We present a brief account of Anatol Roshko's research and educational contributions to fluid mechanics, focusing on the spirit of his transformative ideas and legacy.

David J. Benney (1930–2015) was an applied mathematician and fluid dynamicist whose highly original work has shaped our understanding of nonlinear wave and instability processes in fluid flows. This article discusses the new paradigm he pioneered in the study of nonlinear phenomena, which transcends fluid mechanics, and it highlights the common threads of his research contributions, namely, resonant nonlinear wave interactions; the derivation of nonlinear evolution equations, including the celebrated nonlinear Schrödinger equation for modulated wave trains; and the significance of three-dimensional disturbances in shear flow instability and transition.

A spectacular resurgence of interest in the topic of ocean wave/sea ice interactions has unfolded over the last two decades, fueled primarily by the deleterious ramifications of global climate change on the polar seas. The Arctic is particularly affected, with a widespread reduction of the extent, thickness, and compactness of its sea ice during the summer, creating an ice cover that is analogous to that in the Southern Ocean surrounding Antarctica. With the additional fetches over which waves can form and mature within more open ice fields, there has also been a documented global uptrend of winds and wave height, which is most severe at high latitudes. Bigger ocean waves affect the way sea ice forms, contribute to how the ice edge moves, penetrate farther into the sea ice, have more destructive power to break up the ice and to change the distribution of floe sizes because the ice is weaker, and assist in lateral melting. These feedbacks collectively identify a parametrization currently absent from Earth system models, as well as shortcomings in wave forecasts arising from limited understanding of the impact of sea ice on ocean waves.

Rigid or deformable bodies moving through continuously stratified layers or across sharp interfaces are involved in a wide variety of geophysical and engineering applications, with both miscible and immiscible fluids. In most cases, the body moves while pulling a column of fluid, in which density and possibly viscosity differ from those of the neighboring fluid. The presence of this column usually increases the fluid resistance to the relative body motion, frequently slowing down its settling or rise in a dramatic manner. This column also exhibits specific dynamics that depend on the nature of the fluids and on the various physical parameters of the system, especially the strength of the density/viscosity stratification and the relative magnitude of inertia and viscous effects. In the miscible case, as stratification increases, the wake becomes dominated by the presence of a downstream jet, which may undergo a specific instability. In immiscible fluids, the viscosity contrast combined with capillary effects may lead to strikingly different evolutions of the column, including pinch-off followed by the formation of a drop that remains attached to the body, or a massive fragmentation phenomenon. This review discusses the flow organization and its consequences on the body motion under a wide range of conditions, as well as potentialities and limitations of available models aimed at predicting the body and column dynamics.

Since the Annual Review of Fluid Mechanics review of mushy layers by Worster (1997), there have been significant advances in the understanding of convective processes in mushy layers. These advances have come in the areas of (a) more detailed analysis, computation, and understanding of convective instabilities and chimney convection in binary alloys; (b) investigations of diffusive and convective transport processes in ternary alloys; and (c) applications of mushy layer theory in materials science, sea ice, and polar climate modeling, as well as other geophysical applications such as the convective dynamics of the Earth's core. Our objective for this review is to provide an updated account of the understanding of mushy layer convection and related applications and, in doing so, to provide a new resource to the fluid dynamics research community interested in these complex systems.

Shear thickening is the increase of the apparent viscosity as shear rate or shear stress increases. This phenomenon is pronounced in concentrated (dense) suspensions of both colloidal-scale and larger particles, with an abrupt form, known as discontinuous shear thickening, observed as the maximum flowable solid fraction is approached. An overview of observed shear thickening behavior is presented, with a discussion of present understanding of the relationship of suspension shear thickening to granular jamming. Mechanistic arguments for the extreme change in rheological properties are outlined, and recent evidence from experiment and simulation for the role of contact forces is presented. Interactions of particles by fluid mechanical lubrication, contact, and steric and electrostatic forces, together with extreme stresses that may lead to solid deformation, require consideration of surface interactions and their tribological consequences in describing shear thickening.

