Annual Review of Fluid Mechanics - Volume 49, 2017

Bill Reynolds was a remarkably creative scientist who combined a natural curiosity with enormous energy to make significant contributions to fluid mechanics research. In this article, we combine our own recollections with those of many others to capture the aspects of Bill's personality and sense of humor that made him the irrepressible person that he was. We discuss his works on turbulent flow and touch on others that illustrate the wide range of his interests. We survey his involvement in education through classroom teaching and mentoring of research students, and his lifelong support of the Division of Fluid Dynamics of the American Physical Society. And we cover his many contributions during his long career at Stanford University, where he spent his entire working life, especially his seminal role with the Center for Turbulence Research.

Research activities on inflow turbulence generation methods have been vigorous over the past quarter century, accompanying advances in eddy-resolving computations of spatially developing turbulent flows with direct numerical simulation, large-eddy simulation (LES), and hybrid Reynolds-averaged Navier-Stokes–LES. The weak recycling method, rooted in scaling arguments on the canonical incompressible boundary layer, has been applied to supersonic boundary layer, rough surface boundary layer, and microscale urban canopy LES coupled with mesoscale numerical weather forecasting. Synthetic methods, originating from analytical approximation to homogeneous isotropic turbulence, have branched out into several robust methods, including the synthetic random Fourier method, synthetic digital filtering method, synthetic coherent eddy method, and synthetic volume forcing method. This article reviews major progress in inflow turbulence generation methods with an emphasis on fundamental ideas, key milestones, representative applications, and critical issues. Directions for future research in the field are also highlighted.

Space-time correlation is a staple method for investigating the dynamic coupling of spatial and temporal scales of motion in turbulent flows. In this article, we review the space-time correlation models in both the Eulerian and Lagrangian frames of reference, which include the random sweeping and local straining models for isotropic and homogeneous turbulence, Taylor's frozen-flow model and the elliptic approximation model for turbulent shear flows, and the linear-wave propagation model and swept-wave model for compressible turbulence. We then focus on how space-time correlations are used to develop time-accurate turbulence models for the large-eddy simulation of turbulence-generated noise and particle-laden turbulence. We briefly discuss their applications to two-point closures for Kolmogorov's universal scaling of energy spectra and to the reconstruction of space-time energy spectra from a subset of spatial and temporal signals in experimental measurements. Finally, we summarize the current understanding of space-time correlations and conclude with future issues for the field.

This review describes recent progress in the fundamental understanding of deformable drop motion through porous media with well-defined microstructures, through rigorous first-principles hydrodynamical simulations and experiments. Tight squeezing conditions, when the drops are much larger than the pore throats, are particularly challenging numerically, as the drops nearly coat the porous material skeleton with small surface clearance, requiring very high surface resolution in the algorithms. Small-scale prototype problems for flow-induced drop motion through round capillaries and three-dimensional (3D) constrictions between solid particles, and for gravity-induced squeezing through round orifices and 3D constrictions, show how forcing above critical conditions is needed to overcome trapping. Scaling laws for the squeezing time are suggested. Large-scale multidrop/multiparticle simulations for emulsion flow through a random granular material with multiple drop breakup show that the drop phase generally moves faster than the carrier fluid; both phase velocities equilibrate much faster to the statistical steady state than does the drop-size distribution.

When a premixed flame propagates in a turbulent flow, not only does turbulence affect the burning rate (e.g., by wrinkling the flame and increasing its surface area), but also the heat release in the flame perturbs the pressure field, and these pressure perturbations affect the turbulent flow and scalar transport. For instance, the latter effects manifest themselves in the so-called countergradient turbulent scalar flux, which has been documented in various flames and has challenged the combustion community for approximately 35 years. Over the past decade, substantial progress has been made in investigating (a) the influence of thermal expansion in a premixed flame on the turbulent flow and turbulent scalar transport within the flame brush, as well as (b) the feedback influence of countergradient scalar transport on the turbulent burning rate. The present article reviews recent developments in this field and outlines issues to be solved in future research.

