Showing papers in "Annual Review of Fluid Mechanics in 1993"

The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows

Abstract: It has often been remarked that turbulence is a subject of great scientific and technological importance, and yet one of the least understood (e.g. McComb 1990). To an outsider this may seem strange, since the basic physical laws of fluid mechanics are well established, an excellent mathematical model is available in the Navier-Stokes equations, and the results of well over a century of increasingly sophisticated experiments are at our disposal. One major difficulty, of course, is that the governing equations are nonlinear and little is known about their solutions at high Reynolds number, even in simple geometries. Even mathematical questions as basic as existence and uniqueness are unsettled in three spatial dimensions (cf Temam 1988). A second problem, more important from the physical viewpoint, is that experiments and the available mathematical evidence all indicate that turbulence involves the interaction of many degrees of freedom over broad ranges of spatial and temporal scales. One of the problems of turbulence is to derive this complex picture from the simple laws of mass and momentum balance enshrined in the NavierStokes equations. It was to this that Ruelle & Takens (1971) contributed with their suggestion that turbulence might be a manifestation in physical

Boundary Mixing and Arrested Ekman Layers: Rotating Stratified Flow Near a Sloping Boundary

Abstract: We are concerned here with the behavior of a rotating, stratified fluid near a sloping rigid boundary, with boundary conditions of zero normal buoyancy flux and no slip. Although this is an interesting fluid dynamical problem in its own right, we have been motivated by two major, and at first sight disparate, topics in physical oceanography. The first, known as "boundary mixing", is concerned with how turbulent mixing at the sloping sides of the density-stratified ocean affects the stratification in the interior. The second topic involves the way in which the combination of strati-

The Impact of Drops on Liquid Surfaces and the Underwater Noise of Rain

Abstract: There will be but few of my readers who have not, in some heavy shower of rain, beguiled the tedium of enforced waiting by watching, perhaps half-unconsciously, the thousand little crystal fountains that start from the surface of pool or river; noting now and then a surrounding coronet of lesser jets, or here and there a bubble that floats for a moment and then vanishes. It is to this apparently insignificant transaction, which always has been and always will be so familiar, and to others of a like nature, that I desire to call the attention of those who are interested in natural phenomena; hoping to share with them some of the delight that I have myself felt, in contemplating the exquisite forms that the camera has revealed, and in watching the progress of a multitude of events, compressed indeed within the limits of a few hundredths of a second, but none the less orderly and inevitable, and of which the sequence is in part easy to anticipate and understand, while in part it taxes the highest mathematical powers to elucidate.

Wave Breaking in Deep Water

Abstract: Every mariner is aware that dangerous large breaking water waves occur on the world's oceans. The scope of this review is somewhat greater. Wave breaking occurs at a large range of scales and we do not restrict ourselves to the deep ocean. "Deep water" in the context of water wave studies implies water sufficiently deep that the surface waves are unaffected by the direct effects of variations in bed topography. Thus even a small pond can support breaking deep-water waves. Shallow water breaking is reviewed in Peregrine (1983). Some comments on the visual aspect of breakers are in order, since direct observation still has a role to play in the study of this complex phenomenon. The most dramatic breakers are plunging breakers where the breaking commences by the wave overturning and forming a forward moving sheet of water which plunges down into the water in front causing splashes, air entrainment, and eddies. Although plunging breakers are common on beaches they are less common on deep water, so much so that some people have argued that they do not occur naturally. However, read Coles (1991) for a distillation of an experienced yachtsman's account of waves at sea. Most other breakers are described as spilling breakers. From their

Vortices in Rotating Fluids

Abstract: The emergence of coherent vortex structures is a characteristic feature of quasi-geostrophic or two-dimensional turbulence and because of their relevance to large-scale geophysical flows, the dynamics of these structures has been studied increasingly over the past decade. In the oceans and in the atmospheres vortices or eddies are abundant. For this reason, the study of isolated vortices in rotating fluids-including their dynamics, instability properties, mutual interaction behavior, and effects due to bottom topog­ raphy-is of fundamental interest for refined models of geostrophic turbulence and of the general oceanic and atmospheric circulations. Pro­ cesses of heat transfer, dispersion of biochemical components, and the transport of other physical properties are closely connected with coherent structures. The dynamics of two-dimensional vortices in homogeneous fluids is also a key problem in free shear flows. With or without background rotation, the main question concerns the stability of these vortices to three­ dimensional disturbances. In addition, two-dimensional vortices also play an important role in tokamak-confined plasmas as well as in astrophysical situations such as accretion discs of neutron stars. During the past decade, considerable insight has been gained in the

Order parameter equations for patterns

Abstract: Patterns of an almost periodic nature appear all over the place. One sees them in cloud streets, in sand ripples on flat beaches and desert dunes, in the morphology of plants and animals, in chemically reacting media, in boundary layers, on weather maps, in geological formations, in interacting laser beams in wide gainband lasers, on the surface of thin buckling shells, and in the grid scale instabilities of numerical algorithms. This review deals with the class of problems into which these examples fall, namely with pattern formation in spatially extended, continuous, dissipative systems which are driven far from equilibrium by an external stress. Under the influence of this stress, the system can undergo a series of symmetry breaking bifurcations or phase transitions and the resulting patterns become more and more complicated, both temporally and spatially, as the stress is increased. Figures 1 through 3 show examples of patterns in lasers, binary and ordinary fluids, and liquid crystals. The goal of theory is to provide a means of understanding and explaining these patterns from a macroscopic viewpoint that both simplifies and unifies classes of problems which are seemingly unrelated at the microscopic level. Convection in a large aspect ratio horizontal layer of fluid heated from below is the granddaddy of canonical examples used to study pattern formation and behavior in spatially extended systems. For low values of the vertical temperature difference, which is the external stress parameter in this case and whose non-dimensional measure is called the Rayleigh

