Annual Review of Fluid Mechanics - Volume 55, 2023

Volumes of this journal typically include one or two historical articles, many of which celebrate the life and impact in fluid mechanics of a recently deceased contributor to the field. The Editorial Committee recently stepped beyond this model to examine whom might have been missed over the years. Naturally, even when a candidate is identified, the passing of time makes it hard to find authors with living memory of the subject. Fortunately, in the case of Professor Dr. Irmgard Flügge-Lotz there is a rare opportunity: An appropriate article appeared in the collection Women in Mathematics, coauthored by her first PhD student John Spreiter and her husband Wilhelm Flügge, both her colleagues at Stanford University. We republish this article to share her remarkable story and contributions in fluid mechanics, as she worked with Prandtl, led a research group at ONERA (Office national d'études et de recherches aérospatiales), and eventually became the first woman professor of engineering at Stanford.

If one opens today a textbook on fluid mechanics, it seems that whereas French scientists of the eighteenth and nineteenth centuries are frequently mentioned, those from more recent times occur rarely; in particular, French contributions to the major breakthroughs of the first half of the twentieth century (boundary layers and turbulence) would appear quite modest. However, study of contemporary documents (PhD theses, journals, correspondence, etc.) reveals remarkable work undertaken by outstanding personalities. A key instigator of these achievements was the French Air Ministry, which, starting in 1929, and with great open-mindedness, created and generously financed four Institutes of Fluid Mechanics and five teaching centers in faculties of science. This reveals the 1930s in their true light as a fruitful decade, with achievements that explain the prominent role played by France in the creation of the International Union of Theoretical and Applied Mechanics (IUTAM) in 1946. This review recounts the story of fluid mechanics in France, with emphasis on the connection between scientific questions and social and cultural issues, in a period marked by two world wars and great strengthening of international relationships.

Transitional–turbulent spots bridge the deterministic laminar state with the stochastic turbulent state and affect the transition zone length in engineering flows. Turbulent spot research over the past four decades has expanded from incompressible flat-plate boundary layer and pipe flow to hypersonic boundary layer flow, turbomachinery flow, channel flow, plane Couette flow, and a range of more complex flows. Progress has been made on the origination, composition, demarcation, growth, mutual interaction, reproduction, sustainability, and self-organization of turbulent spots. The hypothesis that transitional–turbulent spots are a basic module of the fully turbulent boundary layer has been proven through the discovery of locally generated turbulent–turbulent spots dominating the wall layer. Splitting of transitional–turbulent spots in pipe flow has been linked to a life cycle localized in the spot frontal section. This review discusses these advances and outlines future research directions.

Microscopic active droplets are able to swim autonomously in viscous flows. This puzzling feature stems from solute exchanges with the surrounding fluid via surface reactions or their spontaneous solubilization and from the interfacial flows resulting from these solutes’ gradients. Contrary to asymmetric active colloids, these isotropic droplets swim spontaneously by exploiting the nonlinear coupling of solute transport with self-generated Marangoni flows; such coupling is also responsible for secondary transitions to more complex individual and collective dynamics. Thanks to their simple design and their sensitivity to physico-chemical signals, these droplets are fascinating to physicists, chemists, biologists, and fluid dynamicists alike in analyzing viscous self-propulsion and collective dynamics in active-matter systems, developing synthetic cellular models, or performing targeted biomedical or engineering applications. I review here the most recent and significant developments of this rapidly growing field, focusing on the mathematical and physical modeling of these intriguing droplets, together with their experimental design and characterization.

Oceanic motions with spatial scales of 200 m–20 km, called submesoscales, are ubiquitous in the upper ocean and serve as a key intermediary between larger-scale balanced dynamics and unbalanced turbulence. Here, we introduce the fluid dynamics of submesoscales and contrast them with motions at larger and smaller scales. We summarize the various ways in which submesoscales develop due to instabilities that extract potential or kinetic energy from larger-scale balanced currents; some instabilities have counterparts at larger scales, while others are distinct to the submesoscale regime. Submesoscales modify the density stratification in the upper ocean and redistribute energy between scales. These energy transfers are complex, having both up-scale and down-scale components. Submesoscale eddies and fronts also contribute to a spatially heterogeneous distribution of shear and restratification that leave an imprint on upper ocean turbulence. The impact of submesoscales on the Earth's climate remains an exciting research frontier.

Immersed boundary methods (IBMs) are versatile and efficient computational techniques to solve flow problems in complex geometric configurations that retain the simplicity and efficiency of Cartesian structured meshes. Although these methods became known in the 1970s and gained credibility only in the new millennium, they had already been conceived and implemented at the beginning of the 1960s, even if the early computers of those times did not allow researchers to exploit their potential. Nowadays IBMs are established numerical schemes employed for the solution of many complex problems in which fluid mechanics may account for only part of the multiphysics dynamics. Despite the indisputable advantages, these methods also have drawbacks, and each problem should be carefully analyzed before deciding which particular IBM implementation is most suitable and whether additional modeling is necessary. High–Reynolds number flows constitute one of the main limitations of IBMs owing to the resolution of thin wall shear layers, which cannot benefit from anisotropic grid refinement at the boundaries. To alleviate this weakness, researchers have developed IBM-compliant wall models and local grid refinement strategies, although in these cases possible pitfalls must also be considered.