Buoyant plumes form when glacial ice melts directly into the ocean or when subglacial meltwater is discharged to the ocean at depth. They play a key role in regulating heat transport from the ocean to the ice front, and in exporting glacial meltwater to the open ocean. This review summarizes current understanding of the dynamics of these plumes, focusing on theoretical developments and their predictions for submarine melt rates. These predictions are sensitive to ocean temperature, the magnitude and spatial distribution of subglacial discharge, the ambient stratification, and, in the case of sub–ice shelf plumes, the geometry of the ice shelf. However, current understanding relies heavily on parameterizations of melting and entrainment, for which there is little in the way of validation. New observational and experimental constraints are needed to elucidate the structure of the plumes and lend greater confidence to the models.

Turbulent flows in porous media occur in a wide variety of applications, from catalysis in packed beds to heat exchange in nuclear reactor vessels. In this review, we summarize the current state of the literature on methods to model such flows. We focus on a range of Reynolds numbers, covering the inertial regime through the asymptotic turbulent regime. The review emphasizes both numerical modeling and the development of averaged (spatially filtered) balances over representative volumes of media. For modeling the pore scale, we examine the recent literature on Reynolds-averaged Navier–Stokes (RANS) models, large-eddy simulation (LES) models, and direct numerical simulations (DNS). We focus on the role of DNS and discuss how spatially averaged models might be closed using data computed from DNS simulations. A Darcy–Forchheimer-type law is derived, and a prior computation of the permeability and Forchheimer coefficient is presented and compared with existing data.

Acoustic tweezers powerfully enable the contactless collective or selective manipulation of microscopic objects. Trapping is achieved without pretagging, with forces several orders of magnitude larger than optical tweezers at the same input power, limiting spurious heating and enabling damage-free displacement and orientation of biological samples. In addition, the availability of acoustical coherent sources from kilo- to gigahertz frequencies enables the manipulation of a wide spectrum of particle sizes. After an introduction of the key physical concepts behind fluid and particle manipulation with acoustic radiation pressure and acoustic streaming, we highlight the emergence of specific wave fields, called acoustical vortices, as a means to manipulate particles selectively and in three dimensions with one-sided tweezers. These acoustic vortices can also be used to generate hydrodynamic vortices whose topology is controlled by the topology of the wave. We conclude with an outlook on the field's future directions.

Metal films of nanoscale thickness, deposited on substrates and exposed to laser heating, provide systems that involve several interesting multiphysics effects. In addition to fluid mechanical aspects associated with a free boundary setup, other relevant physical effects include phase change, thermal flow, and liquid–solid interactions. Such films are challenging to model, in particular because inertial effects may be relevant, and large contact angles require care when considering the long-wave formulation. Applications of nanoscale metal films are numerous, and the materials science community is actively pursuing more complex setups involving templated films and substrates, bimetallic films and alloys, and a variety of elemental film geometries. The goal of this review is to discuss our current understanding of thin metal film systems, while also providing an overview of the challenges in this research area, which stands at the intersection of fluid mechanics, materials science, and thermal physics.

Soft porous solids can change their shapes by absorbing liquids via capillarity. Such poro-elasto-capillary interactions can be seen in the wrinkling of paper, swelling of cellulose sponges, and morphing of resurrection plants. Here, we introduce physical principles relevant to the phenomena and survey recent advances in the understanding of swelling and shrinkage of bulk soft porous media due to wetting and drying. We then consider various morphing modes of porous sheets, which are induced by localized wetting and swelling of soft porous materials. We focus on physical insights with the aim of triggering novel experimental findings and promoting practical applications.

The laws of wetting are well known for drops on rigid surfaces but change dramatically when the substrate is soft and deformable. The combination of wetting and the intricacies of soft polymeric interfaces have provided many rich examples of fluid–structure interactions, both in terms of phenomenology and from a fundamental perspective. In this review we discuss experimental and theoretical progress on the statics and dynamics of soft wetting. In this context we critically revisit the foundations of capillarity, such as the nature of solid surface tension, the microscopic mechanics near the contact line, and the dissipative mechanisms that lead to unexpected spreading dynamics.

