Annual Review of Fluid Mechanics - Volume 32, 2000

Interest in novel forms of marine propulsion and maneuvering has sparked a number of studies on unsteadily operating propulsors. We review recent experimental and theoretical work identifying the principal mechanism for producing propulsive and transient forces in oscillating flexible bodies and fins in water, the formation and control of large-scale vortices. Connection with studies on live fish is made, explaining the observed outstanding fish agility.

Granular materials segregate. Small differences in either size or density lead to flow-induced segregation, a complex phenomenon without parallel in fluids. Modeling of mixing and segregation processes requires the confluence of several tools, including continuum and discrete descriptions (particle dynamics, Monte Carlo simulations, cellular automata computations) and, often, considerable geometrical insight. None of these viewpoints, however, is wholly satisfactory by itself. Moreover, continuum and discrete descriptions of granular flows are regime dependent, and this fact may require adopting different subviewpoints. This review organizes a body of knowledge that forms—albeit imperfectly—the beginnings of an expandable continuum framework for the description of mixing and segregation of granular materials. We focus primarily on noncohesive particles, possibly differing in size, density, shape, etc. We present segregation mechanisms and models for size and density segregation and introduce chaotic advection, which appears in noncircular tumblers. Chaotic advection interacts in nontrivial ways with segregation in granular materials and leads to unique equilibrium structures that serve as a prototype for systems displaying organization in the midst of disorder.

This review pertains to the body of work dealing with internal recirculating flows generated by the motion of one or more of the containing walls. These flows are not only technologically important, they are of great scientific interest because they display almost all fluid mechanical phenomena in the simplest of geometrical settings. Thus corner eddies, longitudinal vortices, nonuniqueness, transition, and turbulence all occur naturally and can be studied in the same closed geometry. This facilitates the comparison of results from experiment, analysis, and computation over the whole range of Reynolds numbers. Considerable progress has been made in recent years in the understanding of three-dimensional flows and in the study of turbulence. The use of direct numerical simulation appears very promising.

The active control of sound waves has become an extraordinarily large and vigorous area of academic research and technological development. In this paper we describe the physical principles underlying the control of sound and review their application in a wide range of contexts. One scenario involves the control of noise from a primary source by the introduction of secondary sources, and this technique is described for fields in ducts, in free space, in enclosures (with particular reference to aircraft cabins), and for turbomachinery. A second scenario involves the use of the active control of sound to eliminate large-scale oscillations in more complicated flows, in which part of an unstable feedback cycle is mediated via acoustic waves. Successful applications of this idea include the control of combustion instabilities and compressor surge.

This article reviews some aspects of the roles that laboratory experiments have played in the study of orographic effects in the Earth's atmosphere and oceans. The review focuses on, but is not restricted to, physical systems for which the effects of both background stratification and rotation are important. In the past, such laboratory studies have been largely decoupled from attempts to make quantitative comparisons with the results of numerical-model studies or observations from field programs. Rather, they have been used mostly in the important task of better understanding the physics of rotating and stratified flows. Furthermore, most laboratory experiments concerned with the effects of orography on either homogeneous or stratified rotating fluids have considered laminar flows, whereas their counterpart flows in the atmosphere and ocean are turbulent. We argue that laboratory investigations are likely to be more useful in addressing critical environmental problems if the studies are more closely allied with numerical-modeling efforts. The latter, in turn, should be tied to field projects, with the overall objective of improving our ability to predict the behavior of natural systems. In this same spirit, we conclude that far more attention should be given to the laboratory simulation of the turbulent characteristics of natural flows. The availability of rapidly developing technology to acquire and analyze laboratory data provides the capability necessary to support the increasingly important roles that laboratory experiments can play in understanding and predicting the behavior of our natural environment.

Passive scalar behavior is important in turbulent mixing, combustion, and pollution and provides impetus for the study of turbulence itself. The conceptual framework of the subject, strongly influenced by the Kolmogorov cascade phenomenology, is undergoing a drastic reinterpretation as empirical evidence shows that local isotropy, both at the inertial and dissipation scales, is violated. New results of the complex morphology of the scalar field are reviewed, and they are related to the intermittency problem. Recent work on other aspects of passive scalar behavior—its spectrum, probability density function, flux, and variance—is also addressed.

We concentrate on the rich effects that surface tension has on free and forced surface waves for linear, nonlinear, and especially strongly nonlinear waves close to or at breaking or their limiting form. These effects are discussed in the context of standing gravity and gravity-capillary waves, Faraday waves, and parasitic capillary waves. Focus is primarily on post-1989 research. Regarding standing waves, new waveforms and the large effect that small capillarity can have are considered. Faraday waves are discussed principally with regard to viscous effects, hysteresis, and limit cycles; nonlinear waveforms of low mode numbers; contact-line effects and surfactants; breaking and subharmonics; and drop ejection. Pattern formation and chaotic and nonlinear dynamics of Faraday waves are mentioned only briefly. Gravity and gravity-capillary wave generation of parasitic capillaries and dissipation are considered at length. We conclude with our view on the direction of future research in these areas.

