Annual Review of Fluid Mechanics - Volume 50, 2018

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.

The dynamics and rheology of suspensions of rigid, non-Brownian fibers in Newtonian fluids are reviewed. Experiments, theories, and computer simulations are considered, with an emphasis on suspensions at semidilute and concentrated conditions. In these suspensions, interactions between the particles strongly influence the microstructure and rheological properties of the suspension. The interactions can arise from hydrodynamic disturbances, giving multibody interactions at long ranges and pairwise lubrication forces over short distances. For concentrated suspensions, additional interactions due to excluded volume (contacts) and adhesive forces are addressed. The relative importance of the various interactions as a function of fiber concentration is assessed.

This review discusses a recently developed optimization technique for analyzing the nonlinear stability of a flow state. It is based on a nonlinear extension of nonmodal analysis and, in its simplest form, consists of finding the disturbance to the flow state of a given amplitude that experiences the largest energy growth at a certain time later. When coupled with a search over the disturbance amplitude, this can reveal the disturbance of least amplitude—called the minimal seed—for transition to another state such as turbulence. The approach bridges the theoretical gap between (linear) nonmodal theory and the (nonlinear) dynamical systems approach to fluid flows by allowing one to explore phase space at a finite distance from the reference flow state. Various ongoing and potential applications of the technique are discussed.

The cell is a mechanical machine, and continuum mechanics of the fluid cytoplasm and the viscoelastic deforming cytoskeleton play key roles in cell physiology. We review mathematical models of intracellular fluid mechanics, from cytoplasmic fluid flows, to the flow of a viscous active cytoskeletal gel, to models of two-phase poroviscous flows, to poroelastic models. We discuss application of these models to cell biological phenomena, such as organelle positioning, blebbing, and cell motility. We also discuss challenges of understanding fluid mechanics on the cellular scale.

Microrheological study of complex fluids traces its roots to the work of the botanist Robert Brown in the early nineteenth century. Indeed, passive microrheology and Brownian motion are one and the same. Once thought to reveal a fundamental life force, the phenomenon was ultimately leveraged by Einstein in proof of the atomic nature of matter (Haw 2006). His work simultaneously paved the way for modern-day passive microrheology by connecting observable particle motion—diffusion—to solvent properties—the viscosity—via the well-known Stokes–Einstein relation. Advances in microscopy techniques in the last two decades have prompted extensions of the original model to generalized forms for passive probing of complex fluids. In the last decade, active microrheology has emerged as a means by which to interrogate the nonequilibrium behavior of complex fluids, in particular, the non-Newtonian rheology of dynamically heterogeneous and microscopically small systems. Here we review theoretical and computational approaches and advances in both passive and active microrheology, with a focus on the extent to which these techniques preserve the connection between single-particle motion and flow properties, as well as the rather surprising recovery of non-Newtonian flow behavior observed in bulk rheology.

Granular materials composed of particles with differing grain sizes, densities, shapes, or surface properties may experience unexpected segregation during flow. This review focuses on kinetic sieving and squeeze expulsion, whose combined effect produces the dominant gravity-driven segregation mechanism in dense sheared flows. Shallow granular avalanches that form at the surface of more complex industrial flows such as heaps, silos, and rotating drums provide ideal conditions for particles to separate, with large particles rising to the surface and small particles percolating down to the base. When this is combined with erosion and deposition, amazing patterns can form in the underlying substrate. Gravity-driven segregation and velocity shear induce differential lateral transport, which may be thought of as a secondary segregation mechanism. This allows larger particles to accumulate at flow fronts, and if they are more frictional than the fine grains, they can feedback on the bulk flow, causing flow fingering, levee formation, and longer runout of geophysical mass flows.

An overview of the acoustics of boundary layer flows over rough surfaces and surfaces with discontinuities at low Mach number is presented. Roughness noise is dominated by dipole radiation produced by unsteady tangential pressure forces on the uneven surface. Pressure fluctuations may be generated by turbulence of the overriding boundary layer or by the wakes of upstream roughness features, but in either case the sound can be predicted from the wall pressure frequency spectrum and the surface geometry. Small discontinuities, such as steps and gaps, are special cases of isolated two-dimensional roughness. Forward steps are much louder than backward steps because the former generate strong turbulence close to the step. Gap noise is dominated by any exposed forward-step portion of the gap. Rounding can substantially reduce forward step noise, and moderate sweep does not alter the noise-generation mechanism.

The supply of oxygen and nutrients to tissues is performed by the blood system and involves a net leakage of fluid outward at the capillary level. One of the principal functions of the lymphatic system is to gather this fluid and return it to the blood system to maintain overall fluid balance. Fluid in the interstitial spaces is often at subatmospheric pressure, and the return points into the venous system are at pressures of approximately 20 cmH2O. This adverse pressure difference is overcome by the active pumping of collecting lymphatic vessels, which feature closely spaced one-way valves and contractile muscle cells in their walls. Passive vessel squeezing causes further pumping. The dynamics of lymphatic pumping have been investigated experimentally and mathematically, revealing complex behaviors that indicate that the system performance is robust against minor perturbations in pressure and flow. More serious disruptions can lead to incurable swelling of tissues called lymphedema.

Throughout history, capillary systems have aided the establishment of the fundamental laws of blood flow and its non-Newtonian properties. The advent of microfluidics technology in the 1990s propelled the development of highly integrated lab-on-a-chip platforms that allow highly accurate replication of vascular systems' dimensions, mechanical properties, and biological complexity. Applications include the detection of pathological changes to red blood cells, white blood cells, and platelets at unparalleled sensitivity and the efficacy assessment of drug treatment. Recent efforts have aimed at the development of microfluidics-based tests usable in a clinial environment or the replication of more complex diseases such as thrombosis. These microfluidic disease models enable the study of onset and progression of disease as well as the identification of key players and risk factors, which have led to a spectrum of clinically relevant findings.