Annual Review of Fluid Mechanics - Volume 47, 2015

Sommerfeld's affiliation with fluid mechanics started when he began his career as an assistant of the mathematician Felix Klein at Göttingen. He always regarded fluid mechanics as a particular challenge. In 1904, he published a theory of hydrodynamic lubrication. Four years later, he conceived an approach for the analysis of flow instability (the Orr-Sommerfeld approach) as an attempt to account for the transition from laminar to turbulent flow. The onset of turbulence also became a major challenge for some of his pupils, in particular Ludwig Hopf and Fritz Noether. Both contributed considerably to elaborate the Orr-Sommerfeld theory. Heisenberg's doctoral work was another attempt in this quest. When Sommerfeld published his lectures on theoretical physics during World War II, he dedicated one of the six volumes to the mechanics of continuous media. With chapters on boundary layer theory and turbulence, it exceeded the scope of contemporary theoretical physics—revealing Sommerfeld's persistent appreciation of fluid mechanics. He resorted to Prandtl's Göttingen school of fluid mechanics in order to stay abreast of the rapid development of these specialties.

This review article focuses on the modeling of complex granular flows employing the discrete element method (DEM) approach. The specific topic discussed is the application of DEM models for the study of the flow behavior of nonspherical, flexible, or cohesive particles, including particle breakage. The major sources of particle cohesion—liquid induced, electrostatics, van der Waals forces—and their implementation into DEM simulations are covered. These aspects of particle flow are of great importance in practical applications and hence are the significant foci of research at the forefront of current DEM modeling efforts. For example, DEM simulations of nonspherical grains can provide particle stress information needed to develop constitutive models for continuum-based simulations of large-scale industrial processes.

We review constitutive modeling of solutions and melts of linear polymers, focusing on changes in rheological behavior in shear and extensional flow as the concentration increases from unentangled dilute, to entangled, to dense melt. The rheological changes are captured by constitutive equations, prototypes of which are the FENE-P model for unentangled solutions and the DEMG model for entangled solutions and melts. From these equations, and supporting experimental data, for dilute solutions, the extensional viscosity increases with the strain rate from the low–strain rate to the high–strain rate asymptote, but in the densely entangled state, the high–strain rate viscosity is lower than the low–shear rate value, especially when orientation-dependent friction is accounted for. In shearing flow, shear thinning increases dramatically as the entanglement density increases, which can eventually lead to a shear-banding inhomogeneity. Recent improvements in constitutive modeling are paving the way for robust and accurate numerical simulations of polymer fluid mechanics and industrial processing of polymers.

High-speed printing processes are a leading technology for the large-scale manufacture of a new generation of nanoscale and microscale devices. Central to all printing processes is the transfer of liquid from one surface to another, a seemingly simple operation that is still not well understood. A useful idealization of liquid transfer is a liquid bridge with moving contact lines being deformed between two separating surfaces. The fluid mechanics of such bridges are relevant not only to printing, but also to other important applications, such as adhesion, tribology, biology, oil recovery, and microfluidics.

This article reviews evidence concerning the cornerstone dissipation scaling of turbulence theory: , with Cϵ=const., ϵ the dissipation rate of turbulent kinetic energy , and an integral length scale characterizing the energy-containing turbulent eddies. This scaling is intimately linked to the Richardson-Kolmogorov equilibrium cascade. Accumulating evidence shows that a significant nonequilibrium region exists in various turbulent flows in which the energy spectrum has Kolmogorov's −5/3 wave-number scaling over a wide wave-number range, yet Cϵ∼Re^mI/ReⁿL, with m≈1≈n, ReI a global/inlet Reynolds number, and ReL a local turbulence Reynolds number.

Small objects that are more dense than water may still float at the air-water interface because of surface tension. Whether this is possible depends not only on the density and size of the object, but also on its shape and surface properties, whether other objects are nearby, and how gently the object is placed at the interface. This review surveys recent work to quantify when objects can float and when they must sink. Much interest in this area has been driven by studies of the adaptations of water-walking insects to life at interfaces. I therefore discuss these results in the context of this and other applications.

Typical fluid particle trajectories are sensitive to changes in their initial conditions. This makes the assessment of flow models and observations from individual tracer samples unreliable. Behind complex and sensitive tracer patterns, however, there exists a robust skeleton of material surfaces, Lagrangian coherent structures (LCSs), shaping those patterns. Free from the uncertainties of single trajectories, LCSs frame, quantify, and even forecast key aspects of material transport. Several diagnostic quantities have been proposed to visualize LCSs. More recent mathematical approaches identify LCSs precisely through their impact on fluid deformation. This review focuses on the latter developments, illustrating their applications to geophysical fluid dynamics.

