized stenosis are presented. The two inlet conditions are an asymmetric mean inlet velocity profile and an asymmetric mean inlet velocity profile plus secondary flow, as found downstream of a bend. The stenosis is modelled as an axisymmetric 75% area reduction occlusion with a length-to-diameter ratio of 2. The flow was forced by a 10-harmonic carotid artery-inspired waveform with mean, maximum and minimum Reynolds numbers of 364, 1424 and 24, respectively, and a Womersley number of 4.6. Laser Doppler velocimetry and particle image velocimetry were used to characterize the spatial and temporal evolution of a baseline case (no disturbances) as well as the two physiologically relevant inlet conditions. The asymmetric inlet velocity profile was found to reduce the region of influence of the stenosis by forcing the stenotic jet towards the tube wall via an induced non-uniform radial pressure gradient, similar to the Coanda effect. Curvature-induced secondary flow was found to play a minor role in the near-stenosis region. Vortex ring formation was relatively unaffected by the mean velocity gradient and secondary flow. Evidence of remnants of the starting vortex ring was observed far downstream in all cases. © 2008 Cambridge University Press.

Description: The linear stability analysis of an uniform shear flow of granular materials is revisited using several cases of a Navier-Stokes-level constitutive model in which we incorporate the global equation of states for pressure and thermal conductivity (which are accurate up to the maximum packing density νm) and the shear viscosity is allowed to diverge at a density νm (〈νm), with all other transport coefficients diverging at νm. It is shown that the emergence of shear-banding instabilities (for perturbations having no variation along the streamwise direction), that lead to shear-band formation along the gradient direction, depends crucially on the choice of the constitutive model. In the framework of a dense constitutive model that incorporates only collisional transport mechanism, it is shown that an accurate global equation of state for pressure or a viscosity divergence at a lower density or a stronger viscosity divergence (with other transport coefficients being given by respective Enskog values that diverge at νm) can induce shear-banding instabilities, even though the original dense Enskog model is stable to such shear-banding instabilities. For any constitutive model, the onset of this shear-banding instability is tied to a universal criterion in terms of constitutive relations for viscosity and pressure, and the sheared granular flow evolves toward a state of lower 'dynamic' friction, leading to the shear-induced band formation, as it cannot sustain increasing dynamic friction with increasing density to stay in the homogeneous state. A similar criterion of a lower viscosity or a lower viscous-dissipation is responsible for the shear-banding state in many complex fluids. © 2008 Cambridge University Press.

Description: Complementary low-dimensional techniques are modified to estimate the most energetic turbulent features of a Mach 0.85 axisymmetric jet in the flow's near-field regions via spectral linear stochastic estimation. This model estimate is three-dimensional, comprises all three components of the velocity field and is time resolved. The technique employs the pressure field as the unconditional input, measured within the hydrodynamic periphery of the jet flow where signatures (pressure) are known to comprise a reasonable footprint of the turbulent large-scale structure. Spectral estimation coefficients are derived from the joint second-order statistics between coefficients that are representative of the low-order pressure field (Fourier-azimuthal decomposition) and of the low-order velocity field (proper orthogonal decomposition). A bursting-like event is observed in the low-dimensional estimate and is similar to what was found in the low-speed jet studies of others. A number of low-dimensional estimates are created using different velocity-pressure mode combinations from which predictions of the far-field acoustics are invoked using Lighthill's analogy. The overall sound pressure level (OASPL) directivity is determined from the far-field prediction, which comprises qualitatively similar trends when compared to direct measurements at r/D=75. Retarded time topologies of the predicted field at 90° and 30° are also shown to manifest, respectively, high- and low-frequency wave-like motions when using a combination of only the low-order velocity modes (m=0, 1, 2). This work thus constitutes a first step in developing low-dimensional and dynamical system models from hydrodynamic pressure signatures for estimating and predicting the behaviour of the energy-containing events that govern many of the physical constituents of turbulent flows. © 2008 Cambridge University Press.

Description: When surface wetting drives liquids to invade porous media or microstructured materials with uniform channels, the penetration distance is known to increase as the square root of time. We demonstrate, experimentally and theoretically, that shape variations of the channel, in the flow direction, modify this 'diffusive' response. At short times, the shape variations are not significant and the imbibition is still diffusive. However, at long times, different power-law responses occur, and their exponents are uniquely connected to the details of the geometry. Experiments performed with conical tubes clearly show the two theoretical limits. Several extensions of these ideas are described. © 2008 Cambridge University Press.

