Showing papers in "Annual Review of Fluid Mechanics in 1988"

Secondary Instability of Boundary Layers

Abstract: The problem of transition from laminar to turbulent flow in viscous bound­ ary layers is of great practical interest. The low skin-friction coefficient of laminar boundary-layer flow is very attractive to those who lay out the engines or pay the fuel for high-speed vehicles such as airplanes. However, the low mixing of fluid properties such as chemical species, heat, or momen­ tum may be intolerable for others who design these engines or cope with the danger of separation in adverse pressure gradients; they may clearly prefer a turbulent state of the flow. Therefore, it would be highly desirable to at least predict, if not to control, whether the flow under consideration is laminar or turbulent. The tremendous efforts of decades of intense research, however, have been to little avail (Reshotko 1976). The empirical en-criterion is still the standard tool in engineering practice, although it is known to ignore essential ingredients of the physics of transition and therefore may dangerously mislead if used beyond the supporting data base. Numerical transition simulations have gained reliability in repro­ ducing the transition process in sufficient detail to extract information unobtainable from laboratory experiments. However, the inherent assumptions of stream wise periodicity and temporal growth of the bound­ ary layer, in addition to the uncertainty of initial conditions, prevent predicting transition in practice. Hence, theory still holds an important place in identifying inherent mechanisms and structures of the transition process and in explaining otherwise unintelligible observations. The past decade saw some important progress in stability theory, slow or fast, depending on the reader's judgment ..

Hamiltonian fluid mechanics

Abstract: This paper reviews the relatively recent application of the methods of Hamiltonian mechanics to problems in fluid dynamics. By Hamiltonian mechanics I mean all of what is often called classical mechanics-the subject of the textbooks by Lanczos ( 1970), Goldstein ( 1 980), and Arnol'd (1978). Since the advent of quantum mechanics, Hamiltonian methods have played an increasingly important role in both the classical and quan­ tum mechanics of particles and fields. By comparison, the introduction of Hamiltonian methods into fluid mechanics has been tardy. Why is this so? In general mechanical systems, the Lagrangian or Hamiltonian equa­ tions of motion are coupled equations governing the locations and veloc­ ities of massive particles or rigid bodies. These coupled equations cannot generally be solved for any subset of the dependent variables without also finding all of the other dependent variables. By contrast, the conventional Eulerian fluid equations are closed equations in the velocity, density, and entropy (regarding pressure as a prescribed function of the density and entropy) that can (in principle) be solved without also finding the trajectory of every fluid particle. Once the velocity field is known, the particle tra­ jectories can always be reconstructed by solving the equations for three independent, passively advected tracers (such as the initial Cartesian com­ ponents), but these extra computations are not required if only the Eulerian fields are sought. In the special case of constant-density flow, the Eulerian equations are dramatically simpler than the general Lagrangian or Hamil­ tonian equations for the fluid. From the Hamiltonian perspective, the extraordinary simplicity of the Eulerian description derives from a symmetry property of the fluid

Instability mechanisms in shear-flow transition

Abstract: Developing an understanding of turbulent shear flow at high Reynolds numbers has been a central problem in the theory of fluid motion for over a century Like all turbulent flows, turbulent shear flow is a fluid motion of complex and irregular character whose exact behavior is very sensitive to small changes in initial or boundary conditions Turbulent shear flows are further characterized by a large range of length and time scales, with energy and momentum transfer predominantly affected by nonlinear (iner­ tial) processes between eddies of different scales In many situations of interest, the external conditions are geometrically and temporally simple, and the flow equations admit a correspondingly simple solution: one example is Hagen-Poiseuille flow in a pipe with a constant pressure gradi­ ent Simple, or laminar, flow is generally preferred at low or moderate Reynolds numbers, while turbulent flow is preferred at high Reynolds

Initial Stage of Water Impact

Abstract: The problem of interaction between a solid body and a liquid with a free surface is a broad subject that includes several significant sections of classical and modern hydrodynamics. In this review we confine our dis­ cussion to processes characterized by strong unsteadiness in their develop­ ment and by the existence of a contact line between the free surface of the liquid and the solid-body surface. Detailed investigation of such processes can be applied to problems in ship building, aviation, and energetics (e.g. slamming problems, and the problems of the landing of flying boats and of high-velocity liquid-drop impact upon structural elements). In a general form, such processes can be described in the following manner: At the initial instant of time t = 0, a solid body touches a free surface of liquid. At this moment the position of the solid body, the domain occupied by the liquid, and the velocity field of the liquid particles are assumed to be known. For t > 0, either the law of body motion or the external forces affecting it are prescribed. The liquid flow and the character of its action upon the body.are to be determined. Interest in this field of hydrodynamics arose more than a half century ago in connection with the problem of the landing of flying boats. The first theories of solid-body impact with a liquid (the penetration theory of von Karm{m and the impact theory of Sedov) were directed at a global description of this process. Many applied problems have since been solved on the basis of these theories. But in some cases, more complete infor­ mation about the process is required. Thus, in studying material erosion it is important to know the stress distribution in the contact zone between the liquid and the solid-body surface. It is also necessary to take into account the peculiarities of the flow velocity field in order to determine the

