Annual Review of Fluid Mechanics - Volume 41, 2009

In view of the earlier publication in this journal of a biography of Theodore von Kármán by Sears & Sears (1979), which referred to his years in Germany at Göttingen (1908 to 1912) and Aachen (1912 to 1930) and at the Guggenheim Aeronautical Laboratory of the California Institute of Technology (GALCIT) from 1930 to 1952, we restrict our review here to his later years (from 1952 until his death in 1963). We also comment on his scientific legacy and identify representative institutions and outstanding workers whose research continues the von Kármán style of work in the general areas of aerothermochemistry and allied fields.

I review the concept of optimal vortex formation and examine its relevance to propulsion in biological and bio-inspired systems, ranging from the human heart to underwater vehicles. By using examples from the existing literature and new analyses, I show that optimal vortex formation can potentially serve as a unifying principle to understand the diversity of solutions used to achieve propulsion in nature. Additionally, optimal vortex formation can provide a framework in which to design engineered propulsions systems that are constrained by pressures unrelated to biology. Finally, I analyze the relationship between optimal vortex formation and previously observed constraints on Strouhal frequency during animal locomotion in air and water. It is proposed that the Strouhal frequency constraint is but one consequence of the process of optimal vortex formation and that others remain to be discovered.

The quantification of uncertainty in computational fluid dynamics (CFD) predictions is both a significant challenge and an important goal. Probabilistic uncertainty quantification (UQ) methods have been used to propagate uncertainty from model inputs to outputs when input uncertainties are large and have been characterized probabilistically. Polynomial chaos (PC) methods have found increased use in probabilistic UQ over the past decade. This review describes the use of PC expansions for the representation of random variables/fields and discusses their utility for the propagation of uncertainty in computational models, focusing on CFD models. Many CFD applications are considered, including flow in porous media, incompressible and compressible flows, and thermofluid and reacting flows. The review examines each application area, focusing on the demonstrated use of PC UQ and the associated challenges. Cross-cutting challenges with time unsteadiness and long time horizons are also discussed.

A left-right (LR) asymmetric body plan is crucial for the development of the human body. The past decade has seen rapid progress in our understanding of the LR symmetry-breaking process in vertebrate development. A series of experimental studies has demonstrated that leftward movement of fluid at the ventral node, designated nodal flow, is the central process in symmetry breaking. Nodal flow is autonomously generated by the posteriorly tilted rotation of cilia. The underlying fluid dynamic mechanism, especially the importance of viscous interactions between the cilia and the cell surface, has been clarified by theoretical analyses. Recent experiments have suggested how this leftward nodal flow can be interpreted to create LR asymmetry. Specifically, leftward transport of lipoprotein particles, called nodal vesicular parcels (NVPs), was uncovered. Nodal flow thus triggers left-specific signaling pathways by transporting signaling molecules to the left side using NVPs.

Chemical cues mediate many critical life processes, such as feeding, reproduction, and benthic settling, for aquatic organisms. Depending on the fluid velocity and flow regime, released chemicals are transported via diffusion, laminar advection, or turbulent advection prior to organism reception. Here, we review transport mechanisms and ecological consequences in each regime. We discuss cue structures in terms of concentration gradients, concentration fluctuations, and spatial patterns and draw conclusions about strategies that animals use to acquire information. In some cases, chemical transport occurs through a combination of mechanisms, which requires a multiscale analysis. Regime and scaling are major themes that emerge from recent research. In particular, nondimensional parameters that combine biological and physical variables reveal general principles under which organisms respond to chemical cues and facilitate defining regimes of behavior.

The initiation and progression of cerebral aneurysms are degenerative processes of the arterial wall driven by a complex interaction of biological and hemodynamic factors. Endothelial cells on the artery wall respond physiologically to blood-flow patterns. In normal conditions, these responses are associated with nonpathological tissue remodeling and adaptation. The combination of abnormal blood patterns and genetics predisposition could lead to the pathological formation of aneurysms. Here, we review recent progress on the basic mechanisms of aneurysm formation and evolution, with a focus on the role of hemodynamic patterns.

It is not known whether the three-dimensional (3D) incompressible Navier-Stokes equations possess unique smooth (continuously differentiable) solutions at high Reynolds numbers. This problem is quite important for basic science, practical applications, and numerical computations. This review presents a selective survey of the current state of the mathematical theory, focusing on the technical source of difficulties encountered with the construction of smooth solutions. It also highlights physical phenomena behind the mathematical challenges.