Description: The linear stability of an erodible sediment bed beneath a turbidity current is analysed, in order to identify potential mechanisms responsible for the formation of longitudinal gullies and channels. On the basis of the three-dimensional Navier-Stokes equations, the stability analysis accounts for the coupled interaction of the three-dimensional fluid and particle motion inside the current with the erodible bed below it. For instability to occur, the suspended sediment concentration of the base flow needs to decay away from the sediment bed more slowly than does the shear stress inside the current. Under such conditions, an upward protrusion of the sediment bed will find itself in an environment where erosion decays more quickly than sedimentation, and so it will keep increasing. Conversely, a local valley in the sediment bed will see erosion increase more strongly than sedimentation, which again will amplify the initial perturbation. The destabilizing effect of the base flow is modulated by the stabilizing perturbation of the suspended sediment concentration and by the shear stress due to a secondary flow structure in the form of counter-rotating streamwise vortices. These streamwise vortices are stabilizing for small Reynolds and Péclet numbers and destabilizing for large values. For a representative current height of O (10-100 m), the linear stability analysis provides the most amplified wavelength in the range of 250-2500 m, which is consistent with field observations reported in the literature. In contrast to previous analyses based on depth-averaged equations, the instability mechanism identified here does not require any assumptions about sub- or supercritical flow, nor does it require the presence of a slope or a slope break. © 2008 Cambridge University Press.

Description: The interaction between two localized disturbances is analysed in a subcritical channel flow through direct numerical simulations. The initial perturbations are in the form of two pairs of counter-rotating vortices. One of them interacts with the wall-normal vorticity layers set up near the wall, by locally compressing or stretching part of them through the straining motion it induces. The breakdown of spanwise symmetry leads to the rapid development of a new wall-normal vorticity patch that is tilted by the shear and rolls up into a new small-scale streamwise vortex. The process results in a localized turbulent spot at later stages of development. A detailed analysis is carried out to determine the role of different parameters entering the physics of the mechanism. Several critical thresholds that trigger the interactive bypass transition process are found and analysed. The similarity parameters resulting from the parametric investigation coincide well with those governing the self-sustaining Reynolds-shear-stress-producing eddies in the buffer layer of a fully developed turbulent wall flow. It is suggested that the mechanism we propose may play a role in the regeneration cycle of the near-wall turbulence-generating structures by bypassing the three-dimensional streak instability mechanism. © 2008 Cambridge University Press.

Description: The boundary layer generated by the propagation of a solitary wave is investigated by means of direct numerical simulations of continuity and Navier-Stokes equations. The obtained results show that, for small wave amplitudes, the flow regime is laminar. Turbulence appears when the wave amplitude becomes larger than a critical value which depends on the ratio between the boundary-layer thickness and the water depth. Moreover, turbulence is generated only during the decelerating phase, or conversely, turbulence is present only behind the wave crest. Even though the horizontal velocity component far from the bed always moves in the direction of wave propagation, the fluid particle velocity near the bottom reverses direction as the irrotational velocity decelerates. The strength and length of time of flow reversal are affected by turbulence appearance. Also the bed shear stress feels the effects of turbulence presence. © 2008 Cambridge University Press.

Description: The lattice Boltzmann method was applied to simulate the free rise of monodisperse non-coalescing spherical bubbles in slightly inclined channels bound by solid walls. The Reynolds number based on the relative velocity between the bubbles and the fluid ranged from 4 to 16, the volume fraction from 5% to 10% and the inclination angle from 2° to 6°. The simulations revealed that the weak buoyancy component normal to the walls led to a layer of bubbles near the upper wall and a depleted layer near the bottom wall. These thin layers drove a nearly viscometric shear flow within the bulk of the channel that allowed an unambiguous determination of the lift force in a sheared homogeneous and freely evolving bubble suspension. The lift force coefficients calculated from our simulations were always higher than those for isolated spherical bubbles, suggesting that the lift force is enhanced by hydrodynamic interactions among the bubbles. Experimental measurements of the velocity gradient in 10% volume fraction bubble suspensions in glycerine-water-electrolyte mixtures in slightly inclined channels yielded lift coefficients in excess of those predicted for isolated bubbles and confirmed the qualitative predictions of the simulations. © 2008 Cambridge University Press.

