Annual Review of Fluid Mechanics - Volume 44, 2012

We are interested in the quality of sound produced by musical instruments and their playability. In wind instruments, a hydrodynamic source of sound is coupled to an acoustic resonator. Linear acoustics can predict the pitch of an instrument. This can significantly reduce the trial-and-error process in the design of a new instrument. We consider deviations from the linear acoustic behavior and the fluid mechanics of the sound production. Real-time numerical solution of the nonlinear physical models is used for sound synthesis in so-called virtual instruments. Although reasonable analytical models are available for reeds, lips, and vocal folds, the complex behavior of flue instruments escapes a simple universal description. Furthermore, to predict the playability of real instruments and help phoneticians or surgeons analyze voice quality, we need more complex models.

The kinematics and dynamics of wall-bounded turbulence are surveyed, with emphasis on the multiscale processes associated with the logarithmic layer and with its interactions with the wall. It is shown that the logarithmic law reflects a momentum cascade and that its structure agrees reasonably well with Townsend's (1961) model of a self-similar family of attached eddies, each of which contains, on average, a sweep-ejection pair, a segment of a large velocity streak, and disorganized vorticity. Those logarithmic eddies are themselves turbulent objects and can be studied in minimal simulation boxes that are much larger than those in the buffer layer. It is argued that, near the wall, the logarithmic eddies are probably the same as the vortex packets identified by experiments, but that their dynamics does not appear to be especially linked to the buffer layer. Further from the wall, they align into longer superstreaks, although the mechanism remains unclear.

Multiphase flows occurring in nature and in technological applications are often turbulent. The large range of length scales and timescales in turbulent multiphase flows makes direct numerical simulation of the microscale governing equations intractable for many applications. In this article we review a systematic approach for developing large-eddy-simulation (LES) tools for dispersed multiphase flows starting from the microscale model. A key intermediate step is the mesoscopic model for the dispersed phase, formulated in terms of kinetic equations, that contains the physical models for the flow. Owing to the phase-space variables, direct solution of the mesoscopic model is usually intractable, and additional mathematical approximations are introduced to arrive at a macroscopic model. We show that self-conditioned LES models can be derived for both the mesoscopic and macroscopic models, but the former is preferred to ensure consistency and physical accuracy. The principal difficulties and open challenges in closing the LES model equations are highlighted.

This article reviews the use of various techniques for membrane filtration, such as Dean and Taylor vortices, pulsatile flows, and dynamic filtration, which can generate high shear rates more efficiently than cross-flow filtration. In dynamic filtration, shear rates are generated not by a pump, but by moving parts or by vibrations. The most successful application of Taylor vortices has been plasma collection from donors in transfusion centers by microfiltration (MF), using small rotating cylindrical filters. Industrial dynamic filtration modules consist of metal disks with vanes or blades rotating between circular flat membranes or rotating ceramic membrane disks. These systems can be operated at high rotation speeds in order to produce very high permeate fluxes, or they can be operated at low speeds and save energy as compared with cross-flow filtration for the same flux. Vibrating modules (i.e., vibratory shear-enhanced processing) consist of a stack of circular membranes oscillating around a vertical shaft at its resonant frequency. While instabilities created by Dean vortices and pulsatile flows are mostly efficient in laminar flow and in MF and ultrafiltration, the benefits of high shear dynamic filtration are even more impressive in nanofiltration and reverse osmosis, as the reduction in concentration polarization not only increases permeate flux as compared with cross-flow filtration, but also decreases microsolute transmission.

