Annual Review of Fluid Mechanics - Volume 45, 2013

This article presents a brief account of the life and work of Hans W. Liepmann, a distinguished fluid dynamicist, an outstanding teacher and leader, and the third Director of the Graduate Aeronautical Laboratories, California Institute of Technology.

This article surveys the contributions of Philip Geoffrey Saffman to our knowledge of fluid-dynamical phenomena both in nature and in the laboratory. We begin with Saffman's first work on fluid mechanics in Cambridge, England, in the mid-1950s and then describe the evolution of his ideas and research, over many diverse areas in fluid mechanics until his final paper in 2002. It is argued that Saffman brought a unique perspective to our interpretation of fluid mechanics as a broad scientific discipline that remains with us today.

Lorenz's theory of available potential energy (APE) remains the main framework for studying the atmospheric and oceanic energy cycles. Because the APE generation rate is the volume integral of a thermodynamic efficiency times the local diabatic heating/cooling rate, APE theory is often regarded as an extension of the theory of heat engines. Available energetics in classical thermodynamics, however, usually relies on the concept of exergy and is usually measured relative to a reference-state maximizing entropy at constant energy, whereas APE's reference state minimizes potential energy at constant entropy. This review seeks to shed light on the two concepts; it covers local formulations of available energetics, alternative views of the dynamics/thermodynamics coupling, APE theory and the second law of thermodynamics, APE production/dissipation, extensions to binary fluids, mean/eddy decompositions, APE in incompressible fluids, APE and irreversible turbulent mixing, and the role of mechanical forcing on APE production.

Because of the difficulty in making measurements under controlled conditions, most of what is known about the fluid dynamics of tornadoes comes from laboratory experiments that produce vortices with features similar to those observed in a tornado. Numerical simulation of laboratory experiments has become a valuable analytical tool owing to the greater ease of extracting data. The success of the numerical simulations has inspired better-defined numerical experiments capable of quantitatively describing the basic features of observed tornado vortices and has motivated simple fluid dynamical explanations. The present article reviews the state of knowledge concerning the fluid dynamics of tornadoes as found in laboratory and numerical analogs.

Inkjet printers eject drops from microscopic nozzles and deposit them on substrates. For a number of years after its initial development, inkjet printing remained a method for visualizing computer output and printing documents. Beginning in the late 1990s, a number of researchers realized that inkjet printers could be employed as robotic pipettes to create microarrays, manufacture three-dimensional parts and spherical particles, print electrical devices, and facilitate combinatorial chemistry. Although most inks are low-viscosity Newtonian fluids, liquids in new applications are complex fluids. At the same time that these new applications were emerging, the replacement of traditional photography by digital imaging and the quest for ever-faster printing speeds resulted in the development of novel printing methods. Whereas most previous reviews of the field have focused on evaluations of well-known printing methods, this review instead presents a critical analysis from a fluid mechanics perspective of the recent developments in nonstandard printing techniques and the increasingly widespread use of nonstandard inks of complex fluids.

Since time immemorial, surface water waves and their subsequent breaking have been studied. Herein we concentrate on breaking surface waves in deep and intermediate water depths. Progress has been made in several areas, including the prediction of their geometry, breaking onset, and especially energy dissipation. Recent progress in the study of geometric properties has evolved such that we can identify possible connections between crest geometry and energy dissipation and its rate. Onset prediction based on the local wave-energy growth rate appears robust, consistent with experiments, although the application of criteria in phase-resolving, deterministic prediction may be limited as calculation of the diagnostic parameter is nontrivial. Parameterization of the dissipation rate has benefited greatly from synergistic field and laboratory investigations, and relationships among the dynamics, kinematics, and the parameterization of the dynamics using geometric properties are now available. Field efforts continue, and although progress has been made, consensus among researchers is limited, in part because of the relatively few studies. Although direct numerical simulations of breaking waves are not yet a viable option, simpler models (e.g., implementation of an eddy viscosity model) have yielded positive results, particularly with regard to energy dissipation.

The large-scale dynamics of the mid-latitude atmosphere and ocean is characterized by a timescale separation between slow balanced motion and fast inertia-gravity waves. As a result of this separation, the two types of motion interact only weakly, and the dynamics can be approximated using balanced models, which filter out the fast waves completely. The separation is not complete, however: The evolution of well-balanced flows inevitably leads to the excitation of inertia-gravity waves through the process of spontaneous generation. Spontaneous generation has fundamental and practical implications: It limits the validity of balanced models and provides a source of inertia-gravity-wave activity. These two aspects are discussed in this review, which focuses on the small-Rossby-number regime ε≪1 corresponding to strong rotation. Theoretical arguments indicate that spontaneous generation is then exponentially small in ε for smooth flows. They are complemented by numerical simulations that identify specific generation mechanisms.

