Annual Review of Fluid Mechanics - Volume 51, 2019

Subrahmanyan Chandrasekhar (1910–1995) is justly famous for his lasting contributions to topics such as white dwarfs and black holes (which led to his Nobel Prize), stellar structure and dynamics, general relativity, and other facets of astrophysics. He also devoted some dozen or so of his prime years to fluid dynamics, especially stability and turbulence, and made important contributions. Yet in most assessments of his science, far less attention is paid to his fluid dynamics work because it is dwarfed by other, more prominent work. Even within the fluid dynamics community, his extensive research on turbulence and other problems of fluid dynamics is not well known. This review is a brief assessment of that work. After a few biographical remarks, I recapitulate and assess the essential parts of this work, putting my remarks in the context of times and people with whom Chandrasekhar interacted. I offer a few comments in perspective on how he came to work on turbulence and stability problems, on how he viewed science as an aesthetic activity, and on how one's place in history gets defined.

The placenta is a multifunctional organ that exchanges blood gases and nutrients between a mother and her developing fetus. In humans, fetal blood flows through intricate networks of vessels confined within villous trees, the branches of which are bathed in pools of maternal blood. Fluid mechanics and transport processes play a central role in understanding how these elaborate structures contribute to the function of the placenta and how their disorganization may lead to disease. Recent advances in imaging and computation have spurred significant advances in simulations of fetal and maternal flows within the placenta across a range of length scales. Models describe jets of maternal blood emerging from spiral arteries into a disordered and deformable porous medium, as well as solute uptake by fetal blood flowing through elaborate three-dimensional capillary networks. We survey recent developments and emerging challenges in modeling flow and transport in this complex organ.

Modeling wall turbulence remains a major challenge, as a sufficient physical understanding of these flows is still lacking. In an effort to move toward a physics-based model, A.A. Townsend introduced the hypothesis that the dominant energy-containing motions in wall turbulence are due to large eddies attached to the wall. From this simple hypothesis, the attached eddy model evolved, which has proven to be highly effective in predicting velocity statistics and providing a framework for interpreting the energy-containing flow physics at high Reynolds numbers. This review summarizes the hypothesis itself and the modeling attempts made thereafter, with a focus on the validity of the model's assumptions and its limitations. Here, we review studies on this topic, which have markedly increased in recent years, highlighting refinements, extensions, and promising future directions for attached eddy modeling.

The leading-edge vortex (LEV) is known to produce transient high lift in a wide variety of circumstances. The underlying physics of LEV formation, growth, and shedding are explored for a set of canonical wing motions including wing translation, rotation, and pitching. A review of the literature reveals that, while there are many similarities in the LEV physics of these motions, the resulting force histories can be dramatically different. In two-dimensional motions (translation and pitch), the LEV sheds soon after its formation; lift drops as the LEV moves away from the wing. Wing rotation, in contrast, incites a spanwise flow that, through Coriolis tilting, balances the streamwise vorticity fluxes to produce an LEV that remains attached to much of the wing and thus sustains high lift. The state of the art of vortex-based modeling to capture both the flow field and corresponding forces of these motions is reviewed, including closure conditions at the leading edge and approaches for data-driven strategies.

The systematic breaking of left–right body symmetry is a familiar feature of human physiology. In humans and many animals, this process originates with asymmetric fluid flow driven by rotating cilia, occurring in a short-lived embryonic organizing structure termed the node. The very low–Reynolds number fluid mechanics of this system is reviewed; important features include how cilia rotation combines with tilt to produce asymmetric flow, boundary effects, time dependence, and the interpretation of particle tracking experiments. The effect of perturbing cilia length and number is discussed and compared in mouse and zebrafish. Whereas understanding of this process has advanced significantly over the past two decades, there is still no consensus on how flow is converted to asymmetric gene expression, with most research focusing on resolving mechanical versus morphogen sensing. The underlying process may be more subtle, probably involving a combination of these effects, with fluid mechanics playing a central role.