An overview of the near and far-field breakup and atomization of a liquid jet by a high speed annular gas jet is presented. The various regimes of liquid jet breakup are discussed in the parameter space of the liquid Reynolds number, the aerodynamic Weber number, and the ratio of the momentum fluxes between the gas and the liquid streams. Recent measurements of the gas-liquid interfacial instabilities are reviewed and used to analyze the underlying physical mechanisms involved in the primary breakup of the liquid jet. This process is shown to consist of the periodic stripping of liquid sheets, or ligaments, which subsequently break up into smaller lumps or drops. Models to predict the liquid shedding frequency, as well as the global parameters of the spray such as the liquid core length and spray spreading angle are discussed and compared with the experiments. The role of the secondary liquid breakup on the far-field atomization of the liquid jet is also considered, and an attempt is made to apply the classical turbulent breakup concepts to explain qualitatively the measurement of the far-field droplet size distribution and its dependence on the liquid to gas mass and momentum flux ratios. Models for the droplet breakup frequency in the far-field region of the jet, and for the daughter-size probability density function, which account for the effect of the liquid loading on the local turbulent dissipation rate in the gas, are discussed in the context of the statistical description of the spray in the far field. The striking effect of the addition of swirl in the gas stream is also examined.

The idealized interactions of shock waves with homogeneous and isotropic turbulence, homogeneous sheared turbulence, turbulent jets, shear layers, turbulent wake flows, and two-dimensional boundary layers have been reviewed. The interaction between a shock wave and turbulence is mutual. A shock wave exhibits substantial unsteadiness and deformation as a result of the interaction, whereas the characteristic velocity, timescales and length scales of turbulence change considerably. The outcomes of the interaction depend on the strength, orientation, location, and shape of the shock wave, as well as the flow geometry and boundary conditions. The state of turbulence and the compressibility of the incoming flow are two additional parameters that also affect the interaction.

The relationship between flow in the arteries, particularly the wall shear stresses, and the sites where atherosclerosis develops has motivated much of the research on arterial flow in recent decades. It is now well accepted that it is sites where shear stresses are low, or change rapidly in time or space, that are most vulnerable. These conditions are likely to prevail at places where the vessel is curved; bifurcates; has a junction, a side branch, or other sudden change in flow geometry; and when the flow is unsteady. These flows, often but not always involving flow separation or secondary motions, are also the most difficult ones in fluid mechanics to analyze or compute. In this article we review the modeling studies and experiments on steady and unsteady, two-and three-dimensional flows in arteries, and in arterial geometries most relevant in the context of atherosclerosis. These include studies of normal vessels—to identify, on the basis of the fluid mechanics, lesion foci—and stenotic vessels, to model and measure flow in vessels after the lesions have evolved into plaques sufficiently large to significantly modify the flow. We also discuss recent work that elucidates many of the pathways by which mechanical forces, primarily the wall shear stresses, are transduced to effect changes in the arterial wall at the cellular, subcellular, and genetic level.

New developments have occurred in recent years in the field of dynamo theory. The increase in computer capacity has permitted simulations of convection-driven dynamos in rotating spherical fluid shells in parameter ranges much closer to those of the Earth's core than has been possible before. The progress in handling flows of liquid sodium in large containers, on the other hand, has opened opportunities for realizations of homogeneous dynamos in the laboratory. These developments will lead to a deeper understanding of the origin of magnetic fields in planets and in stars.

Recent developments in the study of buoyancy-driven convection, magnetoconvection, and convection-driven dynamos in rapidly rotating spherical systems, with application to the fluid parts of the metallic cores of the Earth and other planets and satellites, are reviewed. While the fluid motions driven by convection generate and sustain magnetic fields by magnetohydrodynamic dynamo processes, the pattern and strength of the convective motions that control dynamo action are critically influenced by the combined and inseparable effects of rotation, magnetic fields, and spherical geometry. Emphasis is placed on the key dynamic feature of rotating spherical magnetohydrodynamics—the interaction between the Coriolis and Lorentz forces and the resulting effect on convection and magnetohydrodynamic processes. It is shown that the small value of the Ekman number, a result of rapid rotation and small viscosity in the fluid parts of planetary cores, causes severe difficulties in modeling planetary dynamos. There exist huge disparities, as a direct consequence of a small Ekman number, in the spatial, temporal, and amplitude scales of a convection-driven dynamo. The use of hyperviscosity removes these difficulties, but at the same time it alters the key dynamics in a fundamental and undesirable way. A convection-driven dynamo solution in rotating spherical systems at a sufficiently small Ekman number that is dynamically relevant to planetary fluid cores is yet to be achieved and remains a great challenge.