Because of gravitational interactions with their companions, the rotational dynamics of planets and stars involve periodic perturbations of their shape, the direction of their rotational vector, and their rotation rate. These perturbations correspond in planetary terms to tides, precession, and longitudinal libration. We review here the flows driven by those mechanical forcings on rotating spheres and ellipsoids. Special focus is placed on the associated instabilities and on the various routes toward turbulence recently studied. The key point is that mechanical forcings do not provide the energy to the excited flows: They convey part of the available rotational energy and generate intense fluid motions through the excitation of localized jets, shear layers, and resonant inertial modes. Hence, even very small forcings may have large-scale consequences. Mechanically driven flows thus play a fundamental role in planets and stars, significantly influencing their shape, their rotational dynamics, and their magnetic field.

Turbulent fountains arise when a localized flow, free to entrain fluid from its surroundings, is opposed by a buoyancy force. This review cites numerous examples to highlight their wide occurrence in nature and in industry. The breadth of the literature reviewed is significant, drawing from over half a century of progress, and we initially focus on axisymmetric, small–density difference fountains in uniform environments. Many aspects of their rich dynamical behavior, including that of their rise heights and fluctuations in height, are described and encapsulated within the fountain classification presented. Drawing from detailed experimental data sets, dimensional considerations, recent numerical studies, and numerous successful extensions to the original theoretical model for a fountain, we implicitly highlight the current predictive capability offered. The turbulent entrainment of ambient fluid, the effects of environmental stratification, and the role of confinement on a fountain are all discussed. Finally, we suggest future avenues of research.

Acoustic waves carry information about their source and collect information about their environment as they propagate. This article reviews how these information-carrying and -collecting features of acoustic waves that travel through fluids can be exploited for remote sensing. In nearly all cases, modern acoustic remote sensing involves array-recorded sounds and array signal processing to recover multidimensional results. The application realm for acoustic remote sensing spans an impressive range of signal frequencies (10⁻² to 10⁷ Hz) and distances (10⁻² to 10⁷ m) and involves biomedical ultrasound imaging, nondestructive evaluation, oil and gas exploration, military systems, and Nuclear Test Ban Treaty monitoring. In the past two decades, approaches have been developed to robustly localize remote sources; remove noise and multipath distortion from recorded signals; and determine the acoustic characteristics of the environment through which the sound waves have traveled, even when the recorded sounds originate from uncooperative sources or are merely ambient noise.

This review examines different stages of the coalescence process of liquid drops on a planar interface under different conditions. Depending on the application, drops coalescence under the influence of applied external shear stress. The focus of this review is on the effect of the viscous stress, Marangoni stress, and electric field stress on the outcome of this process, particularly on the time of coalescence and partial coalescence. Theoretical progress and experiments of this phenomenon are examined, and a future outlook of this area of research is given.

Yves Couder, Emmanuel Fort, and coworkers recently discovered that a millimetric droplet sustained on the surface of a vibrating fluid bath may self-propel through a resonant interaction with its own wave field. This article reviews experimental evidence indicating that the walking droplets exhibit certain features previously thought to be exclusive to the microscopic, quantum realm. It then reviews theoretical descriptions of this hydrodynamic pilot-wave system that yield insight into the origins of its quantum-like behavior. Quantization arises from the dynamic constraint imposed on the droplet by its pilot-wave field, and multimodal statistics appear to be a feature of chaotic pilot-wave dynamics. I attempt to assess the potential and limitations of this hydrodynamic system as a quantum analog. This fluid system is compared to quantum pilot-wave theories, shown to be markedly different from Bohmian mechanics and more closely related to de Broglie's original conception of quantum dynamics, his double-solution theory, and its relatively recent extensions through researchers in stochastic electrodynamics.

This review uses as a vehicular example the jet-flame configuration to examine some phenomena that emerge in nonpremixed gaseous combustion as a result of the interaction between the temperature-sensitive chemical reaction, typical of combustion, and the convective and diffusive transport. These include diffusion-controlled flames, edge flames and their role in flame attachment, triple flames and their role as ignition fronts, and strain-induced extinction, including flame-vortex interactions. The aim is to give an overall view of the fluid dynamics of nonpremixed combustion and to review the most relevant contributions.

Recent advances in imaging techniques have allowed physicians to obtain robust measurements of intracardiac flows in the clinical setting. Consequently, the physiological implications of intraventricular fluid dynamics are beginning to be understood. Initial data show that these flows involve complex fluid-structure interactions and mixing phenomena that are modified by disease. Here we critically review the most important aspects of intraventricular fluid mechanics relevant for clinical applications. We discuss current image and numerical methods for assessing intraventricular flows, as well as implemented approaches to analyze their impact on cardiac function. The physiological and clinical insights provided by such techniques are discussed both in health and in disease. The final goal is to encourage research in the application of fluid dynamic foundations to patient-based clinical data. A huge potential is anticipated not only in terms of the basic science of large-scale biological systems, but also in practical terms of improving patient care.