Density variations in fluid flows can arise due to acoustic or thermal fluctuations, compositional changes during mixing of fluids with different molar masses, or phase inhomogeneities. In particular, thermal and compositional (with miscible fluids) density variations have many similarities, such as in how the flow interacts with a shock wave. Two limiting cases have been of particular interest: (a) the single-fluid non-Oberbeck–Boussinesq low–Mach number approximation for flows with temperature variations, which describes vertical convection, and (b) the incompressible limit of mixing between miscible fluids with different molar masses, which describes the Rayleigh–Taylor instability. The equations describing these cases are remarkably similar, with some differences in the molecular transport terms. In all cases, strong inertial effects lead to significant asymmetries of mixing, turbulence, and the shape of mixing layers. In addition, density variations require special attention in turbulence models to avoid viscous contamination of the large scales.

Experiments and numerical simulations have shown that turbulence in transitional wall-bounded shear flows frequently takes the form of long oblique bands if the domains are sufficiently large to accommodate them. These turbulent bands have been observed in plane Couette flow, plane Poiseuille flow, counter-rotating Taylor–Couette flow, torsional Couette flow, and annular pipe flow. At their upper Reynolds number threshold, laminar regions carve out gaps in otherwise uniform turbulence, ultimately forming regular turbulent–laminar patterns with a large spatial wavelength. At the lower threshold, isolated turbulent bands sparsely populate otherwise laminar domains, and complete laminarization takes place via their disappearance. We review results for plane Couette flow, plane Poiseuille flow, and free-slip Waleffe flow, focusing on thresholds, wavelengths, and mean flows, with many of the results coming from numerical simulations in tilted rectangular domains that form the minimal flow unit for the turbulent–laminar bands.

Quantifying submillimeter flows using optical diagnostic techniques is often limited by a lack of spatial resolution and optical access. This review discusses two super-resolution imaging techniques, structured illumination microscopy and total internal reflection fluorescence or microscopy, which can visualize bulk and interfacial flows, respectively, at spatial resolutions below the classic diffraction limits. First, we discuss the theory and applications of structured illumination for optical sectioning, i.e., imaging a thin slice of a flow illuminated over its entire volume. Structured illumination can be used to visualize the interior of multiphase flows such as sprays by greatly reducing secondary scattering. Second, the theory underlying evanescent waves is introduced, followed by a review of how total internal reflection microscopy has been used to visualize interfacial flows over the last 15 years. Both techniques, which are starting to be used in fluid mechanics, could significantly improve quantitative imaging of microscale and macroscale flows.

The ability of some species of owl to fly in effective silence is unique among birds and provides a distinct hunting advantage, but it remains a mystery as to exactly what aspects of the owl and its flight are responsible for this dramatic noise reduction. Crucially, this mystery extends to how the flow physics may be leveraged to generate noise-reduction strategies for wider technological application. We review current knowledge of aerodynamic noise from owls, ranging from live owl noise measurements to mathematical modeling and experiments focused on how owls may disrupt the standard routes of noise generation. Specialized adaptations and foraging strategies are not uniform across all owl species: Some species may not have need for silent flight, or their evolutionary adaptations may not be effective for useful noise reduction for certain species. This hypothesis is examined using mathematical models and borne out where possible by noise measurements and morphological observations of owl feathers and wings.

Fluid–structure interaction is ubiquitous in nature and occurs at all biological scales. Immersed methods provide mathematical and computational frameworks for modeling fluid–structure systems. These methods, which typically use an Eulerian description of the fluid and a Lagrangian description of the structure, can treat thin immersed boundaries and volumetric bodies, and they can model structures that are flexible or rigid or that move with prescribed deformational kinematics. Immersed formulations do not require body-fitted discretizations and thereby avoid the frequent grid regeneration that can otherwise be required for models involving large deformations and displacements. This article reviews immersed methods for both elastic structures and structures with prescribed kinematics. It considers formulations using integral operators to connect the Eulerian and Lagrangian frames and methods that directly apply jump conditions along fluid–structure interfaces. Benchmark problems demonstrate the effectiveness of these methods, and selected applications at Reynolds numbers up to approximately 20,000 highlight their impact in biological and biomedical modeling and simulation.

The term “bioconvection” describes hydrodynamic instabilities and patterns in suspensions of biased swimming microorganisms. Hydrodynamic instabilities arise from coupling between cell swimming behaviors; physical properties of the cells, such as density; and fluid flows. For instance, a combination of viscous and gravitational torques can lead to cells swimming toward downwelling fluid. If the cells are more dense than the fluid, then a gyrotactic instability results. Phototaxis describes the directed response of cells to light, which can also lead to instability. Bioconvection represents a classic system where macroscopic phenomena arise from microscopic cellular behavior in relatively dilute systems. There are ecological consequences for bioconvection and the mechanisms involved as well as potential for industrial exploitation. The focus of this review is on progress measuring and modeling gyrotactic and phototactic bioconvection. It builds on two earlier reviews of bioconvection and recent interest in active matter, describing progress and highlighting open problems.