Basic fluid equations are the main ingredient in the development of theories of Rayleigh–Taylor buoyancy-induced instability. Turbulence arises in the late stage of the instability evolution as a result of the proliferation of active scales of motion. Fluctuations are maintained by the unceasing conversion of potential energy into kinetic energy. Although the dynamics of turbulent fluctuations is ruled by the same equations controlling the Rayleigh–Taylor instability, here only phenomenological theories are currently available. The present review provides an overview of the most relevant (and often contrasting) theoretical approaches to Rayleigh–Taylor turbulence together with numerical and experimental evidence for their support. Although the focus is mainly on the classical Boussinesq Rayleigh–Taylor turbulence of miscible fluids, the review extends to other fluid systems with viscoelastic behavior, affected by rotation of the reference frame, and, finally, in the presence of reactions.

Cloud entrainment, the mixing between cloudy and clear air at the boundary of clouds, constitutes one paradigm for the relevance of small scales in the Earth system: By regulating cloud lifetimes, meter- and submeter-scale processes at cloud boundaries can influence planetary-scale properties. Understanding cloud entrainment is difficult given the complexity and diversity of the associated phenomena, which include turbulence entrainment within a stratified medium, convective instabilities driven by radiative and evaporative cooling, shear instabilities, and cloud microphysics. Obtaining accurate data at the required small scales is also challenging, for both simulations and measurements. During the past few decades, however, high-resolution simulations and measurements have greatly advanced our understanding of the main mechanisms controlling cloud entrainment. This article reviews some of these advances, focusing on stratocumulus clouds, and indicates remaining challenges.

Numerical simulations are extensively used to investigate the motion of suspended particles in a fluid and their influence on the dynamics of the overall flow. Contexts range from the rheology of concentrated suspensions in a viscous fluid to the dynamics of particle-laden turbulent flows. This review summarizes several current approaches to the numerical simulation of rigid particles suspended in a flow, pointing out both common features and differences, along with their primary range of application. The focus is on non-Brownian systems for which thermal fluctuations do not play a role, whereas interparticle forces may result in particle self-assembly. Applications may include the motion of a few isolated particles with complex shape or the collective dynamics of many suspended particles.

Internal gravity waves are a key process linking the large-scale mechanical forcing of the oceans to small-scale turbulence and mixing. In this review, we focus on internal waves generated by barotropic tidal flow over topography. We review progress made in the past decade toward understanding the different processes that can lead to turbulence during the generation, propagation, and reflection of internal waves and how these processes affect mixing. We consider different modeling strategies and new tools that have been developed. Simulation results, the wealth of observational material collected during large-scale experiments, and new laboratory data reveal how the cascade of energy from tidal flow to turbulence occurs through a host of nonlinear processes, including intensified boundary flows, wave breaking, wave-wave interactions, and the instability of high-mode internal wave beams. The roles of various nondimensional parameters involving the ocean state, roughness geometry, and tidal forcing are described.

This article reviews the fundamental physics of vapor bubbles in liquids. Work on bubble growth and condensation for stationary and translating bubbles is summarized and the differences with bubbles containing a permanent gas stressed. In particular, it is shown that the natural frequency of a vapor bubble is proportional not to the inverse radius, as for a gas bubble, but to the inverse radius raised to the power 2/3. Permanent gas dissolved in the liquid diffuses into the bubble with strong effects on its dynamics. The effects of the diffusion of heat and mass on the propagation of pressure waves in a vaporous bubbly liquid are discussed. Other topics briefly touched on include thermocapillary flow, plasmonic nanobubbles, and vapor bubbles in an immiscible liquid.