In the past decade, the volvocine green algae, spanning from the unicellular Chlamydomonas to multicellular Volvox, have emerged as model organisms for a number of problems in biological fluid dynamics. These include flagellar propulsion, nutrient uptake by swimming organisms, hydrodynamic interactions mediated by walls, collective dynamics and transport within suspensions of microswimmers, the mechanism of phototaxis, and the stochastic dynamics of flagellar synchronization. Green algae are well suited to the study of such problems because of their range of sizes (from 10 μm to several millimeters), their geometric regularity, the ease with which they can be cultured, and the availability of many mutants that allow for connections between molecular details and organism-level behavior. This review summarizes these recent developments and highlights promising future directions in the study of biological fluid dynamics, especially in the context of evolutionary biology, that can take advantage of these remarkable organisms.

Intravascular blood clots form in an environment in which hydrodynamic forces dominate and in which fluid-mediated transport is the primary means of moving material. The clotting system has evolved to exploit fluid dynamic mechanisms and to overcome fluid dynamic challenges to ensure that clots that preserve vascular integrity can form over the wide range of flow conditions found in the circulation. Fluid-mediated interactions between the many large deformable red blood cells and the few small rigid platelets lead to high platelet concentrations near vessel walls where platelets contribute to clotting. Receptor-ligand pairs with diverse kinetic and mechanical characteristics work synergistically to arrest rapidly flowing cells on an injured vessel. Variations in hydrodynamic stresses switch on and off the function of key clotting polymers. Protein transport to, from, and within a developing clot determines whether and how fast it grows. We review ongoing experimental and modeling research to understand these and related phenomena.

We provide a comprehensive and systematic description of the diverse microbubble generation methods recently developed to satisfy emerging technological, pharmaceutical, and medical demands. We first introduce a theoretical framework unifying the physics of bubble formation in the wide variety of existing types of generators. These devices are then classified according to the way the bubbling process is controlled: outer liquid flows (e.g., coflows, cross flows, and flow-focusing flows), acoustic forcing, and electric fields. We also address modern techniques developed to produce bubbles coated with surfactants and liquid shells. The stringent requirements to precisely control the bubbling frequency, the bubble size, and the properties of the coating make microfluidics the natural choice to implement such techniques.

“If you find yourself in a hole, stop digging.” Although Denis Healey's famous adage (Metcalfe 2007) may offer sound advice for politicians, it is less relevant to worms, clams, and other higher organisms that rely on their digging ability for survival. In this article, we review recent work on the development of simple models that elucidate the fundamental principles underlying digging and burrowing strategies employed by biological systems. Four digging regimes are identified based on dimensionless digger size and the dimensionless inertial number. We select biological organisms to represent three of the four regimes: razor clams, sandfish, and nematodes. Models for all three diggers are derived and discussed, and analogies are drawn to low–Reynolds number swimmers.

This review describes and classifies the trajectories of sports projectiles that have spherical symmetry, cylindrical symmetry, or (almost) no symmetry. This classification allows us to discuss the large diversity observed in the paths of spherical balls, the flip properties of shuttlecocks, and the optimal position and stability of ski jumpers.

Dynamic stall is an incredibly rich fluid dynamics problem that manifests itself on an airfoil during rapid, transient motion in which the angle of incidence surpasses the static stall limit. It is an important element of many manmade and natural flyers, including helicopters and supermaneuverable aircraft, and low–Reynolds number flapping-wing birds and insects. The fluid dynamic attributes that accompany dynamic stall include an eruption of vorticity that organizes into a well-defined dynamic stall vortex and massive excursions in aerodynamic loads that can couple with the airfoil structural dynamics. The dynamic stall process is highly sensitive to surface roughness that can influence turbulent transition and to local compressibility effects that occur at free-stream Mach numbers that are otherwise incompressible. Under some conditions, dynamic stall can result in negative aerodynamic damping that leads to limit-cycle growth of structural vibrations and rapid mechanical failure. The mechanisms leading to negative damping have been a principal interest of recent experiments and analysis. Computational fluid dynamic simulations and low-order models have not been good predictors so far. Large-eddy simulation could be a viable approach although it remains computationally intensive. The topic is technologically important owing to the desire to develop next-generation rotorcraft that employ adaptive rotor dynamic stall control.