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from experiments, field measurements, and large-scale simulations at multiple spatiotemporal scales. Machine learning (ML) offers a wealth of techniques to extract information from data that can be translated into knowledge about the underlying fluid mechanics. Moreover, ML algorithms can augment domain knowledge and automate tasks related to flow control and optimization. This article presents an overview of past history, current developments, and emerging opportunities of ML for fluid mechanics. We outline fundamental ML methodologies and discuss their uses for understanding, modeling, optimizing, and controlling fluid flows. The strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experiments, and simulations. ML provides a powerful information-processing framework that can augment, and possibly even transform, current lines of fluid mechanics research and industrial applications.

Many electrochemical and microfluidic systems involve voltage-driven transport of ions from a fluid electrolyte toward an ion-selective interface. These systems are governed by intimate coupling between fluid flow, mass transport, and electrostatic effects. When counterions are driven toward a selective interface, this coupling is shown to lead to a hydrodynamic instability called electroconvection. This phenomenon is an example of electrochemistry inducing flow, which in turn affects the transport and ohmic resistance of the bulk electrolyte. These effects have implications in a wide range of applications, including ion separation, electrodeposition, and microfluidic processes that incorporate ion-selective elements. This review surveys recent investigations of electroconvection with an emphasis on quantitative experimental and theoretical analyses and computational modeling of this phenomenon. Approaches for control and manipulation of this phenomenon in canonical settings are also discussed.

By modifying a physical property of a solution like its density or viscosity, chemical reactions can modify and even trigger convective flows. These flows in turn affect the spatiotemporal distribution of the chemical species. A nontrivial coupling between reactions and flows then occurs. We present simple model systems of this chemo-hydrodynamic coupling. In particular, we illustrate the possibility of chemical reactions controlling or triggering viscous fingering, Rayleigh–Taylor, double-diffusive, and convective dissolution instabilities. We discuss laboratory experiments performed to study these phenomena and compare the experimental results to theoretical predictions. In each case we contrast the chemo-hydrodynamic patterns and instabilities with those that develop in nonreactive systems and unify the different dynamics in terms of the common features of the related spatial mobility profiles.

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.

The dynamics and deformations of immersed flexible fibers are at the heart of important industrial and biological processes, induce peculiar mechanical and transport properties in the fluids that contain them, and are the basis for novel methods of flow control. Here we focus on the low–Reynolds number regime where advances in studying these fiber–fluid systems have been especially rapid. On the experimental side, this is due to new methods of fiber synthesis, microfluidic flow control, and microscope-based tracking measurement techniques. Likewise, there have been continuous improvements in the specialized mathematical modeling and numerical methods needed to capture the interactions of slender flexible fibers with flows, boundaries, and each other.

Major experimental and theoretical studies on microcirculation and hemorheology are reviewed with the focus on mechanics of blood flow and the vascular wall. Flow of the blood formed elements (red blood cells (RBCs), white blood cells or leukocytes (WBCs) and platelets) in individual arterioles, capillaries and venules, and in microvascular networks is discussed. Mechanical and rheological properties of the formed elements and their interactions with the vascular wall are reviewed. Short-term and long-term regulation of the microvasculature is discussed; the modes of regulation include metabolic, myogenic and shear-stress-dependent mechanisms as well as vascular adaptation such as angiogenesis and vascular remodeling.

The coupling of fluid dynamics and biology at the level of the cell is an intensive area of investigation because of its critical role in normal physiology and disease. Microcirculatory flow has been a focus for years, owing to the complexity of cell-cell or cell-glycocalyx interactions. Noncirculating cells, particularly those that comprise the walls of the circulatory system, experience and respond biologically to fluid dynamic stresses. In this article, we review the more recent studies of circulating cells, with an emphasis on the role of the glycocalyx on red-cell motion in small capillaries and on the deformation of leukocytes passing through the microcirculation. We also discuss flows in the vicinity of noncirculating cells, the influence of fluid dynamic shear stress on cell biology, and diffusion in the lipid bi-layer, all in the context of the important fluid-dynamic phenomena.