Description: We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor-Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail. © 2008 Cambridge University Press.

Description: Experiments were done on sink flow turbulent boundary layers over a wide range of streamwise pressure gradients in order to investigate the effects on the mean velocity profiles. Measurements revealed the existence of non-universal logarithmic laws, in both inner and defect coordinates, even when the mean velocity descriptions departed strongly from the universal logarithmic law (with universal values of the Kármán constant and the inner law intercept). Systematic dependences of slope and intercepts for inner and outer logarithmic laws on the strength of the pressure gradient were observed. A theory based on the method of matched asymptotic expansions was developed in order to explain the experimentally observed variations of log-law constants with the non-dimensional pressure gradient parameter (Δp = (ν/ρUτ3)dp/dx). Towards this end, the system of partial differential equations governing the mean flow was reduced to inner and outer ordinary differential equations in self-preserving form, valid for sink flow conditions. Asymptotic matching of the inner and outer mean velocity expansions, extended to higher orders, clearly revealed the dependence of slope and intercepts on pressure gradient in the logarithmic laws. © 2008 Cambridge University Press.

Description: The theory of two-layer hydraulics is extended to topography with co-varying width and height. When these variations of the non-dimensional width and total depth have a power law relationship, the solutions can still be presented in the Froude-number plane for both unidirectional and exchange flows. These differ from previous solutions, which were limited to treating width and height variations separately. © 2008 Cambridge University Press.

Description: Two-point hot-wire measurements of streamwise velocity were performed in the logarithmic and wake regions of turbulent pipe flow for Reynolds numbers, based on pipe diameter, ranging from 7.6 × 104 to 8.3 × 106 at four wall-normal positions with azimuthal probe separation. The azimuthal correlations were found to be consistent with the presence of very large-scale coherent regions of low-wavenumber, low-momentum fluid observed in previous studies of wall-bounded flows and were found to be independent of changing Reynolds number and surface roughness effects. At the edge of the logarithmic layer the azimuthal scale determined from the correlations was found to be similar to that observed for channel flows but larger than that observed for boundary layers, inconsistent with the concept of a universal logarithmic region. As the wall-normal position increased outside the logarithmic layer, there was a decrease in azimuthal scale relative to that of channel flow. Using cross-spectral analysis, high-wavenumber motion was found to grow azimuthally with wall-normal distance at a faster rate than the low-wavenumber motions. © 2008 Cambridge University Press.

Description: Periodic linear waves in a vertically sheared flow are considered in a continuously stratified layer of rotating fluid between homogeneous layers along a sloping bottom. This generalized Phillips' configuration has cyclonic horizontal shear and supports the Rossby modes related to the thickness variations of the homogeneous layers and inertia-gravity waves (IGW). While long Rossby modes with streamwise wavenumber κ 〈 f/V (f is the Coriolis parameter, V is the maximum velocity) can be approximated by a neutral balanced solution, short waves with κ 〉 f/V are found to have an inertial critical level and unbalanced gravity-wave-like structure beyond this level. Such ageostrophic unstable normal modes are shown explicitly to couple short Rossby waves with Doppler-shifted gravity waves. They exist even for small Froude number, although the growth rate of ageostrophic unstable modes is exponentially small in Froude number as in the Eady model. This lack of balance in continuously stratified flows agrees with the ultraviolet problem for Ripa's sufficient conditions of stability in a multi-layer model when the number of layers tends to infinity. © 2008 Cambridge University Press.

