Annual Review of Fluid Mechanics - Volume 56, 2024

Stephen H. Davis (1939–2021) was an applied mathematician, fluid dynamicist, and materials scientist who lead the field in his contributions to interfacial dynamics, thermal convection, thin films, and solidification for over 50 years. Here, we briefly review his personal and professional life and some of his most significant contributions to the field.

This review highlights major developments and milestones during the early days of numerical simulation of turbulent flows and its use to increase our understanding of turbulence phenomena. The period covered starts with the first simulations of decaying homogeneous isotropic turbulence in 1971–1972 and ends about 25 years later. Some earlier history of the progress in weather prediction is included if relevant. Only direct simulation, in which all scales of turbulence are accounted for explicitly, and large-eddy simulation, in which the effect of the smaller scales is modeled, are discussed. The method by which all scales are modeled, Reynolds-averaged Navier–Stokes, is not covered.

Rotating-disk flows were first considered by von Kármán in a seminal paper in 1921, where boundary layers in general were discussed and, in two of the nine sections, results for the laminar and turbulent boundary layers over a rotating disk were presented. It was not until in 1955 that flow visualization discovered the existence of stationary cross-flow vortices on the disk prior to the transition to turbulence. The rotating disk can be seen as a special case of rotating cones, and recent research has shown that broad cones behave similarly to disks, whereas sharp cones are susceptible to a different type of instability. Here, we provide a review of the major developments since von Kármán's work from 100 years ago, regarding instability, transition, and turbulence in the boundary layers, and we include some analysis not previously published.

We review some fundamentals of turbulent drag reduction and the turbulent drag reduction techniques using streamwise traveling waves of blowing/suction from the wall and wall deformation. For both types of streamwise traveling wave controls, their significant drag reduction capabilities have been well confirmed by direct numerical simulation at relatively low Reynolds numbers. The drag reduction mechanisms by these streamwise traveling waves are considered to be the combination of direct effects due to pumping and indirect effects of the attenuation of velocity fluctuations due to reduced receptivity. Prediction of their drag reduction capabilities at higher Reynolds numbers and attempts at experimental validation are also intensively ongoing toward their practical implementation.

In the last ten years, advances in experimental techniques have enabled remarkable discoveries of how the dynamics of thin gas films can profoundly influence the behavior of liquid droplets. Drops impacting onto solids can skate on a film of air so that they bounce off solids. For drop–drop collisions, this effect, which prevents coalescence, has been long recognized. Notably, the precise physical mechanisms governing these phenomena have been a topic of intense debate, leading to a synergistic interplay of experimental, theoretical, and computational approaches. This review attempts to synthesize our knowledge of when and how drops bounce, with a focus on (a) the unconventional microscale and nanoscale physics required to predict transitions to/from merging and (b) the development of computational models. This naturally leads to the exploration of an array of other topics, such as the Leidenfrost effect and dynamic wetting, in which gas films also play a prominent role.

The fluid dynamics of microswimmers has received attention from the fields of microbiology, microrobotics, and active matter. Microorganisms have evolved organelles termed cilia for propulsion through liquids. Each cilium periodically performs effective and recovery strokes, creating a metachronal wave as a whole and developing a propulsive force. One well-established mathematical model of ciliary swimming is the squirmer model, which focuses on surface squirming velocities. This model is also useful when studying active colloids and droplets. The squirmer model has been recently used to investigate the behaviors of microswimmers in complex environments, their collective dynamics, and the characteristics of active fluids. Efforts have also been made to broaden the range of applications beyond the assortment permitted by the squirmer model, which was established to specifically represent ciliary flow and incorporate biological features. The stress swimmer model imposes stresses above the cell body surface that enforce the no-slip condition. The ciliated swimmer model precisely reproduces the behaviors of each cilium that engages in mutual hydrodynamic interactions. Mathematical models have improved our understanding of various microbial phenomena, including cell–cell and cell–wall interactions and energetics. Here, I review recent advances in the hydrodynamics of ciliary swimming and then discuss future challenges.