Much recent evidence suggests that bone cells sense their mechanical environment via interstitial fluid flow. In this review, we summarize theoretical and experimental approaches to quantify fluid and solute transport in bone, starting with the early investigations of fluid shear stress applied to bone cells. The pathways of bone interstitial fluid and solute movement are high-lighted based on recent theoretical models, as well as a new generation of tracer experiments that have clarified and refined the structure and function of the osteocyte pericellular matrix. Then we trace how the fluid-flow models for mechanotransduction have evolved as new ultrastructural features of the osteocyte lacunar-canalicular porosity have been identified and how more recent in vitro fluid-flow and cell-stretch experiments have helped elucidate at the molecular level the possible pathways for cellular excitation in bone.

The initiation and progression of cerebral aneurysms are degenerative processes of the arterial wall driven by a complex interaction of biological and hemodynamic factors. Endothelial cells on the artery wall respond physiologically to blood-flow patterns. In normal conditions, these responses are associated with nonpathological tissue remodeling and adaptation. The combination of abnormal blood patterns and genetics predisposition could lead to the pathological formation of aneurysms. Here, we review recent progress on the basic mechanisms of aneurysm formation and evolution, with a focus on the role of hemodynamic patterns.

This review places modern research developments in vascular mechanobiology in the context of hemodynamic phenomena in the cardiovascular system and the discrete localization of vascular disease. The modern origins of this field are traced, beginning in the 1960s when associations between flow characteristics, particularly blood flow-induced wall shear stress, and the localization of atherosclerotic plaques were uncovered, and continuing to fluid shear stress effects on the vascular lining endothelial) cells (ECs), including their effects on EC morphology, biochemical production, and gene expression. The earliest single-gene studies and genome-wide analyses are considered. The final section moves from the ECs lining the vessel wall to the smooth muscle cells and fibroblasts within the wall that are fluid me chanically activated by interstitial flow that imposes shear stresses on their surfaces comparable with those of flowing blood on EC surfaces. Interstitial flow stimulates biochemical production and gene expression, much like blood flow on ECs.

In the past decade the volvocine green algae, spanning from the unicellular Chlamydomonas to multicellular Volvox, have emerged as model organisms for a number of problems in biological fluid dynamics. These include flagellar propulsion, nutrient uptake by swimming organisms, hydrodynamic interactions mediated by walls, collective dynamics and transport within suspensions of microswimmers, the mechanism of phototaxis, and the stochastic dynamics of flagellar synchronization. Green algae are well suited to the study of such problems because of their range of sizes (from 10 μm to several millimetres), their geometric regularity, the ease with which they can be cultured and the availability of many mutants that allow for connections between molecular details and organism-level behavior. This review summarizes these recent developments and highlights promising future directions in the study of biological fluid dynamics, especially in the context of evolutionary biology, that can take advantage of these remarkable organisms.

Intravascular blood clots form in an environment in which hydrodynamic forces dominate and in which fluid-mediated transport is the primary means of moving material. The clotting system has evolved to exploit fluid dynamic mechanisms and to overcome fluid dynamic challenges to ensure that clots that preserve vascular integrity can form over the wide range of flow conditions found in the circulation. Fluid-mediated interactions between the many large deformable red blood cells and the few small rigid platelets lead to high platelet concentrations near vessel walls where platelets contribute to clotting. Receptor-ligand pairs with diverse kinetic and mechanical characteristics work synergistically to arrest rapidly flowing cells on an injured vessel. Variations in hydrodynamic stresses switch on and off the function of key clotting polymers. Protein transport to, from, and within a developing clot determines whether and how fast it grows. We review ongoing experimental and modeling research to understand these and related phenomena.

John Lumley's contributions to the theory, modeling, and experiments on turbulent flows played a seminal role in the advancement of our understanding of this subject in the second half of the twentieth century. We discuss John's career and his personal style, including his love and deep knowledge of vintage wine and vintage cars. His intellectual contributions range from abstract theory to applied engineering. Here we discuss some of his major advances, focusing on second-order modeling, proper orthogonal decomposition, path-breaking experiments, research on geophysical turbulence, and important contributions to the understanding of drag reduction. John Lumley was also an influential teacher whose books and films have molded generations of students. These and other aspects of his professional career are described.