Description: The steady propagation of an air finger into a fluid-filled tube of uniform rectangular cross-section is investigated. This paper is primarily focused on the influence of the aspect ratio, α, on the flow properties, but the effects of a transverse gravitational field are also considered. The three-dimensional interfacial problem is solved numerically using the object-oriented multi-physics finite-element library oomph-lib and the results agree with our previous experimental results (de Lózar et al. Phys. Rev. Lett. vol. 99, 2007, article 234501) to within the ±1% experimental error. At a fixed capillary number Ca (ratio of viscous to surface-tension forces) the pressure drops across the finger tip and relative finger widths decrease with increasing α. The dependence of the wet fraction m (the relative quantity of liquid that remains on the tube walls after the propagation of the finger) is more complicated: m decreases with increasing α for low Ca but it increases with α at high Ca. Our results also indicate that the system is approximately quasi-two-dimensional for α ≥ 8, when we obtain quantitative agreement with McLean & Saffman's two-dimensional model for the relative finger width as a function of the governing parameter 1/ B = 12α2Ca. The action of gravity causes an increase in the pressure drops, finger widths and wet fractions at fixed capillary number. In particular, when the Bond number (ratio of gravitational to surface-tension forces) is greater than one the finger lifts off the bottom wall of the tube leading to dramatic increases in the finger width and wet fraction at a given Ca. For α 〉 3 a previously unobserved flow regime has been identified in which a small recirculation flow is situated in front of the finger tip, shielding it from any contaminants in the flow. In addition, for α ≳ 2 the capillary number, Cac, above which global recirculation flows disappear has been observed to follow the simple empirical law: Cac2/3α = 1.21. © 2008 Cambridge University Press.

Description: This paper examines the evolution of a two-dimensional vortex which initially consists of an axisymmetric monopole vortex with a perturbation of azimuthal wavenumber m = 2 added to it. If the perturbation is weak, then the vortex returns to an axisymmetric state and the non-zero Fourier harmonics generated by the perturbation decay to zero. However, if a finite perturbation threshold is exceeded, then a persistent nonlinear vortex structure is formed. This structure consists of a coherent vortex core with two satellites rotating around it. The paper considers the formation of these satellites by taking an asymptotic limit in which a compact vortex is surrounded by a weak skirt of vorticity. The resulting equations match the behaviour of a normal mode riding on the vortex with the evolution of fine-scale vorticity in a critical layer inside the skirt. Three estimates of inviscid thresholds for the formation of satellites are computed and compared: two estimates use qualitative diagnostics, the appearance of an inflection point or neutral mode in the mean profile. The other is determined quantitatively by solving the normal mode/critical-layer equations numerically. These calculations are supported by simulations of the full Navier-Stokes equations using a family of profiles based on the tanh function. © 2008 Cambridge University Press.

Description: Laminar-to-turbulent transition of pipe flows occurs, for sufficiently high Reynolds numbers, in the form of slugs. These are initiated by disturbances in the entrance region of a pipe flow, and grow in length in the axial direction as they move downstream. Sequences of slugs merge at some distance from the pipe inlet to finally form the state of fully developed turbulent pipe flow. This formation process is generally known, but the randomness in time of naturally occurring slug formation does not permit detailed study of slug flows. For this reason, a special test facility was developed and built for detailed investigation of deterministically generated slugs in pipe flows. It is also employed to generate the puff flows at lower Reynolds numbers. The results reveal a high degree of reproducibility with which the triggering device is able to produce puffs. With increasing Reynolds number, 'puff splitting' is observed and the split puffs develop into slugs. Thereafter, the laminar-to-turbulent transition occurs in the same way as found for slug flows. The ring-type obstacle height, h, required to trigger fully developed laminar flows to form first slugs or puffs is determined to show its dependence on the Reynolds number, Re = DU/ν (where D is the pipe diameter, U is the mean velocity in the axial direction and ν is the kinematic viscosity of the fluid). When correctly normalized, h+ turns out to be independent of Reτ (where h+ = hUτ/ν, Reτ = DUτ/ν and Uτ = √τwρ; τw is the wall shear stress and ρ is the density of the fluid). © 2008 Cambridge University Press.

