Annual Review of Fluid Mechanics - Volume 42, 2010

This review describes how singular perturbation theory grew out of Prandtl's fluid dynamical boundary-layer theory of 1904. Developments were centered at Göttingen until 1933, when research spread worldwide. After that, singular perturbations developed more rapidly as the subject became centered within applied mathematics.

We discuss the coupling processes between surface gravity waves and adjacent winds and currents in turbulent boundary layers. These processes mediate exchanges of momentum, heat, and gases between the atmosphere and ocean and thus are of global significance for climate. Surface waves grow primarily by pressure-form stress from airflow over the waveforms, and they dissipate in the open sea by wave breaking that injects and stirs momentum, energy, and bubbles into the ocean. Wave motions pump wind eddies that control fluxes across the lower atmosphere. Flow separation occurs behind steep wave crests, and at high winds the crests flatten into spume, which diminishes the drag coefficient. In the ocean the Lagrangian-mean wave velocity, Stokes drift, induces a vortex force and material transport. These generate Langmuir circulations penetrating throughout the boundary layer and enhancing entrainment at the stratified interior interface in combination with other turbulent eddies and inertial-shear instability.

Geomorphology is concerned with the shaping of Earth's surface. A major contributing mechanism is the interaction of natural fluids with the erodible surface of Earth, which is ultimately responsible for the variety of sedimentary patterns observed in rivers, estuaries, coasts, deserts, and the deep submarine environment. This review focuses on fluvial patterns, both free and forced. Free patterns arise spontaneously from instabilities of the liquid-solid interface in the form of interfacial waves affecting either bed elevation or channel alignment: Their peculiar feature is that they express instabilities of the boundary itself rather than flow instabilities capable of destabilizing the boundary. Forced patterns arise from external hydrologic forcing affecting the boundary conditions of the system. After reviewing the formulation of the problem of morphodynamics, which turns out to have the nature of a free boundary problem, I discuss systematically the hierarchy of patterns observed in river basins at different scales.

Shear bands, localized regions where shear flows concentrate, form in many complex fluids under a wide range of circumstances. In this review, we outline the main mechanisms that cause shear banding in complex fluids with granularity: foams, emulsions, colloidal suspensions, and granular matter. Apart from shear bands caused by continuum-scale mechanisms such as stress inhomogeneities and flow instabilities, we discuss a range of shear-banding phenomena for which the particle scale plays a crucial role.

This review discusses the use of the combination of surface roughness and hydrophobicity for engineering large slip at the fluid-solid interface. These superhydrophobic surfaces were initially inspired by the unique water-repellent properties of the lotus leaf and can be employed to produce drag reduction in both laminar and turbulent flows, enhance mixing in laminar flows, and amplify diffusion-osmotic flows. We review the current state of experiments, simulations, and theory of flow past superhydrophobic surfaces. In addition, the designs and limitations of these surfaces are discussed, with an eye toward implementing these surfaces in a wide range of applications.

Turbulent dispersed multiphase flows are common in many engineering and environmental applications. The stochastic nature of both the carrier-phase turbulence and the dispersed-phase distribution makes the problem of turbulent dispersed multiphase flow far more complex than its single-phase counterpart. In this article we first review the current state-of-the-art experimental and computational techniques for turbulent dispersed multiphase flows, their strengths and limitations, and opportunities for the future. The review then focuses on three important aspects of turbulent dispersed multiphase flows: the preferential concentration of particles, droplets, and bubbles; the effect of turbulence on the coupling between the dispersed and carrier phases; and modulation of carrier-phase turbulence due to the presence of particles and bubbles.

The article surveys the current state of our understanding of turbidity currents, with an emphasis on their fluid mechanics. It highlights the significant role these currents play within the global sediment cycle, and their importance in environmental processes and in the formation of hydrocarbon reservoirs. Events and mechanisms governing the initiation of turbidity currents are reviewed, along with experimental observations and findings from field studies regarding their internal velocity and density structure. As turbidity currents propagate over the seafloor, they can trigger the evolution of a host of topographical features through the processes of deposition and erosion, such as channels, levees, and sediment waves. Potential linear instability mechanisms are discussed that may determine the spatial scales of these features. Finally, the hierarchy of available theoretical models for analyzing the dynamics of turbidity currents is outlined, ranging from dimensional analysis and integral models to both depth-averaged and depth-resolving simulation approaches.