Large-amplitude internal waves induce currents and turbulence in the bottom boundary layer (BBL) and are thus a key driver of sediment movement on the continental margins. Observations of internal wave–induced sediment resuspension and transport cover significant portions of the world's oceans. Research on BBL instabilities, induced by internal waves, has identified several mechanisms by which the BBL is energized and sediment may be resuspended. Due to the complexity of the induced currents, process-oriented research using theory, direct numerical simulations, and laboratory experiments has played a vital role. However, experiments and simulations have inherent limitations as analogs for oceanic conditions due to disparities in Reynolds number and grid resolution, respectively. Parameterizations are needed for modeling resuspension from observed data and in larger-scale models, with the efficacy of parameterizations based on the quadratic stress largely determining the accuracy of present field-scale efforts.

The presence of electric fields in immiscible multifluid flows induces Maxwell stresses at sharp interfaces that can produce electrohydrodynamic phenomena of practical importance. Electric fields can be stabilizing or destabilizing depending on their strength and orientation. In microfluidics, fields can be used to drive systems out of equilibrium to produce hierarchical patterning, mixing, and phase separation. We describe nonlinear theories of electrohydrodynamic instabilities in immiscible multilayer flows in several geometries, including flows over or inside planar or topographically structured substrates and channels and flows in cylinders and cylindrical annuli. Matched asymptotic techniques are developed for two- and three-dimensional flows, and reduced-dimension nonlinear models are derived and studied. When all regions are slender, electrostatic extensions to lubrication or shallow-wave theories are derived. In the presence of nonslender layers, nonlocal terms emerge naturally to modify the evolution equations. Analysis and computations provide a plethora of dynamics, including nonlinear traveling waves, spatiotemporal chaos, and singularity formation. Direct numerical simulations are used to evaluate the models and go beyond their range of validity to quantify phenomena such as electric field–induced directed patterning, suppression of Rayleigh–Taylor instabilities, and electrostatically induced pumping in microchannels. Comparisons of theory and simulations with available experiments are included throughout.

Lakes and other confined water bodies are not exposed to tides, and their wind forcing is usually much weaker compared to ocean basins and estuaries. Hence, convective processes are often the dominant drivers for shaping mixing and stratification structures in inland waters. Due to the diverse environments of lakes—defined by local morphological, geochemical, and meteorological conditions, among others—a fascinating variety of convective processes can develop with remarkably unique signatures. Whereas the classical cooling-induced and shear-induced convections are well-known phenomena due to their dominant roles in ocean basins, other convective processes are specific to lakes and often overlooked, for example, sidearm, under-ice, and double-diffusive convection or thermobaric instability and bioconvection. Additionally, the peculiar properties of the density function at low salinities/temperatures leave distinctive traces. In this review, we present these various processes and connect observations with theories and model results.

This review focuses on direct numerical simulations (DNS) of turbulent flows laden with droplets or bubbles. DNS of these flows are more challenging than those of flows laden with solid particles due to the surface deformation in the former. The numerical methods discussed are classified by whether the initial diameter of the bubble/droplet is smaller or larger than the Kolmogorov length scale and whether the instantaneous surface deformation is fully resolved or obtained via a phenomenological model. Also discussed are numerical methods that account for the breakup of a single droplet or bubble, as well as multiple droplets or bubbles in canonical turbulent flows.

Mixing is the operation by which a system evolves under stirring from one state of simplicity—the initial segregation of the constituents—to another state of simplicity—their complete uniformity. Between these extremes, patterns emerge, possibly interact, and die sooner or later. This review summarizes recent developments on the problem of mixing in its lamellar representation. This point of view visualizes a mixture as a set of stretched lamellae, or sheets, possibly interacting with each other. It relies on a near-exact formulation of the Fourier equation on a moving substrate and allows one to bridge the spatial structure and evolution of the concentration field with its statistical content in a direct way. Within this frame, one can precisely describe both the dynamics of the concentration levels in a mixture as a function of the intensity of the stirring motions at the scale of a single lamella and the interaction rule between adjacent lamellae, thus offering a detailed representation of the mixture content, its structure, and their evolution in time.

