Annual Review of Fluid Mechanics - Volume 36, 2004

After early work by Newton, the eighteenth and early nineteenth century French mathematicians Laplace, Lagrange, Poisson, and Cauchy made real theoretical advances in the linear theory of water waves; in Germany, Gerstner considered nonlinear waves, and the brothers Weber performed fine experiments. Later in Britain during 1837–1847, Russell, Green, Kelland, Airy, and Earnshaw all made substantial contributions, setting the scene for subsequent work by Stokes and others.

Coating is the process of applying thin liquid layers to a substrate, often a moving web. Complex coating processes can be approached through examination of their fluid mechanical components. The flow elements reviewed in this article include the boundary layer along a moving wall, the dynamic wetting line, withdrawal from a pool, flow metered by a narrow channel, die flow, flow on an incline, the freely falling liquid curtain, premetered coating with a small gap, and flow after coating. Although some flow elements are well studied and understood, others require additional investigation. Genuinely predictive modeling of complex coating processes is not yet possible and coating practice remains largely empirical. Nonetheless, coating science is sufficiently advanced that physical insights and mathematical models greatly benefit design and practice.

Since Leibovich's comprehensive review of Langmuir circulation in 1983 there have been substantial advances in modeling (notably the construction of Large Eddy Simulation models) and in observations using novel techniques that together have led to a radical change in understanding the phenomena. It is now regarded as one of the several turbulent processes driven by wind and waves in the upper layers of large bodies of water, influential in producing and maintaining the uniform surface mixed layer and in driving dispersion.

Early concepts in shock wave drag reduction enabled modern aeronautical systems, and continuing research progress in this arena is crucial for significant improvements in long haul transports and various military platforms and weapons. The research area is rich in concepts/approaches, but many of these have not progressed into the realm of application. This is due in part to a lack of knowledge on the part of the fluids research community concerning the multidisciplinary “real-world” design space/metrics and a consequent lack of the requisite breadth and depth of research information required to evaluate/apply the concept. The article reviews the extant wave drag reduction approaches that are (a) well understood/applied, (b) under active study/indicate considerable promise, and (c) those in the nascent stage only.

This paper reviews the current state of the art in accidental explosion modeling using methods based on computational fluid dynamics (CFD) in the petrochemical process industries. We discuss the problem in terms of its industrial importance and its technical difficulty, which stems mainly from the large range of length and timescales that must be represented. Explicit representation of all scales is not feasible due to limitations of computational cost, and modeling of unresolved physical features is required. We also discuss geometry modeling using the porosity/distributed resistance (PDR) method and review relevant combustion modeling. We describe an advanced CFD approach using unstructured adaptive gridding and discuss its usefulness in the context of results obtained for both two dimensional and three dimensional simulations of gas explosion phenomena in complex geometries.

Almost all vessels carrying fluids within the body are flexible, and interactions between an internal flow and wall deformation often underlie a vessel's biological function or dysfunction. Such interactions can involve a rich range of fluid-mechanical phenomena, including nonlinear pressure-drop/flow-rate relations, self-excited oscillations of single-phase flow at high Reynolds number and capillary-elastic instabilities of two-phase flow at low Reynolds number. We review recent advances in understanding the fundamental mechanics of flexible-tube flows, and discuss physiological applications spanning the cardiovascular system (involving wave propagation and flow-induced instabilities of blood vessels), the respiratory system (involving phonation, the closure and reopening of liquid-lined airways, and Marangoni flows on flexible surfaces), and elsewhere in the body (involving active peristaltic transport driven by fluid-structure/muscle interactions).

Online, continuous, two-phase flow measurement is often necessary, particularly in the oil and gas industry. In this article, we describe some of the commercially most important techniques for gas-liquid, gas-solid, liquid-solid, and liquid-liquid flows, and provide associated illustrative sketches and regime maps. These techniques involve Venturi pressure drop, Coriolis, electromagnetic, and cross-correlation flow meters, gamma-ray absorption and gradio-manometer densitometers, and local electrical and fiber-optic sensors, for which we describe the principles of operation and interpretation. References are given to more comprehensive texts and papers; these are representative rather than exhaustive. It is emphasized that empirical calibration is the norm and that detailed fluid-mechanical analysis has so far played little part in instrument design and operation.

We review the experimental evidence on turbulent flows over rough walls. Two parameters are important: the roughness Reynolds number ks⁺, which measures the effect of the roughness on the buffer layer, and the ratio of the boundary layer thickness to the roughness height, which determines whether a logarithmic layer survives. The behavior of transitionally rough surfaces with low ks⁺ depends a lot on their geometry. Riblets and other drag-reducing cases belong to this regime. In flows with δ/k ≲ 50, the effect of the roughness extends across the boundary layer, and is also variable. There is little left of the original wall-flow dynamics in these flows, which can perhaps be better described as flows over obstacles. We also review the evidence for the phenomenon of d-roughness. The theoretical arguments are sound, but the experimental evidence is inconclusive. Finally, we discuss some ideas on how rough walls can be modeled without the detailed computation of the flow around the roughness elements themselves.