Leaves falling in air and bubbles rising in water provide daily examples of nonstraight paths associated with the buoyancy-driven motion of a body in a fluid. Such paths are relevant to a large variety of applicative fields such as mechanical engineering, aerodynamics, meteorology, and the biomechanics of plants and insect flight. Although the problem has attracted attention for ages, it is only recently that the tremendous progress in the development of experimental and computational techniques and the emergence of new theoretical concepts have led to a better understanding of the underlying physical mechanisms. This review attempts to bring together the main recent experimental, computational, and theoretical advances obtained on this fascinating subject. To this end it describes the first steps of the transition in the wake of a fixed body and its connection with the onset and development of the path instability of moving bodies. Then it analyzes the kinematics and dynamics of various types of bodies along typical nonstraight paths and how the corresponding information can be used to build low-dimensional predictive models.

This review describes mean and turbulent flow and mass transport in the presence of aquatic vegetation. Within emergent canopies, the turbulent length scales are set by the stem diameter and spacing, and the mean flow is determined by the distribution of the canopy frontal area. Near sparse submerged canopies, the bed roughness and near-bed turbulence are enhanced, but the velocity profile remains logarithmic. For dense submerged canopies, the drag discontinuity at the top of the canopy generates a shear layer, which contains canopy-scale vortices that control the exchange of mass and momentum between the canopy and the overflow. The canopy-scale vortices penetrate a finite distance into the canopy, δe, set by the canopy drag. This length scale segregates the canopy into two regions: The upper canopy experiences energetic turbulent transport, controlled by canopy-scale vortices, whereas the lower canopy experiences diminished transport, associated with the smaller stem-scale turbulence. The canopy-scale vortices induce a waving motion in flexible blades, called a monami.

Electrorheological (ER) fluids, consisting of solid particles dispersed in an insulating liquid, display the special characteristic of electric-field-induced rheological variations. Nearly six decades after their discovery, ER fluids have emerged as materials of increasing scientific fascination and practical importance. This review traces the mechanisms responsible for these fluids' ER response and their attendant theoretical underpinnings. In particular, ER fluids are divided into two different types, dielectric electrorheological (DER) and giant electrorheological (GER), which reflect the underlying electric susceptibility arising from the induced dielectric polarization and the orientational polarization of molecular dipoles, respectively. The formulation of a continuum ER hydrodynamics is described in some detail. As an electric-mechanical interface, ER fluids have broad application potential in electrifying the control of mechanical devices. This review focuses on their applications in microfluidic chips, in which GER fluids have enabled a variety of digitally controlled functionalities.

Nonlinear gyrokinetics is the major formalism used for both the analytical and numerical descriptions of low-frequency microturbulence in magnetized plasmas. Its derivation from noncanonical Lagrangian methods and field-theoretic variational principles is summarized. Basic properties of gyrokinetic physics are discussed, including polarization and the concept of the gyrokinetic vacuum, equilibrium statistical mechanics, and the two fundamental constituents of gyrokinetic turbulence, namely drift waves and zonal flows. Numerical techniques are described briefly, and illustrative simulation results are presented. Advanced topics include the transition to turbulence, the nonlinear saturation of turbulence by coupling to damped gyrokinetic eigenmodes, phase-space cascades, subcritical turbulence, and momentum conservation.

Recent remarkable progress in computing power and numerical analysis is enabling us to fill a gap in the dynamical systems approach to turbulence. A significant advance in this respect has been the numerical discovery of simple invariant sets, such as nonlinear equilibria and periodic solutions, in well-resolved Navier-Stokes flows. This review describes some fundamental and practical aspects of dynamical systems theory for the investigation of turbulence, focusing on recently found invariant solutions and their significance for the dynamical and statistical characterization of low-Reynolds-number turbulent flows. It is shown that the near-wall regeneration cycle of coherent structures can be reproduced by such solutions. The typical similarity laws of turbulence, i.e., the Prandtl wall law and the Kolmogorov law for the viscous range, as well as the pattern and intensity of turbulence-driven secondary flow in a square duct can also be represented by these simple invariant solutions.