Insects, birds, and bats that power and control flight by flapping their wings perform excellent flight stability and maneuverability by rapidly and continuously varying their wing motions. This article provides an overview of the state of the art of vortex-dominated, unsteady flapping aerodynamics from the viewpoint of diversity and uniformity associated with dominant vortices, particularly of the relevant physical aspects of the flight of insects and vertebrates in the low- and intermediate-Reynolds-number (Re) regime of 10⁰ to 10⁶. After briefly describing wing morphology and kinematics, we discuss the main vortices generated by flapping wings and the aerodynamic forces associated with these structures, focusing on leading-edge vortices (LEVs), wake vortices, and vortices generated by wing motions over a broad Re range. The LEVs are intensified by dynamic wing morphing in bird and bat flight, producing a significantly elevated vortex lift. The complex wake vortices are the footprints of lift generation; thus, the time-averaged vortex lift can be estimated from wake velocity data. Computational fluid dynamics modeling, quasi-steady models, and vortex lift models are useful tools to elucidate the intrinsic relationships between the lift and the dominant vortices in the near- and far-fields in flapping flight.

Reproductive biomechanics, a broad and developing field, contains fluid mechanics problems at every stage. In particular, the human female reproductive system is a complex and dynamic fluid-structure system. Until recently, the majority of this research focused on the early moments of reproduction—namely, the transport phenomena that dominate fertilization and implantation. However, in the past two decades, fluid mechanics has begun to be used in investigations of all aspects surrounding pregnancy, labor, and delivery. In this review, we discuss human reproduction starting with the nonpregnant uterus through implantation, delivery, and lactation and breastfeeding. We cover physiologic changes from the transformation of the uterus and the cervical remodeling process to the development of the placenta and the beginning of lactation. We examine the role of reproductive fluids such as amniotic fluid and vernix caseosa, and how force is transferred during labor.

When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy particles, with mass densities larger than that of the carrying fluid, can detach from the flow. This results in preferential sampling, small-scale fractal clustering, and large relative velocities. To describe these effects of particle inertia, one must consider both particle positions and velocities in phase space. In recent years, statistical phase-space models have significantly contributed to our understanding of inertial-particle dynamics in turbulence. These models help to identify the key mechanisms and nondimensional parameters governing the particle dynamics and have made qualitative and, in some cases, quantitative predictions. This article reviews statistical phase-space models for the dynamics of small, yet heavy, spherical particles in turbulence. We evaluate their effectiveness by comparing their predictions with results from numerical simulations and laboratory experiments, and we summarize their successes and failures.

This review focuses on how the modeling of dense granular media has advanced over the last 15 years. The jumping-off point of our review is the μ(I) rheology for dry granular flow, which opened the door to generic flow field modeling but was primarily geared toward problems involving small monodisperse grains of simple shapes. Our review focuses on advances in modeling more material types and behaviors including new approaches for modeling finite-grain-size effects or nonlocality, polydispersity and unmixing, and nontrivial grain shapes. We also discuss growing application areas with tractable order-reduction strategies with a focus on intrusion and locomotion problems.

The gas dynamics of single-phase nonreacting fluids whose thermodynamic states are close to vapor-liquid saturation, close to the vapor-liquid critical point, or in supercritical conditions differs quantitatively and qualitatively from the textbook gas dynamics of dilute, ideal gases. Due to nonideal fluid thermodynamic properties, unconventional gas dynamic effects are possible, including nonclassical rarefaction shock waves and the nonmonotonic variation of the Mach number along steady isentropic expansions. This review provides a comprehensive theoretical framework of the fundamentals of nonideal compressible fluid dynamics (NICFD). The relation between nonideal gas dynamics and the complexity of the fluid molecules is clarified. The theoretical, numerical, and experimental tools currently employed to investigate NICFD flows and related applications are reviewed, followed by an overview of industrial processes involving NICFD, ranging from organic Rankine and supercritical CO2 cycle power systems to supercritical processes. The future challenges facing researchers in the field are briefly outlined.

Until recently, observations of the giant planets of our Solar System were confined to sampling relatively shallow regions of their atmospheres, leaving many uncertainties as to the dynamics of deeper layers. The Cassini and Juno missions to Saturn and Jupiter, however, have begun to address these issues, for example, by measuring their gravity and magnetic fields. The results show that the zonally coherent jets and cloud bands extend to levels where the electrical conductivity of the fluid becomes significant, whereas large-scale vortices, such as the Great Red Spot, are relatively shallow but may have deep-seated roots. The polar regions also exhibit intense cyclonic vortices that, on Jupiter, arrange themselves into remarkably regular “vortex crystals.” Numerical models seem able to capture some of this complexity, but many issues remain unresolved, suggesting a need for models that can represent both deep and shallow processes sufficiently realistically to compare with observations.

Bubble plumes are ubiquitous in nature. Instances in the natural world include the release of methane and carbon dioxide from the seabed or the bottom of a lake and from a subsea oil well blowout. This review describes the dynamics of bubble plumes and their various spreading patterns in the surrounding environment. We explore how the motion of the plume is affected by the density stratification in the external environment, as well as by internal processes of dissolution of the bubbles and chemical reaction. We discuss several examples, such as natural disasters, global warming, and fishing techniques used by some whales and dolphins.

