Annual Review of Fluid Mechanics - Volume 52, 2020

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.