Annual Review of Fluid Mechanics - Volume 53, 2021

This review focuses on Leonardo da Vinci's work and thought related to fluid mechanics as it is presented in a lifetime of notebooks, letters, and artwork. It shows how Leonardo's remaining works offer a complicated picture of unfinished, scattered, and frequently revisited hypotheses and conclusions. It argues that experimentation formed an important mechanism for Leonardo's thought about natural fluid flows, which was an innovation to the scientific thinking of his day, but which did not always lead him to the conclusions of modern fluid mechanics. It highlights the multiple and ambiguous meanings of turbulence in his works. It examines his thinking suggestive of modern concepts such as the no-slip condition, hydraulic jump, cardiovascular vortices, conservation of volume, and the distinctive path of ascending bubbles we now term Leonardo's paradox, among others. It demonstrates how Leonardo thought through analogies, building-block flow patterns, and synthesis, leading both to successes—especially in the management of water—and to failures, perhaps most obviously in his pursuit of human flight.

A viscous solvent laminar flow may be strongly modified by the addition of a tiny amount of long polymer molecules, resulting in a chaotic flow called elastic turbulence (ET). ET is attributed to polymer stretching, which generates elastic stress and its back reaction on the flow. Its properties are analogous to those observed in hydrodynamic turbulence, although the formal similarity does not imply a similarity in physical mechanisms underlining these two types of random motion. Here we review the statistical and spectral properties and the spatial structure of the velocity field, the statistical and spectral properties of pressure fluctuations, and scaling of the friction factor of ET in wall-bounded and unbounded flow geometries, as observed in experiments and numerical simulations and described by theory for a wide range of control parameters and polymer concentrations.

Sediment-laden gravity currents, or turbidity currents, are density-driven flows that transport vast quantities of particulate material across the floor of lakes and oceans. Turbidity currents are generated by slope failure or initiated when a sediment-laden flow enters into a lake or ocean; here, lofting or convective sedimentation processes may control flow dynamics. Depending upon the internal turbulent mixing, which keeps particles in suspension, turbidity currents can travel for thousands of kilometers across the seafloor. However, despite several competing theories, the process for the ultralong runout of these flows remains enigmatic. Turbidity currents often generate large sinuous channel–levee systems, and the dynamics of how turbidity currents flow around channel bends are strongly influenced by internal density and velocity structure, with large-scale flows being modified by the Coriolis force. Therefore, understanding some of the largest sedimentary structures on the Earth's surface depends on understanding the turbulence processes within turbidity currents.

Extreme events in fluid flows, waves, or structures interacting with them are critical for a wide range of areas, including reliability and design in engineering, as well as modeling risk of natural disasters. Such events are characterized by the coexistence of high intrinsic dimensionality, complex nonlinear dynamics, and stochasticity. These properties severely restrict the application of standard mathematical approaches, which have been successful in other areas. This review focuses on methods specifically formulated to deal with these properties and it is structured around two cases: (a) problems where an accurate but expensive model exists and (b) problems where a small amount of data and possibly an imperfect reduced-order model that encodes some physics about the extremes can be employed.

Understanding how turbulence leads to the enhanced irreversible transport of heat and other scalars such as salt and pollutants in density-stratified fluids is a fundamental and central problem in geophysical and environmental fluid dynamics. This review discusses recent research activity directed at improving community understanding, modeling, and parameterization of the subtle interplay between energy conversion pathways, instabilities, turbulence, external forcing, and irreversible mixing in density-stratified fluids. The conceptual significance of various length scales is highlighted, and in particular, the importance is stressed of overturning or scouring in the formation and maintenance of layered stratifications, i.e., robust density distributions with relatively deep and well-mixed regions separated by relatively thin interfaces of substantially enhanced density gradient.

The removal of unwanted entities or soiling material from surfaces is an essential operation in many personal, industrial, societal, and environmental applications. The use of liquid cleansers for cleaning and decontamination is ubiquitous, and this review seeks to identify commonality in the fluid flow phenomena involved, particularly in those that determine the effectiveness of such operations. The state of quantitative understanding and modeling is reviewed in relation to the topics of (a) the cleanser contacting the soiled area, (b) processes by which the cleanser effects soil removal, and (c) transport of the soil or its derivatives away from the surface. This review focuses on rigid substrates and does not consider processes based on gas flows or bubbles.