Turbulent jet noise is a controversial fluid mechanical puzzle that has amused and bewildered researchers for more than half a century. Whereas numerical simulations are now capable of simultaneously predicting turbulence and its radiated sound, the theoretical framework that would guide noise-control efforts is incomplete. Wave packets are intermittent, advecting disturbances that are correlated over distances far exceeding the integral scales of turbulence. Their signatures are readily distinguished in the vortical, turbulent region; the irrotational, evanescent near field; and the propagating far field. We review evidence of the existence, energetics, dynamics, and acoustic efficiency of wave packets. We highlight how extensive data available from simulations and modern measurement techniques can be used to distill acoustically relevant turbulent motions. The evidence supports theories that seek to represent wave packets as instability waves, or more general modal solutions of the governing equations, and confirms the acoustic importance of these structures in the aft-angle radiation of high subsonic and supersonic jets. The resulting unified view of wave packets provides insights that can help guide control strategies.

This review discusses how drops can levitate on a cushion of vapor when brought in contact with a hot solid. This is the so-called Leidenfrost phenomenon, a dynamical and transient effect, as vapor is injected below the liquid and pressed by the drop weight. The absence of solid/liquid contact provides unique mobility for the levitating liquid, contrasting with the usual situations in which contact lines induce adhesion and enhanced friction: hence a frictionless motion, and the possibility of bouncing after impact. All these characteristics can be combined to create devices in which self-propulsion is obtained, using asymmetric textures on the hot solid surface.

We describe the development of mathematical models of ice sheets, focusing on underlying physics and the minimal components that successful models must contain. Our review describes the basic fluid dynamical ice-flow models currently in use; points out numerous poorly understood thermomechanical feedbacks in ice flow; and describes the current, often poorly constrained, state of models for ice-sheet sliding and subglacial drainage, as well as their role in ice-stream dynamics. We conclude with a survey of marine ice-sheet models, outlining recent developments of self-consistent free-boundary models and ongoing research into three-dimensional marine ice sheets.

Aqueous foams are complex fluids composed of gas bubbles tightly packed in a surfactant solution. Even though they generally consist only of Newtonian fluids, foam flow obeys nonlinear laws. This can result from nonaffine deformations of the disordered bubble packing as well as from a coupling between the surface flow in the surfactant monolayers and the bulk liquid flow in the films, channels, and nodes. A similar coupling governs the permeation of liquid through the bubble packing that is observed when foams drain due to gravity. We review the experimental state of the art as well as recent models that describe the interplay of the processes at multiple length scales involved in foam drainage and rheology.

The speed at which a liquid can move over a solid surface is strongly limited when a three-phase contact line is present, separating wet from dry regions. When enforcing large contact line speeds, this leads to the entrainment of drops, films, or air bubbles. In this review, we discuss experimental and theoretical progress revealing the physical mechanisms behind these dynamical wetting transitions. In this context, we discuss microscopic processes that have been proposed to resolve the moving–contact line paradox and identify the different dynamical regimes of contact line motion.

Motivated by the need to resolve the condensation-coalescence bottleneck in warm rain formation, a significant number of studies have emerged in the past 15 years concerning the growth of cloud droplets by water-vapor diffusion and by collision-coalescence in a turbulent environment. With regard to condensation, recent studies suggest that small-scale turbulence alone does not produce a significant broadening of the cloud-droplet spectrum because of the smearing of droplet-scale fluctuations by rapid turbulent and gravitational mixing. However, different diffusional-growth histories associated with large-eddy hopping could lead to a significant spectral broadening. In contrast, small-scale turbulence in cumulus clouds makes a significant contribution to the collision-coalescence of droplets, enhancing the collection kernel up to a factor of 5, especially for droplet pairs with a low gravitational collision rate. This moderate level of enhancement has a significant impact on warm rain initiation. The multiscale nature of turbulent cloud microphysical processes and open research issues are delineated throughout.

Fluid mechanics is involved in the growth, progression, metastasis, and therapy of cancer. Blood vessels transport oxygen and nutrients to cancerous tissues, provide a route for metastasizing cancer cells to distant organs, and deliver drugs to tumors. The irregular and leaky tumor vasculature is responsible for increased interstitial pressure in the tumor microenvironment, whereas multiscale flow-structure interaction processes control tumor growth, metastasis, and nanoparticle-mediated drug delivery. We outline these flow-mediated processes, along with related experimental and computational methods for the diagnosis, predictive modeling, and therapy of cancer.

