Annual Review of Fluid Mechanics - Volume 35, 2003

Full-scale icing experiments and, therefore, certification time and cost can be significantly reduced by developing calculation methods to evaluate the aircraft and system performance for a wide range of icing conditions. This article summarizes calculation methods for icing that include ice accretion, ice system performance, and icing effects on aircraft.

The more violent impacts of water waves on walls create velocities and pressures having magnitudes much larger than those associated with the propagation of ordinary waves under gravity. Insight into these effects has been gained by irrotational-flow computations and by investigating the role of entrained and trapped air in wave impacts. This review focuses on the results of theoretical work, making particular note of the value of considering pressure impulse, and highlights the aspects that are poorly understood.

Drag reduction in wall-bounded flows can be achieved by transverse motions imposed by passive means, e.g., riblets, or by external forcing, such as wall oscillation or transverse traveling-wave excitation. In this article, we review possible physical mechanisms responsible for turbulent drag reduction and corresponding near-wall flow modification.

This paper reviews recent advances in our understanding of the origin and hierarchy of organized flow structures in fluidized beds, distinction between bubbling and nonbubbling systems, and stages of bubble evolution. Experimental data and theory suggest that, at high particle concentrations, the particle-phase pressure arising from flow-induced velocity fluctuations decreases with increasing concentration of particles. This, in turn, implies that nonhydrodynamic stresses must be present to impart stability to a uniformly fluidized bed at very high particle concentrations. There is ample evidence to support an argument that, in commonly encountered gas-fluidized beds, yield stresses associated with enduring particle networks are present in the window of stable bed expansion, where the particles are essentially immobile until bubbling commences. However, some recent data on gas-fluidized beds of agglomerates of cohesive particles suggest that there exists a window of bed expansion where the bed does manifest a smooth appearance to the naked eye and the particles are mobile; at higher gas velocities the bed bubbles visibly. The mechanics of such beds remain to be fully explained.

In this review we describe the aerodynamic problems that must be addressed in order to design a successful small aerial vehicle. The effects of Reynolds number and aspect ratio (AR) on the design and performance of fixed-wing vehicles are described. The boundary-layer behavior on airfoils is especially important in the design of vehicles in this flight regime. The results of a number of experimental boundary-layer studies, including the influence of laminar separation bubbles, are discussed. Several examples of small unmanned aerial vehicles (UAVs) in this regime are described. Also, a brief survey of analytical models for oscillating and flapping-wing propulsion is presented. These range from the earliest examples where quasi-steady, attached flow is assumed, to those that account for the unsteady shed vortex wake as well as flow separation and aeroelastic behavior of a flapping wing. Experiments that complemented the analysis and led to the design of a successful ornithopter are also described.

A review is given of the stability of complex fluids subject to homogeneous states of shearing, a research field that is scarcely two decades old. For the benefit of fluid mechanicians, a brief, somewhat historical overview is presented of material instability in elastoplastic solids, where one finds a considerable body of experiment and a rich source of theoretical concepts including Hadamard instability, strain localization, and nonlocal constitutive models. A survey is then given of recent theoretical and experimental studies of instability with shear banding in various complex fluids, including micellar solutions, particulate suspensions, and rapidly sheared granular media. Various stability analyses are encapsulated in a mathematical dynamical-systems model for constitutive equations of the rate-type, and a general linear-stability theory is given for viscoelastic fluids in unbounded homogeneous shear flows. A general form of (Kelvin) wave-vector stretching is shown to play a key role in the growth of Fourier modes, as illustrated by recent computations for granular shear flow. The Fourier description also provides an explicit representation of higher-gradient (nonlocal) effects as higher-order powers of wave number.

The issue of the physical mechanism(s) that control the efficiency with which the density field in stably stratified fluid is mixed by turbulent processes has remained enigmatic. Similarly enigmatic has been an explanation of the numerical value of ∼0.2, which is observed to characterize this efficiency experimentally. We review recent work on the turbulence transition in stratified parallel flows that demonstrates that this value is not only numerically predictable but also that it is expected to be a nonmonotonic function of the Richardson number that characterizes preturbulent stratification strength. This value of the mixing efficiency appears to be characteristic of the late-time behavior of the turbulent flow that develops after an initially laminar shear flow has undergone the transition to turbulence through an intermediate instability of Kelvin-Helmholtz type.