Fragmentation of bubbles and droplets in turbulence produces a dispersed phase spanning a broad range of scales, encompassing everything from droplets in nanoemulsions to centimeter-sized bubbles entrained in breaking waves. Along with deformation, fragmentation plays a crucial role in enhancing interfacial area, with far-reaching implications across various industries, including food, pharmaceuticals, and ocean engineering. However, understanding and modeling these processes are challenging due to the complexity of anisotropic and inhomogeneous turbulence typically involved, the unknown residence time in regions with different turbulence intensities, and difficulties arising from the density and viscosity ratios. Despite these challenges, recent advances have provided new insights into the underlying physics of deformation and fragmentation in turbulence. This review summarizes existing works in various fields, highlighting key results and uncertainties, and examining the impact on turbulence modulation, drag reduction, and heat and mass transfer.

Large-scale circulation of the atmosphere in the Earth's extratropics is dominated by eddies, eastward (westerly) zonal winds, and their interaction. Eddies not only bring about weather variabilities but also help maintain the average state of climate. In recent years, our understanding of how large-scale eddies and mean flows interact in the extratropical atmosphere has advanced significantly due to new dynamical constraints on finite-amplitude eddies and the related eddy-free reference state. This article reviews the theoretical foundations for finite-amplitude Rossby wave activity and related concepts. Theory is then applied to atmospheric data to elucidate how angular momentum is redistributed by the generation, transmission, and dissipation of Rossby waves and to reveal how an anomalously large wave event such as atmospheric blocking may arise from regional eddy-mean flow interaction.

High-speed disperse multiphase flows are present in numerous environmental and engineering applications with complex interactions between turbulence, shock waves, and particles. Compared with its incompressible counterpart, compressible two-phase flows introduce new scales of motion that challenge simulations and experiments. This review focuses on gas–particle interactions spanning subsonic to supersonic flow conditions. An overview of existing Mach-number-dependent drag laws is presented, with origins from eighteenth-century cannon firings and new insights from particle-resolved numerical simulations. The equations of motion and phenomenology for a single particle are first reviewed. Multiparticle systems spanning dusty gases to dense suspensions are then discussed from numerical and experimental perspectives.

Ventilation is central to human civilization. Without it, the indoor environment rapidly becomes uncomfortable or dangerous, but too much ventilation can be expensive. We spend much of our time indoors, where we are exposed to pollutants and can be infected by airborne diseases. Ventilation removes pollution and bioaerosols from indoor sources but also brings in pollution from outdoors. To determine an appropriate level of ventilation and an appropriate way of providing it, one must understand that the needs for ventilation extend beyond simple thermal comfort; the quality of indoor air is at least as important. An effective ventilation system will remove unwanted contaminants, whether generated within the space by activities or by the simple act of breathing, and ensure that the ventilation system does not itself introduce or spread contaminants from elsewhere. This review explores how ventilation flows in buildings influence personal exposure to indoor pollutants and the spread of airborne diseases.

By taking into account the inhomogeneity introduced by the presence of a solid boundary, slip-flow theory extends the range of applicability of the venerable Navier–Stokes description to smaller scales and into the regime where confinement starts to be important. Due to the inherently atomistic nature of solid–fluid interactions at their interface, slip flow can be described, at least in principle, predictively at this level. This review aims to summarize our current understanding of slip flow at the atomistic level in dilute gases and dense liquids. The discussion extends over the similarities and differences between slip in gases and liquids, characterization and measurement of slip by molecular simulation methods, models for predicting slip, and open questions requiring further investigation.

Understanding and predicting turbulent flow phenomena remain a challenge for both theory and applications. The nonlinear and nonlocal character of small-scale turbulence can be comprehensively described in terms of the velocity gradients, which determine fundamental quantities like dissipation, enstrophy, and the small-scale topology of turbulence. The dynamical equation for the velocity gradient succinctly encapsulates the nonlinear physics of turbulence; it offers an intuitive description of a host of turbulence phenomena and enables establishing connections between turbulent dynamics, statistics, and flow structure. The consideration of filtered velocity gradients enriches this view to express the multiscale aspects of nonlinearity and flow structure in a formulation directly applicable to large-eddy simulations. Driven by theoretical advances together with growing computational and experimental capabilities, recent activities in this area have elucidated key aspects of turbulence physics and advanced modeling capabilities.