A Boger fluid is an elastic liquid with a constant viscosity. Because the viscosity is independent of shear rate or nearly so, elastic effects can be separated from viscous effects in viscoelastic flows because the latter effects can be determined with Newtonian fluids. Boger fluids are dilute polymer solutions generally made with a solvent sufficiently viscous that stresses due to elasticity are measurable. This article closely examines rheological characteristics and reviews flows with Boger fluids, flows for which investigators have found the onset and magnitude of elastic effects through the use of these fluids. Constitutive equations for viscoelastic fluids are evaluated through comparisons to experimental data, including the simple Oldroyd-B equation, which is physically sensible but only marginally accurate. A significant benefit of the introduction of Boger fluids has been the clear identification of a flow instability due to elasticity alone.

Investigators have modeled oceanic and atmospheric vortices in the laboratory in a number of different ways, employing background rotation, density effects, and geometrical confinement. In this article, we address barotropic vortices in a rotating fluid, emphasizing generation techniques, instability issues, and topography effects in particular. We then review work on vortices in shallow fluid layers, including topography effects on vortices in coastal areas and the role of vortices in tidal exchange between two connected basins.

We review studies of the statistics of isotropic turbulence in an incompressible fluid at high Reynolds numbers using direct numerical simulation (DNS) from the viewpoint of fundamental physics. The Reynolds number achieved by the largest DNS, with 4096³ grid points, is comparable with the largest Reynolds number in laboratory experiments. The high-quality DNS data in the inertial subrange and the dissipative range enable the examination of detailed statistics at small scales, such as the normalized energy-dissipation rate, energy and energy-flux spectra, the intermittency of the velocity gradients and increments, scaling exponents, and flow-field structure. We emphasize basic questions of turbulence, universality in the sense of Kolmogorov's theory, and the dependence of the statistics on the Reynolds number and scale.

Detached-eddy simulation (DES) was first proposed in 1997 and first used in 1999, so its full history can be surveyed. A DES community has formed, with adepts and critics, as well as new branches. The initial motivation of high–Reynolds number, massively separated flows remains, for which DES is convincingly more capable presently than either unsteady Reynolds-averaged Navier-Stokes (RANS) or large-eddy simulation (LES). This review discusses compelling examples, noting the visual and quantitative success of DES. Its principal weakness is its response to ambiguous grids, in which the wall-parallel grid spacing is of the order of the boundary-layer thickness. In some situations, DES on a given grid is then less accurate than RANS on the same grid or DES on a coarser grid. Partial remedies have been found, yet dealing with thickening boundary layers and shallow separation bubbles is a central challenge. The nonmonotonic response of DES to grid refinement is disturbing to most observers, as is the absence of a theoretical order of accuracy. These issues also affect LES in any nontrivial flow. This review also covers the numerical needs of DES, gridding practices, coupling with different RANS models, derivative uses such as wall modeling in LES, and extensions such as zonal DES and delayed DES.

In this review we discuss the morphodynamics of tidal inlet systems that are typical of barrier coasts formed during a period of continuous sea-level rise during the Holocene. The morphodynamics concerns feedbacks between three major components: the hydrodynamics of tidal currents and wind waves; the erosion, deposition, and transport of sediment under the action of the former hydrodynamic agencies; and the morphology proper, which results from the divergence of the sediment transport. We discuss the morphodynamics of the different units that characterize a tidal inlet system: the overall system, the ebb-tidal delta, the tidal channels, channel networks, tidal bars and meanders, and finally the intertidal zone of tidal flats and salt marshes. In most of these units, stability analysis is a major guide to the establishment of equilibrium structures.

This article focuses on the feedback control of turbulence for skin friction reduction and reviews the state of the art of control algorithms and distributed microsensors and microactuators. From a viewpoint of possible practical applications, we discuss only the control schemes based on the wall-surface sensing of shear stress and pressure fluctuations with their assessment in direct numerical simulation. The rapid development of microelectromechanical systems (MEMS) flow sensors/actuators is sketched, and a prototype feedback control system assembled for a turbulent channel flow is introduced. Finally, several major remaining issues in control algorithms and massive fabrication of microdevices are discussed.