Anisotropic particles are common in many industrial and natural turbulent flows. When these particles are small and neutrally buoyant, they follow Lagrangian trajectories while exhibiting rich orientational dynamics from the coupling of their rotation to the velocity gradients of the turbulence field. This system has proven to be a fascinating application of the fundamental properties of velocity gradients in turbulence. When particles are not neutrally buoyant, they experience preferential concentration and very different preferential alignment than neutrally buoyant tracer particles. A vast proportion of the parameter range of anisotropic particles in turbulence is still unexplored, with most existing research focusing on the simple foundational cases of axisymmetric ellipsoids at low concentrations in homogeneous isotropic turbulence and in turbulent channel flow. Numerical simulations and experiments have recently developed a fairly comprehensive picture of alignment and rotation in these cases, and they provide an essential foundation for addressing more complex problems of practical importance. Macroscopic effects of nonspherical particle dynamics include preferential concentration in coherent structures and drag reduction by fiber suspensions. We review the models used to describe nonspherical particle motion, along with numerical and experimental methods for measuring particle dynamics.

The implementation of advanced low-emission aircraft engine technologies and the reduction of noise from airframe, fan, and jet exhaust have made noise contributions from an engine core increasingly important. Therefore, meeting future ambitious noise-reduction goals requires the consideration of engine-core noise. This article reviews progress on the fundamental understanding, experimental analysis, and modeling of engine-core noise; addresses limitations of current techniques; and identifies opportunities for future research. After identifying core-noise contributions from the combustor, turbomachinery, nozzles, and jet exhaust, they are examined in detail. Contributions from direct combustion noise, originating from unsteady combustion, and indirect combustion noise, resulting from the interaction of flow-field perturbations with mean-flow variations in turbine stages and nozzles, are analyzed. A new indirect noise-source contribution arising from mixture inhomogeneities is identified by extending the theory. Although typically omitted in core-noise analysis, the impact of mean-flow variations and nozzle-upstream perturbations on the jet-noise modulation is examined, providing potential avenues for future core-noise mitigation.

Similar to other renewable energy sources, wind energy is characterized by a low power density. Hence, for wind energy to make considerable contributions to the world's overall energy supply, large wind farms (on- and offshore) consisting of arrays of ever larger wind turbines are being envisioned and built. From a fluid mechanics perspective, wind farms encompass turbulent flow phenomena occurring at many spatial and temporal scales. Of particular interest to understanding mean power extraction and fluctuations in wind farms are the scales ranging from 1 to 10 m that comprise the wakes behind individual wind turbines, to motions reaching 100 m to kilometers in scale, inherently associated with the atmospheric boundary layer. In this review, we summarize current understanding of these flow phenomena (particularly mean and second-order statistics) through field studies, wind tunnel experiments, large-eddy simulations, and analytical modeling, emphasizing the most relevant features for wind farm design and operation.

The fast growth of microfluidic applications based on complex fluids is a result of the unique fluid dynamics of these systems, enabling the creation of devices for health care or biological and chemical analysis. Microchannels designed to focus, concentrate, or separate particles suspended in viscoelastic liquids are becoming common. The key fluid dynamical issue on which such devices work is viscoelasticity-induced lateral migration. This phenomenon was discovered in the 1960s in macroscopic channels and has received great attention within the microfluidic community in the past decade. This review presents the current understanding, both from experiments and theoretical analysis, of viscoelasticity-driven cross-flow migration. Examples of promising microfluidic applications show the unprecedented capabilities offered by such technology based on geometrically simple microchannels and rheologically complex liquids.

Physical interactions between a fluid and structure, potentially manifested as self-sustained or divergent oscillations, can be sensitive to many parameters whose values are uncertain. Of interest here are aircraft aeroelastic interactions, which must be accounted for in aircraft certification and design. Deterministic prediction of these aeroelastic behaviors can be difficult owing to physical and computational complexity. New challenges are introduced when physical parameters and elements of the modeling process are uncertain. By viewing aeroelasticity through a nondeterministic prism, where key quantities are assumed stochastic, one may gain insights into how to reduce system uncertainty, increase system robustness, and maintain aeroelastic safety. This article reviews uncertainty quantification in aeroelasticity using traditional analytical techniques not reliant on computational fluid dynamics; compares and contrasts this work with emerging methods based on computational fluid dynamics, which target richer physics; and reviews the state of the art in aeroelastic optimization under uncertainty. Barriers to continued progress, for example, the so-called curse of dimensionality, are discussed.