Tide-locked planets are planets in which tidal stresses from the host star have spun down the planet's rotation to the point where its length of sidereal day equals its length of year. In a nearly circular orbit, such planets have a permanent dayside and a permanent nightside, leading to extreme heating contrasts. In this article, the atmospheric circulations forced by this heating contrast are explored, with a focus on terrestrial planets; here, “terrestrial” refers to planets with a condensed solid or liquid surface at which most of the incident stellar radiation is absorbed and does not imply habitability in the Earthlike sense. The census of exoplanets contains many terrestrial planets that are very likely to be tide locked, including extremely hot close-orbit planets around Sunlike stars and habitable zone (and hotter) planets around lower-mass stars. The circulations are discussed in terms of fluid dynamical concepts arising from study of the Earth's tropics, supplemented by general circulation model simulations. Even in the relatively simple context of dry (noncondensing) dynamics, there are a number of important unresolved issues that require further study.

The 1969 review by J.R. Melcher and G.I. Taylor defined the field of electrohydrodynamics. Fifty years on, the interaction of weakly conducting (leaky dielectric) fluids with electric fields continues to yield intriguing phenomena. The prototypical system of a drop in a uniform electric field has revealed remarkable dynamics in strong electric fields such as symmetry-breaking instabilities (e.g., Quincke rotation) and streaming from the drop equator. This review summarizes recent experimental and theoretical studies in the area of fluid particles (drop and vesicles) in electric fields, with a focus on the transient dynamics and extreme deformations. A theoretical framework to treat the time evolution of nearly spherical shapes is provided. The model has been successful in describing the dynamics of vesicles (closed lipid membranes) in an electric field, highlighting the broader range of applicability of the leaky dielectric approach.

Bubbles are present in a large variety of emerging applications, from advanced materials to biology and medicine, as either laser-generated or acoustically driven bubbles. In these applications, the bubbles undergo oscillatory dynamics and collapse inside—or near—soft and biological materials. The presence of a soft, viscoelastic medium strongly affects the bubble dynamics, both its linear resonance properties and its nonlinear behavior. Surfactant molecules or solid particles adsorbed on a bubble surface can also modify the bubble dynamics through the rheological properties of the interfacial layer. Furthermore, the interaction of bubbles with biological cells and tissues is highly dependent on the mechanical properties of these soft deformable media. This review covers recent developments in bubble dynamics in soft and biological matter for different confinement conditions: bubbles in a viscoelastic medium, coated by a viscoelastic layer, or in the vicinity of soft confinement or objects. The review surveys current work in the field and illustrates open questions for future research.

Data from experiments and direct simulations of turbulence have historically been used to calibrate simple engineering models such as those based on the Reynolds-averaged Navier–Stokes (RANS) equations. In the past few years, with the availability of large and diverse data sets, researchers have begun to explore methods to systematically inform turbulence models with data, with the goal of quantifying and reducing model uncertainties. This review surveys recent developments in bounding uncertainties in RANS models via physical constraints, in adopting statistical inference to characterize model coefficients and estimate discrepancy, and in using machine learning to improve turbulence models. Key principles, achievements, and challenges are discussed. A central perspective advocated in this review is that by exploiting foundational knowledge in turbulence modeling and physical constraints, researchers can use data-driven approaches to yield useful predictive models.

Hypersonic flows are energetic and result in regions of high temperature, causing internal energy excitation, chemical reactions, ionization, and gas-surface interactions. At typical flight conditions, the rates of these processes are often similar to the rate of fluid motion. Thus, the gas state is out of local thermodynamic equilibrium and must be described by conservation equations for the internal energy and chemical state. Examples illustrate how competition between rates in hypersonic flows can affect aerodynamic performance, convective heating, boundary layer transition, and ablation. The conservation equations are outlined, and the most widely used models for internal energy relaxation, reaction rates, and transport properties are reviewed. Gas-surface boundary conditions are described, including finite-rate catalysis and slip effects. Recent progress in the use of first-principles calculations to understand and quantify critical gas-phase reactions is discussed. An advanced finite-rate carbon ablation model is introduced and is used to illustrate the role of rate processes at hypersonic conditions.