Description: A large-eddy-based methodology for the simulation of turbulent sprays is discussed. The transport equations for the spatially filtered gas phase variables, in which source terms accounting for the droplet effects are added, are solved together with a probabilistic description of the liquid phase. The probabilistic approach for the liquid phase is based on the transport equation for the spatially filtered joint probability density function of the variables required in order to describe the state of the liquid phase. In this equation, unclosed terms representing the filtered Lagrangian rates of change of the variables describing the spray are present. General modelling ideas for subgrid-scale (SGS) effects are proposed. The capabilities of the approach and the validity of the closure models, with particular with respect to the SGS dispersion, are investigated through application to a dilute particle-laden turbulent mixing layer. It is demonstrated that the formulation is able to reproduce very closely the measured properties of both the continuous and dispersed phases. The large-eddy simulation (LES) results are also found to be entirely consistent with the experimentally observed characteristics of droplet-gas turbulence interactions. Consistent with direct numerical simulation (DNS) studies of isotropic turbulence laden with particles where the entire turbulence spectrum is found to be modulated by the presence of particles, the present investigation, which comprises the effects of particle transport upon the large-scale vortical structures of a turbulent shear flow, highlights what appears to be a selective behaviour; few large-scale frequencies gain energy whereas the remaining modes are damped. © 2008 Cambridge University Press.

Description: This theoretical investigation of steady fluid flow through a rigid three-dimensional branching geometry is motivated by applications to haemodynamics in the brain especially, while the flow through a tube with a blockage or through a collapsed tube provides another motivation with a biomedical background. Three-dimensional motion without symmetry is addressed through one mother vessel to two or several daughters. A comparatively long axial length scale of the geometry leads to a longitudinal vortex system providing a slender-flow model for the complete mother-and-daughters flow response. Computational studies and subsequent analysis, along with comparisons, are presented. The relative flow rate varies in terms of an effective Reynolds number dependence, allowing a wide range of flow rates to be examined theoretically; also any rigid cross-sectional shape and ratio of cross-sectional area expansion or contraction from the mother vessel to the daughters can be accommodated in principle in both the computations and the analysis. Swirl production with substantial crossflows is found. The analysis shows that close to any carina (the ridge separating daughter vessels) or carinas at a branch junction either forward or reversed motion can be observed locally at the saddle point even though the bulk of the motion is driven forward into the daughters. The local forward or reversed motion is controlled, however, by global properties of the geometry and incident conditions, a feature which applies to any of the flow rates examined. © 2008 Cambridge University Press.

Description: Internal (gravity) wave attractors may form in closed containers with boundaries non-parallel and non-normal to the gravity vector. Such attractors have been studied from a theoretical point of view, in laboratory experiments and using linear numerical computations. In the present paper two-dimensional numerical simulations of an internal wave attractor are reported, based upon the nonlinear and non-hydrostatic MIT-gcm numerical code. We first reproduce the laboratory experiment of a wave attractor performed by Hazewinkel et al. (J. Fluid Mech. Vol. 598, 2008 p. 373) and obtain very good agreement with the experimental data. We next propose simple ideas to model the thickness of the attractor. The model predicts that the thickness should scale as the 1/3 power of the non-dimensional parameter measuring the ratio of viscous to buoyancy effects. When the attractor is strongly focusing, the thickness should also scale as the 1/3 power of the spatial coordinate along the attractor. Analysis of the numerical data for two different attractors yields values of the exponent close to 1/3, within 30%. Finally, we study nonlinear effects induced by the attractor. © 2008 Cambridge University Press.

Description: The concept of piecewise constant symmetric vortex in the context of three-dimensional baroclinic balanced geophysical flows is explored. The pressure gradients generated by horizontal cylinders and spherical balls of uniform potential vorticity (PV), or uniform material invariants, are obtained either analytically or numerically, in the general case of Boussinesq and f-plane dynamics as well as under the quasi-geostrophic and semigeostrophic dynamical approximations. Based on the order of magnitude of the different terms in the PV inversion equation, approximated PV equations are deduced. In some of these cases, radial solutions are possible and the interior and exterior solutions are found analytically. In the case of non-radial dependence, exterior solutions can be found numerically. Linear, and upper and lower bound approximations to the full PV inversion equations, and their respective solutions, are also included. However, the general solution for the pressure gradient in the vortex exterior does not have spherical symmetry and remains as an important theoretical challenge. It is suggested that, in order to maintain everywhere the inertial and static stability of the balanced geophysical flows, small balls of finite radius, rather than PV singularities, could become, specially in numerical applications, useful mathematical objects. © 2008 Cambridge University Press.