Aerodynamics of Horizontal-Axis Wind Turbines

Abstract: This paper provides an overview of recent research and development pertaining to the aerodynamics of the horizontal-axis wind turbine rotor. A brief overview of the size and nature of the wind energy industry and the types of rotors commonly in use today is provided

Resonant interactions among surface water waves

Abstract: Resonant Interaction Theory (RIT)is reviewed in a variety of dynamical settings with an emphasis on the underlying approximations. The elementary interactions of three- and four-wave resonances is examined as well as deterministic and stochastic models for wavefields comprising either a broad or narrow spectrum of waves interacting in multiple and coupled sets. Some special settings in which higher-order resonances have been examined are reviewed together with Resonant Interaction Experiments (RIE) in a variety of dynamical settings with an emphasis on those aspects that are predicted. Experimental investigations on the applicability of Kelvin's dispersion relation and experiments involving gravity, gravity- capillary, and capillary wavetrains are discussed. Results from comparisons between RIT and RIE are briefly summarised and the particular absence of controlled experiments in some applications is noted.

Surface Waves and Coastal Dynamics

Abstract: This review covers theoretical advances made during the past decade for predicting or understanding wind-induced waves and associated coastal processes. First, the offshore propagation over many wavelengths is discussed. An effective approximation which permits practical calculations of both refraction and diffraction over a mildly sloping bottom is given. For still longer distances nonlinear effects accumulate to become important; recent progress in the parabolic approximation for the refraction and diffraction of short waves is also reviewed. The nearshore region is discussed and the infragravity waves which are caused by nonlinear interactions of short waves within a narrow frequency band are surveyed. The effects of a gradual or sudden change of depth or a steady current on the modulation of short waves and the generation of long infragravity waves is also discussed. A discussion of infragravity waves which resonate in harbours and the strong resonance of edge waves on beaches is made. The final topics are concerned with the causes and effects of bars and ripples on the seabed.

Perspectives on Hypersonic Viscous Flow Research

Abstract: Issues and advances in current hypersonic flow research perceived to be of interest in theoretical fluid/gas dynamics are reviewed. Particular attention is given to the hypersonic aircraft as waverider, computational methods and theoretical development in the study of viscous interaction, and boundary-layer instability and transition studies. In the present framework the study of viscous hypersonic flow faces transition problems of two kinds which represent the two major areas of current research: the turbulence transition in the high Re range and the transition to the free-molecule limit.

Up-To-Date Gasdynamic Models of Hypersonic Aerodynamics and Heat Transfer with Real Gas Properties

Abstract: Hypersonic aerodynamics and heat transfer problems have received renewed interest during the past decade (Anderson 1984). This revival has been due to the design and creation of space vehicles that move along glide reentry trajectories in the upper layers of the Earth's atmosphere (H = 50100 km) at hypersonic velocities (V» < 7.8 km S-I; i.e. Space Shuttle, Buran), and the development of space vehicles with reentry trajectories in the upper atmospheric layers (at altitudes H = 70-100 km) which use aerodynamic braking during recovery from geosynchronous orbit (V OJ = 7-11 km s-') at nominal reentry velocities VOJ = 10 km s-' (Walberg 1983). Typical trajectories of various spacecraft and the regions of different physical and chemical processes in the shock layer near such vehicles are shown in Figure 1. Unlike the aerodynamic and heat transfer characteristics of con­ ventional aircraft, these problems are characterized at reentry (or ascend­ ing) trajectories by a wide range of Reynolds numbers (100 < Re",, ) , large

Flow-Induced Vibrations in Arrays of Cylinders

Abstract: There is extreme variety in flow-induced vibrations; they are observed in many diverse situations ranging from reeds in musical instruments to fluttering panels in supersonic airplanes. In order to keep the discussion within bounds, we will focus on one versatile set of simple geometries: arrays of circular cylinders in cross flow. By changing cylinder arrangement and the parameters of spacing, damping, and mass ratio, several different basic types of self-sustaining oscillations can be produced. Because of the industrial importance of tube bundles in heat exchangers, a wealth of observations and analyses has accumulated in the literature (Naudascher & Rockwell 1980). We limit ourselves to discussing cross flow because of the fundamental differences between parallel-flow instabilities and the separated-flow mech­ anisms occurring in cross flow. In parallel flow in or outside of tubes, the cylindrical walls form continuous flow boundaries which curve when there is a vibrational deflection. The dynamic equation for a single tube is a beam equation with "gyroscopic equation" terms added:

The Structure and Stability of Laminar Flames

Abstract: This review paper on the structure and stability of laminar flames considers such phenomena as heterogeneous mixtures, acoustic instabilities, flame balls and related phenomena, radiation effects, the iodate oxidation of arsenous acid and 'liquid flame fronts', approximate kinetic mechanisms and asymptotic approximations, and tribrachial or triple flames. The topics examined here indicate three themes that may play an important role in laminar flame theory in the coming years: microgravity experiments, kinetic modeling, and turbulence modeling. In the discussion of microgravity experiments it is pointed out that access to drop towers, the Space Shuttle and, in due course, the Space Station Freedom will encourage the development of experiments well designed to isolate the fundamental physics of combustion.