Digital Image Processing in Flow Visualization

Abstract: Flow visualization results from the interaction between light and matter. Classical methods such as shadowgraphy, schlieren photography, and interferometry visualize variation in the index of refraction induced by changes in density, pressure, or temperature. Nonuniformities of these physical observables modify the phase of optical waves, rendered visible by free-space propagation (shadowgraphy), optical processing in the back focal plane of a lens (schlieren photography), or interference with a ref­ erence wave (interferometry). The classical methods visualize variations of the index of refraction or spatial derivatives thereof integrated along the light path through the fluid. Three-dimensional space is projected onto a plane with the corresponding reduction in degrees of freedom. Except for axial symmetric or two-dimensional flows, spatial structures cannot be recovered from a single image. Interior detail may be visualized by illuminating the flow with a sheet of light and imaging scattered radiation from variations in particle density or physical observables. Mie scattering is widely used because particles scatter more efficiently than molecules. Rayleighand Raman-scattering cross sections are small, necessitating intense laser sources for flow visu­ alization. Excellent reviews of classical flow-visualization methods have been pub­ lished, for example, by Merzkirch (1974) and Lauterborn & Vogel (1984) and a beautiful and inspiring collection of pictures by Van Dyke (1982).

Multiphase Flow in Porous Media

Abstract: A development history and current status evaluation are presented for the theory of permeability and percolation. The microscale phenomena treated in this field have proven difficult to analyze due both to their tortuous geometry and the influence of capilarity. Capilary effects may be not only important but predominant, and are differentiated into those at the fluid-fluid interface, and those involving the existence of a contact line between the solid substrate and this interface. Percolation theory has been borrowed from physics and adapted to the two-phase engineering context.

Magnetic Fields in the Solar Convection Zone: Magnetoconvection and Magnetic Buoyancy

Abstract: Article de synthese sur l'activite magnetique du Soleil et de son influence sur la convection. Des simulations numeriques sont presentees en fonction des 2 principales configurations theoriques: champ magnetique vertical horizontal

Fluid models of geological hotspots

Abstract: Plate tectonics has provided a framework for understanding the motion of the large lithospheric blocks (plates) that make up the surface of the Earth. Many large-scale features of the Earth are now known to result from the movements and interactions of these plates. However, some prominent surface features cannot be directly explained by plate tec­ tonics-in particular, the existence of linear island and seamount chains. Wilson (1963) suggested that these chains, such as Hawaii, were formed as the plates passed over fixed regions of the mantle where large amounts of magma (or at least heat) were being produced. These hotspots are long-living sources of volcanoes. They often display "tracks" of previous episodes elsewhere on the plates (Figure 1). The central concept in explain­ ing hotspots is that their ultimate source is below the region of large lateral flow in the mantle. The surface manifestations of hotspots remain fixed with respect to each other (Morgan 1971), or at most move with relative velocities that are almost an order of magnitude ( < 2 cm yC I) less than the plate motions ( < 15 cm yr-I). Other features of hotspots give some clues about their size, shape, and duration, but it is safe to say that all evidence is indirect and inconclusive. The ultimate source may be plumes of hot material rising from the core­ mantle boundary (Morgan 1971, 1972, Whitehead & Luther 1975, Loper & Stacey 1983). This is consistent with evidence that the D" zone (from seismic data), which lies above the core-mantle interface, may be dynam­ ically unstable (Stacey & Loper 1983). However, there are other seismically detected layers within the mantle, most notably the layer at 650 km depth,

Fractals in Fluid Mechanics

Abstract: On montre comment les concepts de fractals fournissent de nouvelles voies pour le traitement des donnees de turbulence

Remote Sensing of the Sea Surface

Abstract: the sea surface provide means for measuring the spatial characteristics of surface waves and the spatial distributions of surface and near-surface oceanic properties over a large area at, in essence, one instant of time. As the techniques have developed, the oceanographer and the marine meteorologist have been provided wit h new sets of eyes that have not only enabled old questions to be answered but have also uncovered a rich set of new phenomena, some imperfectly understood, of ocean current and eddy structure, wave-current inter­ actions, and air-sea interactions more generally. The ability to measure sea­ surface properties without in situ instrumentation enables rapid surveys to be made of sea-surface temperature distributions and ice characteristics, as well as of the distributions of ocean-surface winds, which are so impor­ tant an input to continental and regional weather prediction. The pioneers of remote sensing of the ocean surface were certainly Cox & Munk (1954a,b) and Pierson (1962). In their celebrated study of Sun glitter patterns, Cox & Munk provided the first systematic measurements of the roughness of the sea surface-the components of mean square slope, their probability distributions, and their variations with wind speed. Pierson's stereophotograph ic measurements from two aircraft [the Stereo Wave Observation Project (SWOP)] sampled the sea-surface configuration at several instants in time, which allowed the first direct measurements of the two-dimensional wave spectrum. Simple (and not so simple) optical techniques are still useful in preserving a record of what the eye can see or in recording what happens too fast for the eye to see. Photography from the Earth Resources Technology Satellite (ERTS-I) and from the Space