Since the discovery of Brownian motion in bulk fluids by Robert Brown in 1827, Brownian motion at long timescales has been extensively studied both theoretically and experimentally for over a century. The theory for short-timescale Brownian motion was also well established in the last century, while experimental studies were not accessible until this decade. This article reviews experimental progress on short-timescale Brownian motion and related applications. The ability to measure instantaneous velocity enables new fundamental tests of statistical mechanics of Brownian particles, such as the Maxwell–Boltzmann velocity distribution and the energy equipartition theorem. In addition, Brownian particles can be used as probes to study boundary effects imposed by a solid wall, wettability at solid–fluid interfaces, and viscoelasticity. We propose future studies of fluid compressibility and nonequilibrium physics using short-duration pulsed lasers. Lastly, we also propose that an optically trapped particle can serve as a new testing ground for nucleation in a supersaturated vapor or a supercooled liquid.

Liquid invasion into a porous medium is a phenomenon of great importance in both nature and technology. Despite its enormous importance, there is a surprisingly sparse understanding of the processes occurring on the scale of individual pores and of how these processes determine the global invasion pattern. In particular, the exact influence of the wettability remains unclear besides the limiting cases of very small or very large contact angles of the invading fluid. Most quantitative pore-scale experiments and theoretical considerations have been conducted in effectively two-dimensional (2D) micromodels and Hele–Shaw geometries. Although these pioneering works helped to unravel some of the physical aspects of the displacement processes, the relevance of 2D models has not always been appreciated for natural porous media. With the availability of X-ray microtomography, 3D imaging has become a standard for exploring pore-scale processes in porous media. Applying advanced postprocessing routines and synchrotron microtomography, researchers can image even slow flow processes in real time and extract relevant material parameters like the contact angle from the interfaces in the pore space. These advances are expected to boost both theoretical and experimental understanding of pore-scale processes in natural porous media.

This article reviews the nonlinear stability theories that have been developed to explain laminar–turbulent transition processes in boundary and free shear layers. For such spatially developing shear flows, a high–Reynolds number approach is necessary to account for, in a systematic and self-consistent manner, multiple competing physical factors, such as nonlinearity, nonparallelism, nonequilibrium, and viscosity. While the basic ideas and fundamental mechanisms are rooted in the classical weakly nonlinear theory, which was formulated primarily for exactly parallel flows and on the basis of finite Reynolds number, the high–Reynolds number formulations lead to low-dimensional evolution systems, which differ significantly from the finite–Reynolds number counterparts and better describe the observations. Owing to efforts in the past 30 years or so, nonlinear evolution systems have been derived for inviscid Rayleigh modes, viscous Tollmien–Schlichting waves, (first and second) Mack modes, and cross-flow vortices. Theories have also been developed for nonlinear intermodal interactions, including oblique mode interaction, subharmonic resonance, phase-locked interactions, and fundamental resonance; these underpin many intriguing behaviors in the three-dimensional stages of transition. These theories and results explain several key nonlinear features observed and should play a useful role in guiding future experimental and numerical investigations.

A remarkable number of different flow phenomena contribute critically to the proper functioning of the hearing and balance senses, both of which are hosted by the inner ear. This includes quasi-steady and high-frequency Stokes flow, incompressible wave guides, unsteady boundary layers, and fluid–structure interactions between viscous fluids, soft membranes, and hair cell bundles. We present these phenomena, review recent results, and discuss how they relate to the physiology of the vestibular system and the mechanics of hearing. In addition, we study flow phenomena, including gravity-driven particulate flow, magnetohydrodynamics, buoyancy, and steady streaming, that are related to pathologies of the inner ear and relevant to diagnosis and treatment of these diseases.

Fungi are the dark matter of biology, typically leading cryptic lives, buried in soil or inside of plants or other organisms, and emerging into the light only when they build their elegantly engineered fruiting bodies. Ecological success across so many niches has required that they solve many challenging fluid mechanical problems of growth, dispersal, and transport of fluids across networks. Study of fungal life histories by fluid mechanicians has shown their exquisite capability for engineering and revealed new organizing ideas for understanding fungal diversity.