Advances in experimental techniques and the ever-increasing fidelity of numerical simulations have led to an abundance of data describing fluid flows. This review discusses a range of techniques for analyzing such data, with the aim of extracting simplified models that capture the essential features of these flows, in order to gain insight into the flow physics, and potentially identify mechanisms for controlling these flows. We review well-developed techniques, such as proper orthogonal decomposition and Galerkin projection, and discuss more recent techniques developed for linear systems, such as balanced truncation and dynamic mode decomposition (DMD). We then discuss some of the methods available for nonlinear systems, with particular attention to the Koopman operator, an infinite-dimensional linear operator that completely characterizes the dynamics of a nonlinear system and provides an extension of DMD to nonlinear systems.

The field of aero-optics is devoted to the study of the effects of turbulent flow fields on laser beams projected from airborne laser systems. This article reviews the early and present periods of research in aero-optics. Both periods generated impressive amounts of research activity; however, the types and amount of data differ greatly in accuracy, quality, and type owing to the development of new types of instrumentation available to collect and analyze the aberrated wave fronts of otherwise collimated laser beams projected through turbulent compressible flow fields of the type that form over beam directors. This review traces the activities and developments associated with both periods but particularly focuses on the development of modern high-bandwidth wave-front sensors used in the present research period. We describe how these modern wave-front data are collected and analyzed and the fluid mechanic information that can be gleaned from them; the use of these data in the fundamental study of turbulence is emphasized.

The microcirculation is an extensive network of microvessels that distributes blood flow throughout living tissues. Reynolds numbers are much less than 1, and the equations of Stokes flow apply. Blood is a suspension of cells with dimensions comparable to microvessel diameters. Highly deformable red blood cells, which transport oxygen, have a volume concentration (hematocrit) of 40–45% in humans. In the narrowest capillaries, these cells move in single file with a surrounding lubricating layer of plasma. In larger vessels, the red blood cells migrate toward the centerline, reducing the resistance to blood flow. Vessel walls are coated with a layer of macromolecules that restricts flow. At diverging bifurcations, hematocrit is not evenly distributed in the downstream vessels. Other particles are driven toward the walls by interactions with red blood cells. These physiologically important phenomena are discussed here from a fluid mechanical perspective.

The impact of an object on a granular solid is an ubiquitous phenomenon in nature, the scale of which ranges from the impact of a raindrop onto sand all the way to that of a large asteroid on a planet. Despite the obvious relevance of these impact events, the study of the underlying physics mechanisms that guide them is relatively young, with most work concentrated in the past decade. Upon impact, an object starts to interact with a granular bed and experiences a drag force from the sand. This ultimately leads to phenomena such as crater formation and the creation of a transient cavity that upon collapse may cause a jet to appear from above the surface of the sand. This review provides an overview of research that targets these phenomena, from the perspective of the analogous but markedly different impact of an object on a liquid. It successively addresses the drag an object experiences inside a granular bed, the expansion and collapse of the cavity created by the object leading to the formation of a jet, and the remarkable role played by the air that resides within the pores between the grains.

Flows of solid particles are known to exhibit a clustering instability—dynamic microstructures characterized by a dense region of highly concentrated particles surrounded by a dilute region with relatively few particles—that has no counterpart in molecular fluids. Clustering is pervasive in rapid flows. Its presence impacts momentum, heat, and mass transfer, analogous to how turbulence affects single-phase flows. Yet predicting clustering is challenging, again analogous to the prediction of turbulent flows. In this review, we focus on three key areas: (a) state-of-the-art mathematical tools used to study clustering, with an emphasis on kinetic theory–based continuum models, which are critical to the prediction of the larger systems found in nature and industry, (b) mechanisms that give rise to clustering, most of which are explained via linear stability analyses of kinetic theory–based models, and (c) a critical review of validation studies of kinetic theory–based models to highlight the accuracies and limitations of such theories.