This article reviews the principal experimental methods currently available to simultaneously measure all the terms of the velocity gradient tensor of turbulent flows. These methods have been available only for a little more than 20 years. They have provided access to the most fundamental and defining properties of turbulence. The methods include small, multisensor, hot-wire probes that provide single-location, time-resolved measurements of the tensor and various optical arrangements, most of which provide the tensor information over a larger spatial extent but, in most cases, without resolution in time. Data-reduction algorithms, spatial-resolution issues, and the use of Taylor's hypothesis are addressed in evaluating the accuracy of the various methods.

The lubrication of external liquid flow with a bubbly mixture or gas layer has been the goal of engineers for many years, and this article presents the underlying principles and recent advances of this technology. It reviews the use of partial and supercavities for drag reduction of axisymmetric objects moving within a liquid. Partial cavity flows can also be used to reduce the friction drag on the nominally two-dimensional portions of a horizontal surface, and the basic flow features of two-dimensional cavities are presented. Injection of gas can lead to the creation of a bubbly mixture near the flow surface that can significantly modify the flow within the turbulent boundary layer, and there have been significant advances in the understanding of the underlying physical process of drag reduction. Moreover, with sufficient gas flux, the bubbles flowing beneath a solid surface can coalesce to form a thin drag-reducing air layer. The current applications of these techniques to underwater vehicles and surface ships are discussed.

This article reviews the methods of wave–mean interaction theory for classical fluid dynamics, and for geophysical fluid dynamics in particular, providing a few examples for illustration. It attempts to bring the relevant equations into their simplest possible form, which highlights the organizing role of the circulation theorem in the theory. This is juxtaposed with a simple account of superfluid dynamics and the attendant wave–vortex interactions as they arise in the nonlinear Schrödinger equation. Here the fundamental physical situation is more complex than in the geophysical case, and the current mathematical understanding is more tentative. Classical interaction theory might be put to good use in the theoretical and numerical study of quantum fluid dynamics.

This article reviews the range of flows that may be created within thin cylindrical or annular cavities due to the rotation of one of the confining disks. At low Reynolds numbers, the rotation gives rise to an axisymmetric, radially outward motion near the rotor with a return flow along the stationary disk. As the Reynolds number is raised, this base flow gives way to a shear flow populated by discrete vortices, whether of cylindrical or spiral form, near both the rotating and stationary disks. At Reynolds numbers high enough for turbulent flow to occur, in the twentieth century both experimental and computational studies treated the flow as axisymmetric and steady. Recent research has shown, however, that complex organized structures also persist in the turbulent regime.

Atmospheric flows feature length scales from 10⁻⁵ to 10⁵ m and timescales from microseconds to weeks or more. For scales above several kilometers and minutes, there is a natural scale separation induced by the atmosphere's thermal stratification, together with the influences of gravity and Earth's rotation, and the fact that atmospheric-flow Mach numbers are typically small. A central aim of theoretical meteorology is to understand the associated scale-specific flow phenomena, such as internal gravity waves, baroclinic instabilities, Rossby waves, cloud formation and moist convection, (anti-)cyclonic weather patterns, hurricanes, and a variety of interacting waves in the tropics. Single-scale asymptotics yields reduced sets of equations that capture the essence of these scale-specific processes. For studies of interactions across scales, techniques of multiple-scales asymptotics have received increasing recognition in recent years. This article recounts the most prominent scales and associated scale-dependent models and summarizes recent multiple-scales developments.

An aerodynamic instability known as stall occurs in axial compressors as the mass flow rate is reduced and the blade loading reaches its limit. At this limiting condition, an easily recognizable flow breakdown process, known as spike-type stall inception, is observed in most modern compressors. This article begins by examining measurements from both low- and high-speed compressors to explain the characteristic features of spike-type stall. This is followed by a review of past work on compressor stability and an assessment of recent advances in this field. Included here is a study of the three-dimensional flow features that typify spike formation and its eventual growth into a mature stall cell. We also consider the formation criteria for spike-type stall and the means for early detection and possible control. On the computational side, a possible mechanism for spike formation is identified from three-dimensional studies of the flow in the rotor tip region. This mechanism involves tip-clearance backflow at the blade's trailing edge in combination with forward spillage of tip-leakage flow at the leading edge. This flow pattern implies that a successful stall-control technology will have to rely on an effective means of suppressing tip-clearance backflow and forward spillage.