Oceanic lee waves are generated in the deep stratified ocean by the flow of ocean currents over sea floor topography, and when they break, they can lead to mixing in the stably stratified ocean interior. While the theory of linear lee waves is well established, the nonlinear mechanisms leading to mixing are still under investigation. Tidally driven lee waves have long been observed in the ocean, along with associated mixing, but observations of lee waves forced by geostrophic eddies are relatively sparse and largely indirect. Parameterizations of the mixing due to ocean lee waves are now being developed and implemented in ocean climate models. This review summarizes current theory and observations of lee wave generation and mixing driven by lee wave breaking, distinguishing between steady and tidally oscillating forcing. The existing parameterizations of lee wave–driven mixing informed by theory and observations are outlined, and the impacts of the parameterized lee wave–driven mixing on simulations of large-scale ocean circulation are summarized.

We review studies of levitating droplets over liquid–gas interfaces and dry solid surfaces with a focus on the physical mechanisms of levitation under different conditions. A fascinating physical phenomenon of self-organization of levitating droplets into large arrays is described and explanations for this unusual behavior are reviewed. Closely related topics of nonisothermal flotation and levitation of evaporating droplets over a pool of nonvolatile liquid, as well as recent advances in the study of the Leidenfrost effect, are also discussed.

Wall-bounded turbulence exhibits patterns that persist in time and space: coherent structures. These are important for transport processes and form a conceptual framework for important theoretical approaches. Key observed structures include quasi-streamwise and hairpin vortices, as well as the localized spots and puffs of turbulence observed during transition. This review describes recent research on so-called exact coherent states (ECS) in wall-bounded parallel flows at Reynolds numbers Re 10⁴; these are nonturbulent, nonlinear solutions to the Navier–Stokes equations that in many cases resemble coherent structures in turbulence. That is, idealized versions of many of these structures exist as distinct, self-sustaining entities. ECS are saddle points in state space and form, at least in part, the state space skeleton of the turbulent dynamics. While most work on ECS focuses on Newtonian flow, some advances have been made on the role of ECS in turbulent drag reduction in polymer solutions. Emerging directions include applications to control and connections to large-scale structures and the attached eddy model.

This review examines large eddy simulation (LES) models from the perspective of their a priori statistical characteristics. The most well-known statistical characteristic of an LES subgrid-scale model is its dissipation (energy transfer to unresolved scales), and many models are directly or indirectly formulated and tuned for consistency of this characteristic. However, in complex turbulent flows, many other subgrid statistical characteristics are important. These include such quantities as mean subgrid stress, subgrid transport of resolved Reynolds stress, and dissipation anisotropy. Also important are the statistical characteristics of models that account for filters that do not commute with differentiation and of the discrete numerical operators in the LES equations. We review the known statistical characteristics of subgrid models to assess these characteristics and the importance of their a priori consistency. We hope that this analysis will be helpful in continued development of LES models.

Placing mechanical devices into fast-moving tidal streams to generate clean and predictable electricity is a developing technology. This review covers the fundamental fluid mechanics of this application, which is important for understanding how such devices work and how they interact with the tidal stream resource. We focus on how tidal stream turbines and energy generation are modeled analytically, numerically, and experimentally. Owing to the nature of the problem, our review is split into different scales—from turbine to array and regional—and we examine each in turn.

Transient growth and resolvent analyses are routinely used to assess nonasymptotic properties of fluid flows. In particular, resolvent analysis can be interpreted as a special case of viewing flow dynamics as an open system in which free-stream turbulence, surface roughness, and other irregularities provide sources of input forcing. We offer a comprehensive summary of the tools that can be employed to probe the dynamics of fluctuations around a laminar or turbulent base flow in the presence of such stochastic or deterministic input forcing and describe how input–output techniques enhance resolvent analysis. Specifically, physical insights that may remain hidden in the resolvent analysis are gained by detailed examination of input–output responses between spatially localized body forces and selected linear combinations of state variables. This differentiating feature plays a key role in quantifying the importance of different mechanisms for bypass transition in wall-bounded shear flows and in explaining how turbulent jets generate noise. We highlight the utility of a stochastic framework, with white or colored inputs, in addressing a variety of open challenges including transition in complex fluids, flow control, and physics-aware data-driven turbulence modeling. Applications with temporally or spatially periodic base flows are discussed and future research directions are outlined.

This review surveys the dramatic variations in wake structures and flow transitions, in addition to body forces, that appear as the motion of bluff bodies through a fluid occurs increasingly closer to a solid wall. In particular, we discuss the two cases of bluff bodies translating parallel to solid walls at varying heights and bluff bodies impacting on solid walls. In the former case, we highlight the changes to the wake structures as the flow varies from that of an isolated body to that of a body on or very close to the wall, including the effects when the body is rotating. For the latter case of an impacting body, we review the flow structures following impact and their transition to three-dimensionality. We discuss the issue of whether there is solid–solid contact between the bluff body and a wall and its importance to body motion.