Bubbly flows involve bubbles randomly distributed within a liquid. At large Reynolds number, they experience an agitation that can combine shear-induced turbulence (SIT), large-scale buoyancy-driven flows, and bubble-induced agitation (BIA). The properties of BIA strongly differ from those of SIT. They have been determined from studies of homogeneous swarms of rising bubbles. Regarding the bubbles, agitation is mainly caused by the wake-induced path instability. Regarding the liquid, two contributions must be distinguished. The first one corresponds to the anisotropic flow disturbances generated near the bubbles, principally in the vertical direction. The second one is the almost isotropic turbulence induced by the flow instability through a population of bubbles, which turns out to be the main cause of horizontal fluctuations. Both contributions generate a k−3 spectral subrange and exponential probability density functions. The subsequent issue will be to understand how BIA interacts with SIT.

Numerical models of surface tension play an increasingly important role in our capacity to understand and predict a wide range of multiphase flow problems. The accuracy and robustness of these models have improved markedly in the past 20 years, so that they are now applicable to complex, three-dimensional configurations of great theoretical and practical interest. In this review, I attempt to summarize the most significant recent developments in Eulerian surface tension models, with an emphasis on well-balanced estimation, curvature estimation, stability, and implicit time stepping, as well as test cases and applications. The advantages and limitations of various models are discussed, with a focus on common features rather than differences. Several avenues for further progress are suggested.

Turbulence closure models are central to a good deal of applied computational fluid dynamical analysis. Closure modeling endures as a productive area of research. This review covers recent developments in elliptic relaxation and elliptic blending models, unified rotation and curvature corrections, transition prediction, hybrid simulation, and data-driven methods. The focus is on closure models in which transport equations are solved for scalar variables, such as the turbulent kinetic energy, a timescale, or a measure of anisotropy. Algebraic constitutive representations are reviewed for their role in relating scalar closures to the Reynolds stress tensor. Seamless and nonzonal methods, which invoke a single closure model, are reviewed, especially detached eddy simulation (DES) and adaptive DES. Other topics surveyed include data-driven modeling and intermittency and laminar fluctuation models for transition prediction. The review concludes with an outlook.

Simulation of compressible flows became a routine activity with the appearance of shock-/contact-capturing methods. These methods can determine all waves, particularly discontinuous ones. However, additional difficulties may appear in two-phase and multimaterial flows due to the abrupt variation of thermodynamic properties across the interfacial region, with discontinuous thermodynamical representations at the interfaces. To overcome this difficulty, researchers have developed augmented systems of governing equations to extend the capturing strategy. These extended systems, reviewed here, are termed diffuse-interface models, because they are designed to compute flow variables correctly in numerically diffused zones surrounding interfaces. In particular, they facilitate coupling the dynamics on both sides of the (diffuse) interfaces and tend to the proper pure fluid–governing equations far from the interfaces. This strategy has become efficient for contact interfaces separating fluids that are governed by different equations of state, in the presence or absence of capillary effects, and with phase change. More sophisticated materials than fluids (e.g., elastic–plastic materials) have been considered as well.

Internal gravity waves play a primary role in geophysical fluids: They contribute significantly to mixing in the ocean, and they redistribute energy and momentum in the middle atmosphere. Until recently, most studies were focused on plane wave solutions. However, these solutions are not a satisfactory description of most geophysical manifestations of internal gravity waves, and it is now recognized that internal wave beams with a confined profile are ubiquitous in the geophysical context. We discuss the reason for the ubiquity of wave beams in stratified fluids, which is related to the fact that they are solutions of the nonlinear governing equations. We focus more specifically on situations with a constant buoyancy frequency. Moreover, in light of recent experimental and analytical studies of internal gravity beams, it is timely to discuss the two main mechanisms of instability for those beams: (a) the triadic resonant instability generating two secondary wave beams and (b) the streaming instability corresponding to the spontaneous generation of a mean flow.