In this review we describe current scientific and technological issues in the quest to reduce aeroengine noise, in the face of predicted rapid increases in the volume of air traffic, on the one hand, and increasingly strict environmental regulation, on the other. Alongside conventional ducted turbofan designs, new open-rotor contra-rotating power plants are currently under development, which present their own noise challenges. The key sources of tonal and broadband noise, and the way in which noise propagates away from the source, are surveyed in both cases. We also consider in detail two key aspects underpinning the flow physics that continue to receive considerable attention, namely the acoustics of swirling flow and unsteady flow-blade interactions. Finally, we describe possible innovations in open-rotor engine design for low noise.

A thin stream or rope of viscous fluid falling from a sufficient height onto a surface forms a steadily rotating helical coil. Tabletop laboratory experiments in combination with a numerical model for slender liquid ropes reveal that finite-amplitude coiling can occur in four distinct regimes (viscous, gravitational, inertio-gravitational, and inertial) corresponding to different balances among the three principal forces acting on the rope. The model further shows that the onset of coiling has distinct viscous, gravitational, and inertial modes that connect smoothly with the corresponding finite-amplitude regimes. In addition to steady coiling, slender liquid ropes falling onto surfaces can exhibit a remarkable variety of nonstationary behaviors, including propagating spiral waves of air bubbles, supercoiling, the leaping-shampoo (Kaye) effect for non-Newtonian fluids, and the fluid-mechanical sewing machine in which the rope leaves complex stitch patterns on a moving surface.

This review discusses the current understanding of tear-film physiology and mathematical models for some of its dynamics. First, a brief introduction to the tear film and the ocular surface is given. Next, mathematical models for the tear film are discussed, with an emphasis on models that describe the formation and relaxation of the tear film from blinking. Finally, future issues in tear film modeling are presented.

This article provides a critical review of aero-optics with an emphasis on recent developments in computational predictions and the physical mechanisms of flow-induced optical distortions. Following a brief introduction of the fundamental theory and key concepts, computational techniques for aberrating flow fields and optical propagation are discussed along with a brief survey of wave-front sensors used in experimental measurements. New physical understanding generated through numerical and experimental investigations is highlighted for a number of important aero-optical flows, including turbulent boundary layers, separated shear layers, and flow over optical turrets. Approaches for mitigating aero-optical effects are briefly discussed.

This review focuses on the applications of smoothed particle hydrodynamics (SPH) to incompressible or nearly incompressible flow. In the past 17 years, the range of applications has increased as researchers have realized the ability of SPH algorithms to handle complex physical problems. These include the disruption of free surfaces when a wave hits a rocky beach, multifluid problems that may involve the motion of rigid and elastic bodies, non-Newtonian fluids, virtual surgery, and chemical precipitation from fluids moving through fractured media. SPH provides a fascinating tool that has some of the properties of molecular dynamics while retaining the attributes of the macroscopic equations of continuum mechanics.

Fluid mechanical processes are an intrinsic part of several aspects of the physiology and pathology of the human eye. In this article we describe selected phenomena that are amenable to particularly interesting mathematical, experimental, or numerical analyses. We initially focus on glaucoma, a condition often associated with raised intraocular pressure. The mechanics in this disease is by no means fully understood, but we present some of the modeling work that provides a partial explanation. We next focus on other features of the dynamics of the two specialized ocular fluids: the aqueous and vitreous humors. With regard to the aqueous humor, we discuss problems concerning the transport of heat and proteins and the hydration of the cornea. With regard to the vitreous humor, we discuss the possibility of flow, which occurs primarily as a result of saccades or motions of the eyeball. Finally, we describe a model of the degradation of Bruch's membrane in the retina.