Description: We investigate the transient ventilation flow within a confined ventilated space, with high- and low-level openings, when the strength of a low-level point source of heat is changed instantaneously. The steady-flow regime in the space involves a turbulent buoyant plume, which rises from the point source to a well-mixed warm upper layer. The steady-state height of the interface between this layer and the lower layer of exterior fluid is independent of the heat flux, but the upper layer becomes progressively warmer with heat flux. New analogue laboratory experiments of the transient adjustment between steady states identify that if the heat flux is increased, the continuing plume propagates to the top of the room forming a new, warmer layer. This layer gradually deepens, and as the turbulent plume entrains fluid from the original warm layer, the original layer is gradually depleted and disappears, and a new steady state is established. In contrast, if the source buoyancy flux is decreased, the continuing plume is cooler than the original plume, so that on reaching the interface it is of intermediate density between the original warm layer and the external fluid. The plume supplies a new intermediate layer, which gradually deepens with the continuing flow. In turn, the original upper layer becomes depleted, both as a result of being vented through the upper opening of the space, but also due to some penetrative entrainment of this layer by the plume, as the plume overshoots the interface before falling back to supply the new intermediate layer. We develop quantitative models which are in good accord with our experimental data, by combining classical plume theory with models of the penetrative entrainment for the case of a decrease in heating. Typically, we find that the effect of penetrative entrainment on the density of the intruding layer is relatively weak, provided the change in source strength is sufficiently large. However, penetrative entrainment measurably increases the rate at which the depth of the draining layer decreases. We conclude with a discussion of the importance of these results for the control of naturally ventilated spaces. © 2008 Cambridge University Press.

Description: Spatial evolution of small perturbations introduced into an inlet cross-section of fully developed turbulent flow in a long straight circular pipe is investigated via direct numerical simulation (DNS). The turbulent inflow field is extracted from an auxiliary streamwise-periodic simulation running in parallel with the main spatial simulation. It is shown that mean perturbation amplitude ε̄ increases exponentially with distance downstream. The growth rate is found to be constant when normalized by viscous length, ε̄ ∼ exp(0.0021x+) over the considered Reynolds-number range 140 ≤ Reτ ≤ 320. The universal character of perturbation growth is confirmed by channel-flow simulations. © 2008 Cambridge University Press.

Description: In this paper we investigate salt transport during the evaporation and upflow of saline groundwater. We describe a model in which a sharp evaporation - precipitation front separates regions of soil saturated with an air - vapour mixture and with saline water. We then consider two idealized problems. We first investigate equilibrium configurations of the freshwater system when the depth of the soil layer is finite, obtaining results for the location of the front and the upflow of water induced by the evaporation. We then develop a solution for a propagating front in a soil layer of infinite depth and investigate the gravitational stability of the salinity profile which develops below the front, obtaining marginal linear stability conditions in terms of a Rayleigh number and a dimensionless salt saturation parameter. Applying our findings to realistic parameter regimes, we predict that salt fingering is unlikely to occur in low-permeability soils, but is likely in high-permeability (sandy) soils under conditions of relatively low evaporative upflow. © 2008 Cambridge University Press.

Description: This paper is concerned with the nonlinear instability of compressible mixing layers in the regime of small to moderate values of Mach number M, in which subsonic modes play a dominant role. At high Reynolds numbers of practical interest, previous studies have shown that the dominant nonlinear effect controlling the evolution of an instability wave comes from the so-called critical layer. In the incompressible limit (M = 0), the critical-layer dynamics are strongly nonlinear, with the nonlinearity being associated with the logarithmic singularity of the velocity fluctuation (Goldstein & Leib, J. Fluid Mech. vol. 191, 1988, p. 481). In contrast, in the fully compressible regime (M = O (1)), nonlinearity is associated with a simple-pole singularity in the temperature fluctuation and enters in a weakly nonlinear fashion (Goldstein & Leib, J. Fluid Mech. vol. 207, 1989, p. 73). In this paper, we first consider a weakly compressible regime, corresponding to the distinguished scaling M = O (∈1/4), for which the strongly nonlinear structure persists but is affected by compressibility at leading order (where ∈ 〈 1 measures the magnitude of the instability mode). A strongly nonlinear system governing the development of the vorticity and temperature perturbation is derived. It is further noted that the strength of the pole singularity is controlled by Tc′, the mean temperature gradient at the critical level, and for typical base-flow profiles Tc′ is small even when M = O (1). By treating Tc′ as an independent parameter of O (∈1/2), we construct a composite strongly nonlinear theory, from which the weakly nonlinear result for M = O (1) can be derived as an appropriate limiting case. Thus the strongly nonlinear formulation is uniformly valid for O (1) Mach numbers. Numerical solutions show that this theory captures the vortex roll-up process, which remains the most prominent feature of compressible mixing-layer transition. The theory offers an effective tool for investigating the nonlinear instability of mixing layers at high Reynolds numbers. © 2008 Cambridge University Press.