Density stratification due to temperature or salinity variations greatly influences the flow around and the sedimentation of objects such as particles, drops, bubbles, and small organisms in the atmosphere, oceans, and lakes. Density stratification hampers the vertical flow and substantially affects the sedimentation of an isolated object, the hydrodynamic interactions between a pair of objects, and the collective behavior of suspensions in various ways, depending on the relative magnitude of stratification, inertia (advection), and viscous (diffusion) effects. This review discusses these effects and their hydrodynamic mechanisms in some commonly observed fluid–particle transport phenomena in oceans and the atmosphere. Physical understanding of these mechanisms can help us better model these phenomena and, hence, predict their geophysical, engineering, ecological, and environmental implications.

Although face masks have been used for over a century to provide protection against airborne pathogens and pollutants, close scrutiny of their effectiveness has peaked in the past two years in response to the COVID-19 pandemic. The simplicity of face masks belies the complexity of the physical phenomena that determine their effectiveness as a defense against airborne infections. This complexity is rooted in the fact that the effectiveness of face masks depends on the combined effects of respiratory aerodynamics, filtration flow physics, droplet dynamics and their interactions with porous materials, structural dynamics, physiology, and even human behavior. At its core, however, the face mask is a flow-handling device, and in the current review, we take a flow physics–centric view of face masks and the key phenomena that underlie their function. We summarize the state of the art in experimental measurements, as well as the growing body of computational studies that have contributed to our understanding of the factors that determine the effectiveness of face masks. The review also lays out some of the important open questions and technical challenges associated with the effectiveness of face masks.

Hands-On Research in Complex Systems Schools provide an example of how graduate students and young faculty working in resource-constrained environments can apply key mindsets and methods of tabletop experiments to problems at the frontiers of science. Each day during the Schools’ two-week program, participants work in small groups with experienced tabletop scientists in interactive laboratories on topics drawn from diverse disciplines in science and technology. Using modern low-cost tools, participants run experiments and perform associated data analysis together with mathematical and computational modeling. Participants also engage in other scientific professional activities; in particular, they learn best practices for communicating their results visually, orally, and in writing. In this way, the Hands-On Schools foster the development of scientific leaders in low- and middle-income countries.

Circulation of cerebrospinal fluid and interstitial fluid around the central nervous system and through the brain transports not only those water-like fluids but also any solutes they carry, including nutrients, drugs, and metabolic wastes. Passing through brain tissue primarily during sleep, this circulation has implications for neurodegenerative disorders including Alzheimer's disease, for tissue damage during stroke and cardiac arrest, and for flow-related disorders such as hydrocephalus and syringomyelia. Recent experimental results reveal several features of this flow, but other aspects are not fully understood, including its driving mechanisms. We review the experimental evidence and theoretical modeling of cerebrospinal fluid flow, including the roles of advection and diffusion in transporting solutes. We discuss both local, detailed fluid-dynamic models of specific components of the system and global hydraulic models of the overall network of flow paths.

Polar vortices that share many similarities are found in Earth's stratosphere and the atmospheres of Mars and Saturn's moon Titan. These vortices all occur in the winter, and are characterized by high potential vorticity (PV) in polar regions, steep meridional PV gradients and peak zonal winds in middle latitudes, and a cold pole. There are, however, differences in the daily and subseasonal variability, zonal asymmetries, and PV structure among the vortices. These differences are related to differences in the disruption of polar vortices by Rossby waves, the poleward extent of the mean meridional circulation, and condensation of major gases. There are also differences in the transport of gases and particles among the vortices. The range of polar vortex characteristics is likely much larger for terrestrial exoplanets, which include planets with, for example, a wider range of obliquities.

Advances in measuring and understanding separated, nominally two-dimensional (2D) shock-wave/turbulent-boundary-layer interactions (STBLI) have triggered recent campaigns focused on three-dimensional (3D) STBLI, which display far greater configuration diversity. Nonetheless, unifying properties emerge for semi-infinite interactions, taking the form of conical asymptotic behavior where shock-generator specifics become insignificant. The contrast between 2D and 3D separation is substantial; the skewed vortical structure of 3D STBLI reflects the essentially 2D influence of the boundary layer on the 3D character of the swept shock. As with 2D STBLI, conical interactions engender prominent spectral content below that of the turbulent boundary layer. However, the uniform separation length scale, which is crucial to normalizing the lowest-frequency dynamics in 2D STBLI, is absent. Comparatively, the spectra of 3D STBLI are more representative of the mid-frequency, convective, shear-layer dynamics in 2D, while phenomena associated with 2D separation-shock breathing are muted. Asymptotic behavior breaks down in many regions important to 3D-STBLI dynamics, occurring in a configuration-dependent manner. Aspects of inceptive regions near shock generators and symmetry planes are reviewed. Focused efforts toward 3D modal and nonmodalanalyses, moving-shock/boundary-layer interactions, fluid/structure interactions, and flow control are suggested as directions for future work.