This article reviews theory and applications of Koopman modes in fluid mechanics. Koopman mode decomposition is based on the surprising fact, discovered in Mezić (2005), that normal modes of linear oscillations have their natural analogs—Koopman modes—in the context of nonlinear dynamics. To pursue this analogy, one must change the representation of the system from the state-space representation to the dynamics governed by the linear Koopman operator on an infinite-dimensional space of observables. Whereas Koopman in his original paper dealt only with measure-preserving transformations, the discussion here is predominantly on dissipative systems arising from Navier-Stokes evolution. The analysis is based on spectral properties of the Koopman operator. Aspects of point and continuous parts of the spectrum are discussed. The point spectrum corresponds to isolated frequencies of oscillation present in the fluid flow, and also to growth rates of stable and unstable modes. The continuous part of the spectrum corresponds to chaotic motion on the attractor. A method of computation of the spectrum and the associated Koopman modes is discussed in terms of generalized Laplace analysis. When applied to a generic observable, this method uncovers the full point spectrum. A computational alternative is given by Arnoldi-type methods, leading to so-called dynamic mode decomposition, and I discuss the connection and differences between these two methods. A number of applications are reviewed in which decompositions of this type have been pursued. Koopman mode theory unifies and provides a rigorous background for a number of different concepts that have been advanced in fluid mechanics, including global mode analysis, triple decomposition, and dynamic mode decomposition.

It is common for jets of fluid to interact with crossflow. This article reviews our understanding of the physical behavior of this important class of flow in the incompressible and compressible regimes. Experiments have significantly increased in sophistication over the past few decades, and recent experiments provide data on turbulence quantities and scalar mixing. Quantitative data at high speeds are less common, and visualization still forms an important component in estimating penetration and mixing. Simulations have progressed from the Reynolds-averaged methodology to large-eddy and hybrid methodologies. There is a general consensus on the qualitative structure of the flow at low speeds; however, the flow structure at low-velocity ratios (jet speed/crossflow speed) might be fundamentally different from the common notion of shear-layer vortices, counter-rotating vortex pairs, wakes, and horseshoe vortices. Fluid in the near field is strongly accelerated, which affects the jet trajectory, entrainment, and mixing behavior. At low speeds, mixing depends more on Reynolds number than the jet trajectory or spatial extent does. Turbulence kinetic energy budgets are discussed that reveal the considerable nonequilibrium nature of the flow and the consequent challenges posed to time-averaged prediction methodologies. The parameter space at high speeds is fairly large, and even experimentally derived correlations for trajectories show significant scatter. Coherent motions in high-speed jets are seen to entrain large amounts of crossflow fluid but do not mix effectively in the near field.

Particle image velocimetry (PIV) has evolved to be the dominant method for velocimetry in experimental fluid mechanics and has contributed to many advances in our understanding of turbulent and complex flows. In this article we review the achievements of PIV and its latest implementations: time-resolved PIV for the rapid capture of sequences of vector fields; tomographic PIV for the capture of fully resolved volumetric data; and statistical PIV, designed to optimize measurements of mean statistical quantities rather than instantaneous fields. In each implementation, the accuracy and spatial resolution are limited. To advance the method to the next level, we need a completely new approach. We consider the fundamental limitations of two-pulse PIV in terms of its dynamic ranges. We then discuss new paths and developments that hold the promise of achieving a fundamental reduction in uncertainty.

This article presents a review of the fluid dynamics, flow-structure interactions, and acoustics associated with human phonation and speech. Our voice is produced through the process of phonation in the larynx, and an improved understanding of the underlying physics of this process is essential to advancing the treatment of voice disorders. Insights into the physics of phonation and speech can also contribute to improved vocal training and the development of new speech compression and synthesis schemes. This article introduces the key biomechanical features of the laryngeal physiology, reviews the basic principles of voice production, and summarizes the progress made over the past half-century in understanding the flow physics of phonation and speech. Laryngeal pathologies, which significantly enhance the complexity of phonatory dynamics, are discussed. After a thorough examination of the state of the art in computational modeling and experimental investigations of phonatory biomechanics, we present a synopsis of the pacing issues in this arena and an outlook for research in this fascinating subject.

An erodible bed sheared by a fluid flow, gas or liquid, is generally unstable, and bed forms grow. This review discusses the following issues, in light of the recent literature: What are the relevant dynamical mechanisms controlling the emergence of bed forms? Do they form by linear instability or nonlinear processes such as pattern coarsening? What determines their timescales and length scales, so different in air and water? What are the similarities and differences between aeolian and subaqueous patterns? What is the influence of the mode of transport: bed load, saltation, or suspension? Can bed forms emerge under any hydrodynamical regime, laminar and turbulent? Guided by these questions, we propose a unified description of bed-form growth and saturation, emphasizing the hydrodynamical regime in the inner layer and the relaxation phenomena associated with particle transport.

Serious heat-transfer deterioration may occur in fluids at supercritical pressure owing to the effects of buoyancy, flow acceleration, and significant variations in thermophysical properties. Although there have been numerous experimental studies on this subject, no single heat-transfer correlation has been found to be capable of describing this phenomenon accurately. Relatively few experimental studies have been carried out on the fluid mechanics of supercritical flows because of the technical difficulties of dealing with turbulent flows and high heat fluxes simultaneously. Conversely, many computational fluid dynamics studies have examined a number of low-Reynolds-number turbulence models. However, none have reproduced the buoyancy production of turbulence reasonably well because of limitations with the use of a constant turbulent Prandtl number. Direct numerical simulations may provide more insight into the physics of fluids at supercritical pressure within a limited range of flow and heat-transfer conditions.