The modern study of a crowd as a flowing continuum is a recent development. Distinct from a classical fluid because of the property that a crowd has the capacity to think, interesting new physical ideas are involved in its study. An appealing property of a crowd in motion is that the nonlinear, time-dependent, simultaneous equations representing a crowd are conformably mappable. This property makes many interesting applications analytically tractable. In this review examples are given in which the theory has been used to provide possible assistance in the annual Muslim Hajj, to understand the Battle of Agincourt, and, surprisingly, to locate barriers that actually increase the flow of pedestrians above that when there are no barriers present. Modern developments may help prevent some of the approximately two thousand deaths that annually occur in accidents owing to crowding.The field of crowd motion, that is, the field of “thinking fluids,” is an intriguing area of research with great promise.

Turbulence is ubiquitous in atmospheric clouds, which have enormous turbulence Reynolds numbers owing to the large range of spatial scales present. Indeed, the ratio of energy-containing and dissipative length scales is on the order of 10⁵ for a typical convective cloud, with a corresponding large-eddy Reynolds number on the order of 10⁶ to 10⁷. A characteristic trait of high-Reynolds-number turbulence is strong intermittency in energy dissipation, Lagrangian acceleration, and scalar gradients at small scales. Microscale properties of clouds are determined to a great extent by thermodynamic and fluid-mechanical interactions between droplets and the surrounding air, all of which take place at small spatial scales. Furthermore, these microscale properties of clouds affect the efficiency with which clouds produce rain as well as the nature of their interaction with atmospheric radiation and chemical species. It is expected, therefore, that fine-scale turbulence is of direct importance to the evolution of, for example, the droplet size distribution in a cloud. In general, there are two levels of interaction that are considered in this review: (a) the growth of cloud droplets by condensation and (b) the growth of large drops through the collision and coalescence of cloud droplets. Recent research suggests that the influence of fine-scale turbulence on the condensation process may be limited, although several possible mechanisms have not been studied in detail in the laboratory or the field. There is a growing consensus, however, that the collision rate and collision efficiency of cloud droplets can be increased by turbulence-particle interactions. Adding strength to this notion is the growing experimental evidence for droplet clustering at centimeter scales and below, most likely due to strong fluid accelerations in turbulent clouds. Both types of interaction, condensation and collision-coalescence, remain open areas of research with many possible implications for the physics of atmospheric clouds.

This review describes some of the important developments in the numerical investigation of transition to turbulence in wall-bounded and free shear flows during the past decade. The evolution of numerical techniques and models as well as the advances in our theoretical understanding of the physics of laminar-turbulent transition that were achieved using these tools are described. For wall-bounded flows, particular emphasis is placed on investigations studying various scenarios of “bypass transition” in flows that are asymptotically stable. A brief review of investigations into receptivity and control of transitional flows is included.

The recent avalanche of research activity in the field of granular matter has yielded much progress. The use of state-of-the-art (and other) computational and experimental methods has led to the discovery of new states and patterns and enabled detailed tests of theories and models. The application of statistical mechanical methods and phenomenology has contributed to the understanding of the microscopic a nd macroscopic properties of granular systems. Some previously open problems seem to be solved. Fluidized granular systems (rapid granular flows), recently referred to as granular gases, are often modeled by hydrodynamic equations of motion, some of which are based on systematic expansions applied to the pertinent Boltzmann equation. The undeniable success of granular hydrodynamics is somewhat surprising in view of the lack of scale separation in these systems and the neglect of certain correlations in most derivations of the hydrodynamic equations. Microstructures have been recognized as key features of granular gases; explanations for their existence have been proposed, and many of their properties elucidated. Granular-gas multistability can often be traced back to microstructure dynamics. In spite of these and other impressive advances, this field still poses serious challenges.