Nanofluidics has firmly established itself as a new field in fluid mechanics, as novel properties have been shown to emerge in fluids at the nanometric scale. Thanks to recent developments in fabrication technology, artificial nanofluidic systems are now being designed at the scale of biological nanopores. This ultimate step in scale reduction has pushed the development of new experimental techniques and new theoretical tools, bridging fluid mechanics, statistical mechanics, and condensed matter physics. This review is intended as a toolbox for fluids at the nanometer scale. After presenting the basic equations that govern fluid behavior in the continuum limit, we show how these equations break down and new properties emerge in molecular-scale confinement. A large number of analytical estimates and physical arguments are given to organize the results and different limits.

From intracellular protein signaling to embryonic symmetry-breaking, fluid transport ubiquitously drives biological events in living systems. We provide an overview of the fundamental fluid mechanics and transport phenomena across a range of length scales in cellular systems, with emphasis on how cellular functions are influenced by fluid transport. We also highlight how understanding the physical basis of these fluid dynamic phenomena can be implemented to engineer increasingly complex multicellular systems that recapitulate tissue-level functions. Examples discussed include the manipulation of intracellular fluid volume to achieve cell differentiation/dedifferentiation and the use of microfluidic systems to control the spatial and temporal distribution of morphogens and fluid forces to generate vascularized organoids.

Reliable full-scale prediction of drag due to rough wall-bounded turbulent fluid flow remains a challenge. Currently, the uncertainty is at least 10%, with consequences, for example, on energy and transport applications exceeding billions of dollars per year. The crux of the difficulty is the large number of relevant roughness topographies and the high cost of testing each topography, but computational and experimental advances in the last decade or so have been lowering these barriers. In light of these advances, here we review the underpinnings and limits of relationships between roughness topography and drag behavior, focusing on canonical and fully turbulent incompressible flow over rigid roughness. These advances are beginning to spill over into multiphysical areas of roughness, such as heat transfer, and promise broad increases in predictive reliability.

For an infectious disease such as the coronavirus disease 2019 (COVID-19) to spread, contact needs to be established between an infected host and a susceptible one. In a range of populations and infectious diseases, peer-to-peer contact modes involve complex interactions of a pathogen with a fluid phase, such as isolated complex fluid droplets or a multiphase cloud of droplets. This is true for exhalations including coughs or sneezes in humans and animals, bursting bubbles leading to micron-sized droplets in a range of indoor and outdoor settings, or impacting raindrops and airborne pathogens in foliar diseases transferring pathogens from water to air via splashes. Our mechanistic understanding of how pathogens actually transfer from one host or reservoir to the next remains woefully limited, with the global consequences that we are all experiencing with the ongoing COVID-19 pandemic. This review discusses the emergent area of the fluid dynamics of disease transmission. It highlights a new frontier and the rich multiscale fluid physics, from interfacial to multiphase and complex flows, that govern contact between an infected source and a susceptible target in a range of diseases.

Complex fluids exist in nature and are continually engineered for specific applications involving the addition of macromolecules to a solvent, among other means. This imparts viscoelasticity to the fluid, a property responsible for various flow instabilities and major modifications to the fluid dynamics. Recent developments in the numerical methods for the simulation of viscoelastic fluid flows, described by continuum-level differential constitutive equations, are surveyed, with a particular emphasis on the finite-volume method. This method is briefly described, and the main benchmark flows currently used in computational rheology to assess the performance of numerical methods are presented. Outstanding issues in numerical methods and novel and challenging applications of viscoelastic fluids, some of which require further developments in numerical methods, are discussed.

The use of X-ray flow visualization has brought a powerful new tool to the study of multiphase flows. Penetrating radiation can probe the spatial concentration of the different phases without the refraction, diffraction, or multiple scattering that usually produce image artifacts or reduce the signal-to-noise ratio below reliable values in optical visualization of multiphase flows; hence, X-ray visualization enables research into the three-dimensional (3D) structure of multiphase flows characterized by complex interfaces. With the commoditization of X-ray laboratory sources and wider access to synchrotron beam time for fluid mechanics, this novel imaging technique has shed light onto many multiphase flows of industrial and environmental interest under realistic 3D configurations and at realistic operating conditions (high Reynolds numbers and high volume fractions) that had defied study for decades. We present a broad survey of the most commonly studied multiphase flows (e.g., sprays, fluidized beds, bubble columns) in order to highlight the progress X-ray imaging has made in understanding the internal structure and multiphase coupling of these flows, and we discuss the potential of advanced tomography and time-resolved and particle tracking radiography for further study of multiphase flows.