The ocean circulation is a cause and consequence of fluid scale interactions ranging from millimeters to more than 10,000 km. Although the wind field produces a large energy input to the ocean, all but approximately 10% appears to be dissipated within about 100 m of the sea surface, rendering observations of the energy divergence necessary to maintain the full water-column flow difficult. Attention thus shifts to the physically different kinetic energy (KE) reservoirs of the circulation and their maintenance, dissipation, and possible influence on the very small scales representing irreversible molecular mixing. Oceanic KE is dominated by the geostrophic eddy field, and depending on the vertical structure (barotropic versus low-mode baroclinic), direct and inverse energy cascades are possible. The pathways toward dissipation of the dominant geostrophic eddy KE depend crucially on the direction of the cascade but are difficult to quantify because of serious observational difficulties for wavelengths shorter than approximately 100–200 km. At high frequencies, KE is dominated by internal waves with near-inertial frequencies (frequencies near the local Coriolis parameter), whose shears appear to be a major source of wave breaking and mixing in the ocean interior.

This article reviews hydrodynamic and magnetohydrodynamic processes in disks around young stars, encompassing the epochs of molecular-cloud turbulence, dense core collapse, disk formation, disk evolution, and planetesimal formation.

Stars can be fascinating settings in which to study intricate couplings among convection, rotation, magnetism, and shear, usually under distinctly nonlinear conditions that yield vigorous turbulence. The emerging flux and the rotation rates of stars can vary widely, yet there are common elements that must contribute to building and maintaining the vibrantly evolving magnetic activity they exhibit. Some of these elements, such as the rotational shear and meridional flows established by the coupling of convection with rotation, can now be studied in detail within our nearest star using helioseismology. Major three-dimensional numerical simulations help refine our intuitions about such interior dynamics, aided by rapid advances in supercomputing that are improving the fidelity of the modeling. These developments, combined with intense thrusts at new high resolution and continuous observations of solar magnetism and solar oscillations, herald a promising era for exploring such astrophysical fluid dynamics.

Much recent evidence suggests that bone cells sense their mechanical environment via interstitial fluid flow. In this review, we summarize theoretical and experimental approaches to quantify fluid and solute transport in bone, starting with the early investigations of fluid shear stress applied to bone cells. The pathways of bone interstitial fluid and solute movement are highlighted based on recent theoretical models, as well as a new generation of tracer experiments that have clarified and refined the structure and function of the osteocyte pericellular matrix. Then we trace how the fluid-flow models for mechanotransduction have evolved as new ultrastructural features of the osteocyte lacunar-canalicular porosity have been identified and how more recent in vitro fluid-flow and cell-stretch experiments have helped elucidate at the molecular level the possible pathways for cellular excitation in bone.

The Lagrangian description of turbulence is characterized by a unique conceptual simplicity and by an immediate connection with the physics of dispersion and mixing. In this article, we report some motivations behind the Lagrangian description of turbulence and focus on the statistical properties of particles when advected by fully developed turbulent flows. By means of a detailed comparison between experimental and numerical results, we review the physics of particle acceleration, Lagrangian velocity structure functions, and pairs and shapes evolution. Recent results for nonideal particles are discussed, providing an outlook on future directions.

Two-particle dispersion is of central importance to a wide range of natural and industrial applications. It has been an active area of research since Richardson's (1926) seminal paper. This review emphasizes recent results from experiments, high-end direct numerical simulations, and modern theoretical discussions. Our approach is complementary to Sawford's (2001), whose review focused primarily on stochastic models of pair dispersion. We begin by reviewing the theoretical foundations of relative dispersion, followed by experimental and numerical findings for the dissipation subrange and inertial subrange. We discuss the findings in the context of the relevant theory for each regime. We conclude by providing a critical analysis of our current understanding and by suggesting paths toward further progress that take full advantage of exciting developments in modern experimental methods and peta-scale supercomputing.

The cytoskeleton is the primary internal structure of the cell, providing its structural integrity. The rheology and mechanics of the cytoskeleton, therefore, are key to the cell's ability to accomplish its diverse functions in health and disease. Although the importance of the cytoskeleton is well established, the relationship between the microstructural details and the macroscopic rheological behavior of the cytoskeleton remains elusive. A wide range of computational and phenomenological models as well as experimental techniques have been proposed over the past two decades to describe the cytoskeleton, giving rise to several, often contradictory, theories for describing its rheology. This concise review attempts to bring together the key experimental methods and theoretical and computational models regarding cytoskeletal rheology and mechanics.