Conventional mineral waste disposal involves pumping dilute concentration suspensions of tailings to large catchment areas, where the solids settle to form a consolidated base while the excess water is evaporated. Unfortunately, this often takes years, if ever, to occur, and the interim period poses a severe threat to the surrounding countryside and water table. A worldwide movement to increase the concentration of these tailings to pastes for disposal above and below ground, obviating some of these issues, has led to the development of new technologies. Increasing the solids concentrations invariably produces non-Newtonian effects that can mask the underlying nature of the suspension mechanics, resulting in the use of poor pipeline and disposal methods. Combining rheological characterization and analysis with non-Newtonian suspension fluid mechanics provides insight into these flows, both laminar and turbulent. These findings provide the necessary basis for successful engineering designs.

Fire whirls present a powerful intensification of combustion, long studied in the fire research community because of the dangers they present during large urban and wildland fires. However, their destructive power has hidden many features of their formation, growth, and propagation. Therefore, most of what is known about fire whirls comes from scale modeling experiments in the laboratory. Both the methods of formation, which are dominated by wind and geometry, and the inner structure of the whirl, including velocity and temperature fields, have been studied at this scale. Quasi-steady fire whirls directly over a fuel source form the bulk of current experimental knowledge, although many other cases exist in nature. The structure of fire whirls has yet to be reliably measured at large scales; however, scaling laws have been relatively successful in modeling the conditions for formation from small to large scales. This review surveys the state of knowledge concerning the fluid dynamics of fire whirls, including the conditions for their formation, their structure, and the mechanisms that control their unique state. We highlight recent discoveries and survey potential avenues for future research, including using the properties of fire whirls for efficient remediation and energy generation.

The primary purpose of a detonation in a high explosive (HE) is to provide the energy to drive a surrounding confiner, typically for mining or munitions applications. The details of the interaction between an HE detonation and its confinement are essential to achieving the objectives of the explosive device. For the high pressures induced by detonation loading, both the solid HE and confiner materials will flow. The structure and speed of a propagating detonation, and ultimately the pressures generated in the reaction zone to drive the confiner, depend on the induced flow both within the confiner and along the HE–confiner material interface. The detonation–confiner interactions are heavily influenced by the material properties and, in some cases, the thickness of the confiner. This review discusses the use of oblique shock polar analysis as a means of characterizing the possible range of detonation–confiner interactions. Computations that reveal the fluid mechanics of HE detonation–confiner interactions for finite reaction-zone length detonations are discussed and compared with the polar analysis. This includes cases of supersonic confiner flow; subsonic, shock-driven confiner flow; subsonic, but shockless confiner flow; and sonic flow at the intersection of the detonation shock and confiner material interface. We also summarize recent developments, including the effects of geometry and porous material confinement, on detonation–confiner interactions.

Slamming, the violent impact between a liquid and solid, has been known to be important for a long time in the ship hydrodynamics community. More recently, applications ranging from the transport of liquefied natural gas (LNG) in LNG carriers to the harvesting of wave energy with oscillating wave surge converters have led to renewed interest in the topic. The main reason for this renewed interest is that the extreme impact pressures generated during slamming can affect the integrity of the structures involved. Slamming fluid mechanics is challenging to describe, as much from an experimental viewpoint as from a numerical viewpoint, because of the large span of spatial and temporal scales involved. Even the physical mechanisms of slamming are challenging: What physical phenomena must be included in slamming models? An important issue deals with the practical modeling of slamming: Are there any simple models available? Are numerical models viable? What are the consequences for the design of structures? This article describes the loading processes involved in slamming, offers state-of-the-art results, and highlights unresolved issues worthy of further research.

This work reviews present knowledge of double-diffusive convection at low Prandtl number obtained using direct numerical simulations, in both the fingering regime and the oscillatory regime. Particular emphasis is given to modeling the induced turbulent mixing and its impact in various astrophysical applications. The nonlinear saturation of fingering convection at low Prandtl number usually drives small-scale turbulent motions whose transport properties can be predicted reasonably accurately using a simple semi-analytical model. In some instances, large-scale internal gravity waves can be excited by a collective instability and eventually cause layering. The nonlinear saturation of oscillatory double-diffusive convection exhibits much more complex behavior. Weakly stratified systems always spontaneously transition into layered convection associated with very efficient mixing. More strongly stratified systems remain dominated by weak wave turbulence unless they are initialized into a layered state. The effects of rotation, shear, lateral gradients, and magnetic fields are briefly discussed.