Sonoluminescence, the transduction of sound into light, is a phenomenon that pushes fluid mechanics beyond its limit. An initial state with long wavelength and low Mach number, such as is realized for a gas bubble driven by an audible sound field, spontaneously focuses the energy density so as to generate supersonic motion and a different phase of matter, from which are then emitted picosecond flashes of broad-band UV light. Although the most rational picture of sonoluminescence involves the creation of a “cold” dense plasma by an imploding shock wave, neither the imploding shock nor the plasma has been directly observed. Attempts to attack sonoluminescence from the perspective of continuum mechanics have led to interesting issues related to bubble shape oscillations, shock shape instabilities, and shock propagation through nonideal media, and chemical hydrodynamics. The limits of energy focusing that can be achieved from collapsing bubbles in the far-off equilibrium motion of fluids have yet to be determined either experimentally or theoretically.

Lava flows are gravity currents of partially molten rock that cool as they flow, in some cases melting the surface over which they flow but in all cases gradually solidifying until they come to rest. They present a wide range of flow regimes from turbulent channel flows at moderate Reynolds numbers to extremely viscous or plastic, creeping flows, and even brittle rheology may play a role once some solid has formed. The cooling is governed by the coupling of heat transport in the flowing lava with transfer from the lava surface into the surrounding atmosphere or water or into the underlying solid, and it leads to large changes in rheology. Instabilities, mostly resulting from cooling, lead to flow branching, surface folding, rifting, and fracturing, and they contribute to the distinctive styles and surface appearances of different classes of flows. Theoretical and laboratory models have complemented field studies in developing the current understanding of lava flows, motivated by the extensive roles they play in the development of planetary crusts and ore deposits and by the immediate hazards posed to people and property. However, much remains to be learned about the mechanics governing creeping, turbulent, and transitional flows in the presence of large rheology change on cooling and particularly about the advance of flow fronts, flow instabilities, and the development of flow morphology. I introduce the dynamical problems involved in the study of lava flows and review modeling approaches.

The single-point statistics of turbulence in the ‘roughness sub-layer’ occupied by the plant canopy and the air layer just above it differ significantly from those in the surface layer. The mean velocity profile is inflected, second moments are strongly inhomogeneous with height, skewnesses are large, and second-moment budgets are far from local equilibrium. Velocity moments scale with single length and time scales throughout the layer rather than depending on height. Large coherent structures control turbulence dynamics. Sweeps rather than ejections dominate eddy fluxes and a typical large eddy consists of a pair of counter-rotating streamwise vortices, the downdraft between the vortex pair generating the sweep. Comparison with the statistics and instability modes of the plane mixing layer shows that the latter rather than the boundary layer is the appropriate model for canopy flow and that the dominant large eddies are the result of an inviscid instability of the inflected mean velocity profile. Aerodynamic drag on the foliage is the cause both of the unstable inflected velocity profile and of a ‘spectral short cut’ mechanism that removes energy from large eddies and diverts it to fine scales, where it is rapidly dissipated, bypassing the inertial eddy-cascade. Total dissipation rates are very large in the canopy as a result of the fine-scale shear layers that develop around the foliage.

A vapor explosion results from the rapid and intense heat transfer that may follow contact between a hot liquid and a cold, more volatile one. Because it can happen during severe-accident sequences of a nuclear power plan, that is, when a large part of the core is molten, vapor explosions have been widely studied. The different sequences of a vapor explosion are presented, including premixing, triggering, propagation, and expansion. Typical experimental results are also analyzed to understand the involved physics. Then the different physics involved in the sequences are addressed, as well as the present experimental program.

We review the dynamics of stably stratified flows in the regime in which the Froude number is considered small and the Rossby number is of order one or greater. In particular we emphasize the nonpropagating component of the flow field, as opposed to the internal wave component. Examples of such flows range from the later stages of decay of turbulent flows to mesoscale meteorological flows. Results from theoretical analyses, laboratory experiments, and numerical simulations are presented. The limiting form of the equations of motion appears to describe the laboratory experiments and numerical simulations rather well. There are similarities with the dynamics of two-dimensional flows, but three-dimensional effects are clearly important. A number of remaining open issues are discussed.

Predicting the motion of bubbles in dispersed flows is a key problem in fluid mechanics that has a bearing on a wide range of applications from oceanography to chemical engineering. In this review we synthesize the recent progress made in describing bubble motion in inhomogeneous flow. A trident approach consisting of experimental, analytical, and numerical work has given a clearer description of the hydrodynamic forces experienced by isolated bubbles moving either in inviscid flows or in slightly viscous laminar flows. A significant part of the paper is devoted to a discussion of drag, added-mass force, and shear-induced lift experienced by spheroidal bubbles moving in inertially dominated, time-dependent, rotational, nonuniform flows. The important influence of surfactants and shape distortion on bubble motion in a quiescent liquid is highlighted. Examples of bubble motion in inhomogeneous flows combining several of the effects mentioned above are discussed.