Description: Taylor's hypothesis of frozen flow has frequently been used to convert temporal experimental measurements into a spatial domain. This technique has led to the discovery of long meandering structures in the log-region of a turbulent boundary layer. There is some contention over whether Taylor's approximation is valid over large distances. This paper presents an experiment that compares velocity fields constructed using Taylor's approximation with those obtained from particle image velocimetry (PIV), i.e. spatial data, obtained in the logarithmic region of a turbulent boundary layer. © 2008 Cambridge University Press.

Description: The connection between fluid flow and optical flow is explored in typical flow visualizations to provide a rational foundation for application of the optical flow method to image-based fluid velocity measurements. The projected-motion equations are derived, and the physics-based optical flow equation is given. In general, the optical flow is proportional to the path-averaged velocity of fluid or particles weighted with a relevant field quantity. The variational formulation and the corresponding Euler - Lagrange equation are given for optical flow computation. An error analysis for optical flow computation is provided, which is quantitatively examined by simulations on synthetic grid images. Direct comparisons between the optical flow method and the correlation-based method are made in simulations on synthetic particle images and experiments in a strongly excited turbulent jet. © 2008 Cambridge University Press.

Description: Most rational asymptotic studies of non-rotating Rayleigh-Bénard convection and its cousins have been restricted to the linear or weakly nonlinear regime. An important exception occurs for large Rayleigh-number thermal convection at effectively infinite Prandtl number, i.e. fast but very viscous convection. In this scenario, the temperature field exhibits a layer-like structure surrounding an isothermal core and, crucially, the momentum equation linearizes. These features have been exploited by several authors to obtain semi-analytical nonlinear solutions. At O (1) Prandtl number, the fluid dynamics in the vortex core is dominated by nonlinear inertial rather than linear viscous effects, substantially altering the vortex structure. Here, it is shown that a combination of matched asymptotic analysis and global conservation constraints can be used to obtain a semi-analytic yet strongly nonlinear description of two related flows: (i) Rayleigh-Bénard convection between constant heat-flux boundaries at unit Prandtl number, and (ii) Langmuir circulation (LC), a wind and wave-driven convective flow commonly observed in natural water bodies. A simple analytical prediction is given for the roll-vortex amplitude, which is shown to be independent of the horizontal wavenumber of the convection pattern. In marked contrast to weakly nonlinear convection cells, the fully nonlinear asymptotic solutions exhibit flow features relevant to turbulent convection including the complete vertical redistribution of the basic-state temperature (or, for LC, downwind velocity) field. Comparisons with well-resolved pseudospectral numerical simulations of the full two-dimensional governing equations confirm the accuracy of the asymptotic results. © 2008 Cambridge University Press.

Description: We present experiments showing vertical jetting from the apex of a viscous drop which impacts onto a pool of lower viscosity liquid. This jet is produced by the ejecta sheet which emerges from the free surface of the pool, and moves up and wraps around the surface of the drop. When this sheet of liquid converges and collides at the top apex of the drop it produces a thin upward jet at velocities of more than 10 times the drop impact velocity. This jetting occurs for a limited range of impact conditions, where the ejecta speed is sufficient for the sheet to travel around the entire drop periphery, but not so fast that it separates from the drop surface. The lower bound for the jetting region is thereby set by a minimal Reynolds number, but the upper bounds are subject to a maximum-Weber-number criterion. The strongest observed jets appear for viscous drops impacting onto liquid pools with the lowest viscosity as well as lowest surface tension, such as acetone and methanol. Jetting has also been observed for drops which are immiscible with the pool liquid, under a different range of impact conditions. However, jetting is never observed for pools of water, as the surface tension is then significantly larger than that of the drop. We believe that Marangoni stresses act in this case to promote separation of the sheet to prevent the jetting. A movie is available with the online version of the paper. © 2008 Cambridge University Press.