Airflows in the nasal cavities and oral airways are rather complex, possibly featuring a transition to turbulent jet-like flow, recirculating flow, Dean's flow, vortical flows, large pressure drops, prevailing secondary flows, and merging streams in the case of exhalation. Such complex flows propagate subsequently into the tracheobronchial airways. The underlying assumptions for particle transport and deposition are that the aerosols are spherical, noninteracting, and monodisperse and deposit upon contact with the airway surface. Such dilute particle suspensions are typically modeled with the Euler-Lagrange approach for micron particles and in the Euler-Euler framework for nanoparticles. Micron particles deposit nonuniformly with very high concentrations at some local sites (e.g., carinal ridges of large bronchial airways). In contrast, nanomaterial almost coats the airway surfaces, which has implications of detrimental health effects in the case of inhaled toxic nanoparticles. Geometric airway features, as well as histories of airflow fields and particle distributions, may significantly affect particle deposition.

The properties of the structure functions and other small-scale quantities in turbulent Rayleigh-Bénard convection are reviewed, from an experimental, theoretical, and numerical point of view. In particular, we address the question of whether, and if so where in the flow, the so-called Bolgiano-Obukhov scaling exists, i.e., Sθ(r) ∼ r^2/5 for the second-order temperature structure function and Su(r) ∼ r^6/5 for the second-order velocity structure function. Apart from the anisotropy and inhomogeneity of the flow, insufficiently high Rayleigh numbers, and intermittency corrections (which all hinder the identification of such a potential regime), there are also reasons, as a matter of principle, why such a scaling regime may be limited to at most a decade, namely the lack of clear scale separation between the Bolgiano length scale LB and the height of the cell.

A majority of the world's urban centers are located in complex terrain, in which local airflow patterns are driven by pressure gradients and thermal forcing, while being strongly influenced by topographic effects and human (anthropogenic) activities. A paradigm in this context is a city located in a valley surrounded by mountains, slopes, and escarpments, in which the airflow is determined by terrain-induced perturbations to synoptic (background) flow, mesoscale thermal circulation (valley/slope flows) generated by local heating or cooling, and by their interaction with factitious (e.g., buildings and roads) and natural (e.g., vegetation and terrain) elements. The dynamics of airflows intrinsic to urban areas in complex terrain is reviewed here by employing idealized flow configurations to illustrate fundamental processes. Urban flows span a wide range of space and time scales and the emphasis here is on mesoscales (1–100 km). Basic fluid dynamics plays a central role in explaining observations of urban flow and in developing subgrid parameterizations for predictive models.

This review describes a range of natural processes leading to the formation of turbulent buoyant plumes, largely relating to volcanic processes, in which there are localized, intense releases of energy. Phenomena include volcanic eruption columns, bubble plumes in lakes, hydrothermal plumes, and plumes beneath the ice in polar oceans. We assess how the dynamics is affected by heat transfer, particle fallout and recycling, and Earth's rotation, as well as explore some of the mixing of the ambient fluid produced by plumes in a confined geometry.

In microrheology, the local and bulk mechanical properties of a complex fluid are extracted from the motion of probe particles embedded within it. In passive microrheology, particles are forced by thermal fluctuations and probe linear viscoelasticity, whereas active microrheology involves forcing probes externally and can be extended out of equilibrium to the nonlinear regime. Here we review the development, present state, and future directions of this field. We organize our review around the generalized Stokes-Einstein relation (GSER), which plays a central role in the interpretation of microrheology. By discussing the Stokes and Einstein components of the GSER individually, we identify the key assumptions that underpin each, and the consequences that occur when they are violated. We conclude with a discussion of two techniques—multiple particle-tracking and nonlinear microrheology—that have arisen to handle systems in which the GSER breaks down.

With its roots in kinetic theory and the cellular automaton concept, the lattice-Boltzmann (LB) equation can be used to obtain continuum flow quantities from simple and local update rules based on particle interactions. The simplicity of formulation and its versatility explain the rapid expansion of the LB method to applications in complex and multiscale flows. We review many significant developments over the past decade with specific examples. Some of the most active developments include the entropic LB method and the application of the LB method to turbulent flow, multiphase flow, and deformable particle and fiber suspensions. Hybrid methods based on the combination of the Eulerian lattice with a Lagrangian grid system for the simulation of moving deformable boundaries show promise for more efficient applications to a broader class of problems. We also discuss higher-order boundary conditions and the simulation of microchannel flow with finite Knudsen number. Additionally, the remarkable scalability of the LB method for parallel processing is shown with examples. Teraflop simulations with the LB method are routine, and there is no doubt that this method will be one of the first candidates for petaflop computational fluid dynamics in the near future.