Gas-liquid foams are important in applications ranging from oil recovery and mineral flotation to food science and microfluidics. Beyond their practical use, they represent an intriguing prototype of a soft material with a complex, viscoelastic rheological response. Crucially, foams allow detailed access to fluid-dynamical processes on the mesoscale of bubbles underlying the large-scale material behavior. This review emphasizes the importance of the geometry and interaction of mesoscale structural elements for the description of the dynamics of entire foams. Using examples including bulk flow of foam under steady shear, interfacial instabilities, and foam fracture through bubble rupture, this article highlights the wide variety of available theoretical descriptions, ranging from network modeling approaches coupling structural element equations of motion to full continuum models with elastoviscoplastic constitutive relations. Foams offer the opportunity to develop rigorous links between such disparate descriptions, providing a blueprint for physical modeling of dynamical multiscale systems with complex structure.

Understanding inhomogeneous and anisotropic fluid flows requires mathematical and computational tools that are tailored to such flows and distinct from methods used to understand the canonical problem of homogeneous and isotropic turbulence. We review some recent developments in the theory of inhomogeneous and anisotropic turbulence, placing special emphasis on several kinds of quasi-linear approximations and their corresponding statistical formulations. Aspects of quasi-linear theory that have received insufficient attention in the literature are discussed, and open questions are framed.

Iceberg calving accounts for half of the mass discharge from the Greenland and Antarctic ice sheets, which has increased dramatically over the last two decades. Through their displacement and progressive melt, icebergs can impact both the regional and large-scale ocean circulation and marine ecosystems by affecting their stratification and nutrient and carbon cycling. Freshwater input due to iceberg melt has the potential to impact regional sea ice distribution and the global overturning circulation. Notwithstanding their importance, our understanding of where and how icebergs melt is limited and their representation in ocean and climate models is oversimplistic, in part because they are informed by only a handful of observations. As a result, model-based predictions of iceberg melt rates, of the fate of the meltwater, and of its impact on the ocean are highly uncertain. New observational, modeling, and experimental studies are needed to improve our understanding of iceberg melting and hence, the forecasting power of climate models.

Fluid mechanics lies at the heart of many of the physical processes associated with the nascent deep-sea mining industry. The evolution and fate of sediment plumes that would be produced by seabed mining activities, which are central to the assessment of the environmental impact, are entirely determined by transport processes. These processes, which include advection, turbulent mixing, buoyancy, differential particle settling, and flocculation, operate at a multitude of spatiotemporal scales. A combination of historical and recent efforts that combine theory, numerical modeling, laboratory experiments, and field trials has yielded significant progress, including assessing the role of environmental and operational parameters in setting the extent of sediment plumes, but more fundamental and applied fluid mechanics research is needed before models can accurately predict commercial-scale scenarios. Furthermore, fluid mechanics underpins the design and operation of proposed mining technologies, for which there are currently no established best practices.

Over the past several decades, computational fluid dynamics has been increasingly used in the aerospace industry for the design and study of new and derivative aircraft. In this review we survey the CFD application process and note its place and importance within the everyday work of industry. Furthermore, the centrality of geometry and importance of turbulence models, higher-order numerical algorithms, output-based mesh adaptation, and numerical design optimization are discussed. Challenges in each area are noted and specific suggestions for investment are made. The review concludes with an outlook toward a future in which certification by analysis and model-based design are standard practice, along with a reminder of the steps necessary to lead the industry there.

Particles floating at interfaces are commonly observed in nature, as well as in industrial processes. When the particles are non-Brownian particles, large deformations of the interface are created that induce long-ranged capillary interactions and lead to the formation of particle rafts with unique characteristics. In this review we discuss recent efforts in investigating particle raft formation and the role of the rafts’ own weight during dynamic clustering. Under specific conditions, these rafts can ultimately collapse and sink. When subjected to external or internal forces, the raft undergoes large deformations that test the mechanical characteristics of this interfacial composite material. It can behave as a continuous elastic sheet under compression, although its discrete nature can also trigger its fragmentation via interparticle interactions. Finally, armored droplets, drops covered by a protective shell of particles, can lose their integrity when submitted to dynamic deformations, resulting in the ejection of particles or the fracturing of the armor. Open questions to understand the properties of this material are highlighted and future research to understand the fundamental physics of particle rafts, the customization of the cluster formation, or the disassembly of this collective material is suggested.

The evaporation of a sessile droplet of liquid is a complex and multifaceted fundamental topic of enduring scientific interest that is key to numerous physical and biological processes. As a result, in recent decades a considerable multidisciplinary research effort has been directed toward many different aspects of the problem. This review focuses on some of the insights that can be obtained from relatively simple mathematical models and discusses some of the directions in which the field may move in the future.