Description: Liquid-liquid wetting failure is investigated in a two-dimensional Couette system with two immiscible fluids of arbitrary viscosity. The problem is solved exactly using a sharp interface treatment of hydrodynamics (lubrication theory) as a function of the control parameters - capillary number, viscosity ratio and separation of scale - i.e. the slip length versus the macroscopic size of the system. The transition at a critical capillary number, from a stationary to a non-stationary interface, is studied while changing the control parameters. Comparisons with similar existing analyses for other geometries, such as the Landau-Levich problem, are also carried out. A numerical method of analysis is also presented, based on diffuse interface models obtained from multiphase extensions of the lattice Boltzmann equation. Sharp interface and diffuse interface models are quantitatively compared, indicating the correct limit of applicability of the diffuse interface models. © 2008 Cambridge University Press.

Description: To investigate the phenomena of skin-friction drag reduction in a turbulent boundary layer (TBL) at large scales and high Reynolds numbers, a set of experiments has been conducted at the US Navy's William B. Morgan Large Cavitation Channel (LCC). Drag reduction was achieved by injecting gas (air) from a line source through the wall of a nearly zero-pressure-gradient TBL that formed on a flat-plate test model that was either hydraulically smooth or fully rough. Two distinct drag-reduction phenomena were investigated; bubble drag reduction (BDR) and air-layer drag reduction (ALDR). The streamwise distribution of skin-friction drag reduction was monitored with six skin-friction balances at downstream-distance-based Reynolds numbers to 220 million and at test speeds to 20.0 m s-1. Near-wall bulk void fraction was measured at twelve streamwise locations with impedance probes, and near-wall (0 〈 Y 〈 5 mm) bubble populations were estimated with a bubble imaging system. The instrument suite was used to investigate the scaling of BDR and the requirements necessary to achieve ALDR. Results from the BDR experiments indicate that: significant drag reduction (〉25%) is limited to the first few metres downstream of injection; marginal improvement was possible with a porous-plate versus an open-slot injector design; BDR has negligible sensitivity to surface tension; bubble size is independent of surface tension downstream of injection; BDR is insensitive to boundary-layer thickness at the injection location; and no synergetic effect is observed with compound injection. Using these data, previous BDR scaling methods are investigated, but data collapse is observed only with the 'initial zone' scaling, which provides little information on downstream persistence of BDR. ALDR was investigated with a series of experiments that included a slow increase in the volumetric flux of air injected at free-stream speeds to 15.3 m s-1. These results indicated that there are three distinct regions associated with drag reduction with air injection: Region I, BDR; Region II, transition between BDR and ALDR; and Region III, ALDR. In addition, once ALDR was established: friction drag reduction in excess of 80% was observed over the entire smooth model for speeds to 15.3 m s-1 the critical volumetric flux of air required to achieve ALDR was observed to be approximately proportional to the square of the free-stream speed; slightly higher injection rates were required for ALDR if the surface tension was decreased; stable air layers were formed at free-stream speeds to 12.5 m s1 with the surface fully roughened (though approximately 50% greater volumetric air flux was required); and ALDR was sensitive to the inflow conditions. The sensitivity to the inflow conditions can be mitigated by employing a small faired step (10 mm height in the experiment) that helps to create a fixed separation line. © 2008 Cambridge University Press.

Description: A spatially developing supersonic boundary layer at Mach 2 is analysed by means of direct numerical simulation of the compressible Navier-Stokes equations, with the objective of quantitatively characterizing the coherent vortical structures. The study shows structural similarities with the incompressible case. In particular, the inner layer is mainly populated by quasi-streamwise vortices, while in the outer layer we observe a large variety of structures, including hairpin vortices and hairpin packets. The characteristic properties of the educed structures are found to be nearly uniform throughout the outer layer, and to be weakly affected by the local vortex orientation. In the outer layer, typical core radii vary in the range of 5-6 dissipative length scales, and the associated circulation is approximately constant, and of the order of 180 wall units. The statistical properties of the vortical structures in the outer layer are similar to those of an ensemble of non-interacting closed-loop vortices with a nearly planar head inclined at an angle of approximately 20° with respect to the wall, and with an overall size of approximately 30 dissipative length scales. © 2008 Cambridge University Press.