The diversity of the morphologies, propulsion mechanisms, flow environments, and behaviors of planktonic microorganisms has long provided inspiration for fluid physicists, with further intrigue provided by the counterintuitive hydrodynamics of their viscous world. Motivation for studying the fluid dynamics of microplankton abounds, as microorganisms support the food web and control the biogeochemistry of most aquatic environments, particularly the oceans. In this review, we discuss the fluid physics governing the locomotion and feeding of individual planktonic microorganisms (⩽1mm). In the past few years, the field has witnessed an increasing number of exciting discoveries, from the visualization of the flow field around individual swimmers to linkages between microhydrodynamic processes and ecosystem dynamics. In other areas, chiefly the ability of microorganisms to take up nutrients and sense hydromechanical signals, our understanding will benefit from reinvigorated interest, and ample opportunities for breakthroughs exist. When it comes to the fluid mechanics of living organisms, there is plenty of room at the bottom.

When a direct current (DC) electric field is applied across an ion-selective nanoporous membrane or a nanochannel with an overlapping Debye layer, a surprising microvortex instability occurs on the side of the membrane/channel through which counterions enter. Despite its micro and nano length scales, this instability exhibits all the hallmarks of other classical hydrodynamic instabilities—a subharmonic cascade, a wide-band fluctuation spectrum, and a coherent structure dominated by spatiotemporal dynamics. Moreover, the resulting convection enhances the ion flux into the ion-selective medium and gives rise to an overlimiting-current bifurcation in the current-voltage relationship. This hydrodynamically driven nonequilibrium ion flux does not seem to have any equivalent in cell membrane ion channels. Yet, by introducing asymmetric entrances to provide different polarized regions and/or viscous arrest of the vortex instability, one can fabricate a hydrodynamic nanofluidic diode. With other modifications, hysteretic, excitable, and oscillatory ion flux dynamics could also be elicited—all with strong hydrodynamic features.

In physical systems, a reduction in dimensionality often leads to exciting new phenomena. Here we discuss the novel effects arising from the consideration of fluid turbulence confined to two spatial dimensions. The additional conservation constraint on squared vorticity relative to three-dimensional (3D) turbulence leads to the dual-cascade scenario of Kraichnan and Batchelor with an inverse energy cascade to larger scales and a direct enstrophy cascade to smaller scales. Specific theoretical predictions of spectra, structure functions, probability distributions, and mechanisms are presented, and major experimental and numerical comparisons are reviewed. The introduction of 3D perturbations does not destroy the main features of the cascade picture, implying that 2D turbulence phenomenology establishes the general picture of turbulent fluid flows when one spatial direction is heavily constrained by geometry or by applied body forces. Such flows are common in geophysical and planetary contexts, are beautiful to observe, and reflect the impact of dimensionality on fluid turbulence.

Although they lack muscle, plants have evolved a remarkable range of mechanisms to create motion, from the slow growth of shoots to the rapid snapping of carnivorous plants and the explosive rupture of seed pods. Here we review the key fluid mechanics principles used by plants to achieve movements, summarizing current knowledge and recent discoveries. We begin with a brief overview of water transport and material properties in plants and emphasize that the poroelastic timescale of water diffusion through soft plant tissue imposes constraints on the possible mechanisms for motion. We then discuss movements that rely only on the transport of water, from irreversible growth to reversible swelling/shrinking due to osmotic or humidity gradients. We next show how plants use mechanical instabilities—snap buckling, cavitation, and fracture—to speed up their movements beyond the limits imposed by simple hydraulic mechanisms. Finally, we briefly discuss alternative schemes, involving capillarity or complex fluids.

Forest canopies are important components of the terrestrial carbon budget, which has motivated a worldwide effort, FLUXNET, to measure CO2 exchange between forests and the atmosphere. These measurements are difficult to interpret and to scale up to estimate exchange across a landscape. Here we review the effects of complex terrain on the mean flow, turbulence, and scalar exchange in canopy flows, as exemplified by adjustment to forest edges and hills, including the effects of stable stratification. We focus on the fundamental fluid mechanics, in which developments in theory, measurements, and modeling, particularly through large-eddy simulation, are identifying important processes and providing scaling arguments. These developments set the stage for the development of predictive models that can be used in combination with measurements to estimate exchange at the landscape scale.