The characterization of blood flow is important for understanding the function of the cardiovascular system under normal and diseased conditions, designing cardiovascular devices, and diagnosing and treating congenital and acquired cardiovascular disease. Experimental methods, especially magnetic resonance imaging techniques can be used to noninvasively quantify blood flow for diagnosing cardiovascular disease, researching disease mechanisms, and validating assumptions and predictions of mathematical models. Computational methods can be used to simulate blood flow and vessel dynamics, test hypotheses of disease formation under controlled conditions, and evaluate devices that have not yet been built and treatments that have not yet been implemented. In this article we review experimental and computational methods for quantifying blood flow velocity and pressure fields in human arteries. We place particular emphasis on providing an introduction to the physics and applications of magnetic resonance imaging, and surveying lumped parameter, one-dimensional, and three-dimensional numerical methods used to model blood flow.

We review the use of ray models for internal waves, particularly formulations for calculating wave amplitudes along the ray. These are expressed in spatial, wave number, and phase-space coordinates. The choice of formulation affects not only the difficulty of the calculations for rays and caustics but also the degree to which the waves satisfy slowly varying assumptions. We describe several examples taken from atmospheric and oceanic applications that illustrate the variety of options for ray models.

This paper is a short and nonexhaustive survey of some recent developments in optimal shape design (OSD) for fluids. OSD is an interesting field both mathematically and for industrial applications. Existence, sensitivity, and compatibility of discretizations are important theoretical issues. Efficient algorithmic implementations with low complexity are also critical. In this paper we discuss topological optimization, algorithmic differentiation, gradient smoothers, Computer Aided Design (CAD)-free platforms and shock differentiation; all these are applied to a multicriterion optimization for a supersonic business jet.

The coexistence in the deep ocean of a finite, stable stratification, a strong meridional overturning circulation, and mesoscale eddies raises complex questions concerning the circulation energetics. In particular, small-scale mixing processes are necessary to resupply the potential energy removed in the interior by the overturning and eddy-generating process. A number of lines of evidence, none complete, suggest that the oceanic general circulation, far from being a heat engine, is almost wholly governed by the forcing of the wind field and secondarily by deep water tides. In detail however, the budget of mechanical energy input into the ocean is poorly constrained. The now inescapable conclusion that over most of the ocean significant “vertical” mixing is confined to topographically complex boundary areas implies a potentially radically different interior circulation than is possible with uniform mixing. Whether ocean circulation models, either simple box or full numerical ones, neither explicitly accounting for the energy input into the system nor providing for spatial variability in the mixing, have any physical relevance under changed climate conditions is at issue.

We review artificial boundary conditions (BCs) for simulation of inflow, outflow, and far-field (radiation) problems, with an emphasis on techniques suitable for compressible turbulent shear flows. BCs based on linearization near the boundary are usually appropriate for inflow and radiation problems. A variety of accurate techniques have been developed for this case, but some robustness and implementation issues remain. At an outflow boundary, the linearized BCs are usually not accurate enough. Various ad hoc models have been proposed for the nonlinear case, including absorbing layers and fringe methods. We discuss these techniques and suggest directions for future modeling efforts.

Shock wave research was traditionally developed as an element of high-speed gas dynamics supporting supersonic flights and atmospheric reentry of space vehicles. However, recently its scope has expanded to the comprehensive interpretation of shock wave phenomena in nature and the artificial world. In particular, many aspects of volcanoes's explosive eruptions are closely related to shock wave dynamics. One hypothesis proposes that during asteroid impact events that took place millions of years ago underwater shock waves played a decisive role in mass extinction of marine creatures. Shock waves have been successfully applied to medical therapy. Extracorporeal shock wave lithotripsy (ESWL) was a wonderful success in noninvasive removal of urinary tract stones. Recently, shock wave therapy was further developed for the revascularization of cerebral embolism, drug delivery, and other interesting therapeutic methods. This review provides an overview of the state-of-the-art interdisciplinary applications of shock wave research to geophysics and medicine.

Microfluidic devices for manipulating fluids are widespread and finding uses in many scientific and industrial contexts. Their design often requires unusual geometries and the interplay of multiple physical effects such as pressure gradients, electrokinetics, and capillarity. These circumstances lead to interesting variants of well-studied fluid dynamical problems and some new fluid responses. We provide an overview of flows in microdevices with focus on electrokinetics, mixing and dispersion, and multiphase flows. We highlight topics important for the description of the fluid dynamics: driving forces, geometry, and the chemical characteristics of surfaces.

This review summarizes fundamental results and discoveries concerning vortex-induced vibration (VIV), that have been made over the last two decades, many of which are related to the push to explore very low mass and damping, and to new computational and experimental techniques that were hitherto not available. We bring together new concepts and phenomena generic to VIV systems, and pay special attention to the vortex dynamics and energy transfer that give rise to modes of vibration, the importance of mass and damping, the concept of a critical mass, the relationship between force and vorticity, and the concept of “effective elasticity,” among other points. We present new vortex wake modes, generally in the framework of a map of vortex modes compiled from forced vibration studies, some of which cause free vibration. Some discussion focuses on topics of current debate, such as the decomposition of force, the relevance of the paradigm flow of an elastically mounted cylinder to more complex systems, and the relationship between forced and free vibration.