It is classically assumed that the far field of a round turbulent jet discharging into quiescent fluid has a unique behavior characterized only by its momentum flux. However, there is now considerable evidence that different discharge conditions at the jet nozzle exit can give rise to very different far-field flows. Perhaps the most striking examples of these are the bifurcating and blooming jets produced by appropriate combinations of controlled axial and circumferential excitations at the nozzle exit. With the right excitations, a jet can be made to divide into two separate jets (bifurcating jet), each of which carries half the axial momentum and spreads in a manner similar to a single jet. Trifurcating jets can also be produced. Other excitations can produce blooming jets, in which the jet explodes into a shower of vortex rings, producing a far-field flow that is quite unlike a normal unexcited jet. Bifurcating and blooming jets exhibit much greater mixing than normal jets, suggesting possible applications in flow control. This article summarizes our work on bifurcating and blooming jets, which began with our discovery of them in the early 1980s and continued through the mid- 1990s. One of us (D.E.P.) continued exploration of flow control using excited jets, first at the McDonnell Douglas Corporation, and more recently at the Georgia Institute of Technology. The key to flow control is the manipulation of the large vortical structures in the near field of the jet. Ultimately this work, and that of others, led to full-scale testing of jet engine exhaust mixing control. There it was shown that the jet temperature downstream of the engine can be very significantly reduced by application of well-designed and easily implemented excitation at the engine discharge, thereby solving problems encountered during ground operations. Related jet control work by other investigators is included in this review.

Recent advances in achieving textbook multigrid efficiency for fluid simulations are presented. Textbook multigrid efficiency is defined as attaining the solution to the governing system of equations in a computational work that is a small multiple of the operation counts associated with discretizing the system. Strategies are reviewed to attain this efficiency by exploiting the factorizability properties inherent to a range of fluid simulations, including the compressible Navier-Stokes equations. Factorizability is used to separate the elliptic and hyperbolic factors contributing to the target system; each of the factors can then be treated individually and optimally. Boundary regions and discontinuities are addressed with separate (local) treatments. New formulations and recent calculations demonstrating the attainment of textbook efficiency for aerodynamic simulations are shown.

We provide an overview of level set methods, introduced by Osher and Sethian, for computing the solution to fluid-interface problems. These are computational techniques that rely on an implicit formulation of the interface, represented through a time-dependent initial-value partial-differential equation. We discuss the essential ideas behind the techniques, the coupling of these techniques to finite-difference methods for incompressible and compressible flow, and a collection of applications including two-phase flow, ship hydrodynamics, and ink-jet-printhead design.

Recent small-scale turbulence observations allow the mixing regimes in lakes, reservoirs, and other enclosed basins to be categorized into the turbulent surface and bottom boundary layers as well as the comparably quiet interior. The surface layer consists of an energetic wave-affected thin zone at the very top and a law-of-the-wall layer right below, where the classical logarithmic-layer characteristic applies on average. Short-term current and dissipation profiles, however, deviate strongly from any steady state. In contrast, the quasi-steady bottom boundary layer behaves almost perfectly as a logarithmic layer, although periodic seiching modifies the structure in the details. The interior stratified turbulence is extremely weak, even though much of the mechanical energy is contained in baroclinic basin-scale seiching and Kelvin waves or inertial currents (large lakes). The transformation of large-scale motions to turbulence occurs mainly in the bottom boundary and not in the interior, where the local shear remains weak and the Richardson numbers are generally large.

The recent progress in three-dimensional boundary-layer stability and transition is reviewed. The material focuses on the crossflow instability that leads to transition on swept wings and rotating disks. Following a brief overview of instability mechanisms and the crossflow problem, a summary of the important findings of the 1990s is given.

We review the most important theoretical and numerical results obtained in the realm of shell models for the energy-turbulent cascade. We mainly focus here on those results that had or will have some impact on the fluid-dynamics community. In particular, we address the problem of small-scale intermittency by discussing energy–helicity interactions, energy-dissipation multifractality, and universality of intermittency, i.e., independence of anomalous scaling exponents from large-scale forcing and boundary conditions. A multifractal-based description of multiscale and multitime correlation functions in turbulence is also presented. Finally, we also briefly review the analytical difficulties, and hopes, of calculating anomalous exponents.

Increasing urbanization and concern about sustainability and quality of life issues have produced considerable interest in flow and dispersion in urban areas. We address this subject at four scales: regional, city, neighborhood, and street. The flow is one over and through a complex array of structures. Most of the local fluid mechanical processes are understood; how these combine and what is the most appropriate framework to study and quantify the result is less clear. Extensive and structured experimental databases have been compiled recently in several laboratories. A number of major field experiments in urban areas have been completed very recently and more are planned. These have aided understanding as well as model development and evaluation.