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. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 56 is January 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 56 is January 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Interactions between fluid flow and elastic structures are important in many naturally occurring and engineered systems. This review collects and organizes recent theoretical and experimental developments in understanding fluid-structure interactions at low Reynolds numbers. Particular attention is given to the motion of objects moving in close proximity to deformable soft materials and the ensuing interplay between fluid flow and elastic deformation. We discuss how this interplay can be understood in terms of forces and torques, and harnessed in applications such as microrheometry, tribology, and soft robotics. We then discuss the interaction of soft and wet objects close to contact, where intermolecular forces and surface roughness effects become important and are sources of complexity and opportunity. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 56 is January 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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 flow in buildings influences personal exposure to indoor pollutants and the spread of airborne diseases. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 56 is January 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 56 is January 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 56 is January 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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 collision 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. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 56 is January 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 56 is January 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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 realistic ally to compare with observations. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 56 is January 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 56 is January 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.