Showing papers in "Annual Review of Fluid Mechanics in 1983"

Instabilities, Pattern Formation, and Turbulence in Flames

Abstract: l.1 Premixed flames It is well known that the rate of a chemical reaction (W) in a gaseous mixture is an increasing function of tempera­ ture; usually W ex.p( E / RT), where E is a constant, specific to the reaction and called its activation energy, and R is the universal gas constant. The larger E, the stronger the temperature-dependence of the reaction rate. Under normal conditions (atmospheric pressure, room temperature), the reaction rate in the majority of combustible mixtures is negligibly small. At sufficiently high temperatures, however, the reaction will take place at a substantial rate. When a combustible mixture is ignited at some point, e.g. by a spark, a rapid exothermic reaction is initiated; this causes the temperature to rise (via conduction) in the adjacent layer of the mixture, inducing a chemical reaction there, and so on. Thus the reaction, once begun, will spread through the mixture,

Integrable, chaotic, and turbulent vortex motion in two-dimensional flows

Abstract: Vortex dynamics would appear to be exempt from Hardy 's pe ssimi stic verdict On one hand, the evolution of vorticity, and thu s the motion s of vortice s, are essential ingredient s of virtually any real flow Hence vortex dynamic s i s of profound practical importance On the other hand, vortex motion ha s always constituted a mathematically sophi sticated branch of fluid mechanics that continue s to invite the application of novel analyti­ cal techniques Indeed it i s ne ither dull nor commonplace Thi s central role of vorticity in fluid mechanic s i s not difficult to understand A s we know, any velocity field, v, can be split into a sum of two field s, one with the same divergence a s v, and no curl, and one with the same curl a s v and vani shing divergence Thi s important re sult i s due to Stoke s and to Helmholtz ( 1 858 ; see Sommerfeld 1964) In incompre ssi ­ ble flow , a s we deal with exclu sively here, the fir st part i s irrotational and divergencefree and thu s leads to the linear problem o f po tential flow , The second part, however , derive s directly from the vorticity o f the field ' v In the dynamics of thi s part lie s the essence of the problem

The form and Dynamics of Langmuir Circulations

Abstract: When the wind blows at modest speeds over natural bodies of water, numerous streaks or slicks nearly parallel to the wind direction may appear on the surface. This form of surface streakiness is commonplace, and under favorable conditions it is readily apparent to the casual observer. The streaks result from the collection of floating sub­ stances-seaweed, foam from breaking waves, marine organisms, or organic films-into long narrow bands. Flotsam makes the bands visible directly, and compressed films make them visible by the damping of capillary waves, thereby giving the bands a smoother appearance. Naturalists and seafarers often note color variations of the sea due to minute marine organisms. Bainbridge (1957) cited many old descriptions of long narrow "bands," "streaks," or "lanes" including several by Darwin in 1839 during the voyage of the Beagle. James Thomson (1862) described observations of streaks made jointly with his brother, Lord Kelvin, in a paper that also indicated increased abundances of marine life below the streaks. The first connection between the wind and streak directions, among the authors cited by Bainbridge, was made by Collingwood (1868): "if a moderate breeze were blowing and the sea

The Turbulent Wall Jet Measurements and Modeling

Abstract: The turbulent wall jet, even limiting attention to the topographically simple cases beloved of academics, arguably provides more puzzles for those seeking an ordered set of rules to describe turbulence than any other class of turbulent shear layer. Formally, we can regard a wall jet as a boundary layer in which, by virtue of the initially supplied momentum, the velocity over some region in the shear layer exceeds that in the free stream. Wall jets are of great and diverse engineering importance. While some of the best known and most challenging applications lie in the field of advanced airfoil design, these aerodynamic roles are far outweighed in number and, probably, in economic importance by the use of wall jets in problems of heating, cooling or ventilating-areas where traditionally design has proceeded unfettered by any deep concern about the turbu­ lence structure of the flows in question. Two major industrial applications are the film-cooling of the lining walls of gas-turbine combustion chambers and of the leading stages of

The Impact of Compressible Liquids

Abstract: Consideration is given to liquid impact in the supersonic regime in order to characterize pressure loading and other mechanisms which could damage a solid target such as a jet in flight. The liquid ...

Snow Avalanche Motion and Related Phenomena

Abstract: they can strike unexpectedly and violently. The catastrophe at Val d'lsere, where in 1970 thirty-nine people were killed while having break­ fast in a seemingly safe building, is a typical example. Similar or worse disasters have occurred during this century in other countries. The development of ski resorts brings more and more people into contact with the mountain environment and its inherent dangers, creating a need for new roads and better road protection.

Magneto-atmospheric waves

Abstract: A theoretical treatment of magneto-atmospheric waves is presented and applied to the modelling of waves in the solar atmosphere. The waves arise in compressible, stratified, electrically conductive atmospheres within gravitational fields when permeated by a magnetic field. Compression, buoyancy, and distortion of the magnetic field all contribute to the existence of the waves. Basic linearized equations are introduced to describe the waves and attention is given to plane-stratified atmospheres and their stability. A dispersion relation is defined for wave propagation in a plane-stratified atmosphere when there are no plane-wave solutions. Solutions are found for the full wave equation in the presence of either a vertical or a horizontal magnetic field. The theory is applied to describing waves in sunspots, in penumbrae, and flare-induced coronal disturbances.

Complex Freezing-Melting Interfaces in Fluid Flow

Abstract: Much of the early work on problems involving liquid-solid phase change was confined essentially to the cases in which the liquid melt is stagnant or the motion of the liquid is due entirely to the phase-change process itself. In these transient (conduction) phase-change problems, the un­ knowns are the interface that separates the regions of liquid and solid and the temperature distributions in both regions. The interface motion is expressed implicitly in an equation for the conservation of thermal energy at the interface. This introduces a nonlinear character to the problem that has intrigued and challenged engineers and mathematicians since Stefan's (1891) pioneering study of the growth of sea ice. Many powerful analytic and numerical techniques have been reported for dealing with heat-diffusion-controlled freezing or melting problems, and references to the mathematical studies on this subject may be found in several previous surveys by Bankoff (1964), Muehlbauer & Sunderland (1965), Rubinshtein (1967), Ockendon & Hodgkins (1975), and Wilson et al. (1978). In contrast to the earlier studies of phase change in stagnant media, problems in which the melt· material is in motion have recived detailed attention only during the past two decades. The stimulus was provided to a large extent by requirements in the nuclear and "alternate" energy

On the Theory of the Horizontal-Axis Wind Turbine

Abstract: The extraction of energy from the wind is an old idea, one used by sailing ships and windmills for many centuries. The development of ancient windmills was based on empiricism and engineering skill. The develop­ ment of the fluid mechanics, or more specifically the aerodynamics, of windmills (wind turbines in modern· usage) is more recent. The study of the aerodynamics of wind turbines was begun after W orId War I by Betz ( 1926) and Glauert ( l935a) and got a new impulse after the \"energy crisis\" of 1973-74. Nowadays, it is a worldwide field of research, stimulated and guided by national research programs in the US, Sweden, Denmark, The Netherlands, Great Britain, and many other countries.

Fluid Mechanics of Green Plants

Abstract: Why is the study of the biomechanics of green plants important? First, it has been estimated that plant life comprises 99% of the Earth's biomass (Bidwell 1974). Second, green plants are virtually the only ultimate source of food for animals through photosynthesis (the process of conver­ sion of solar energy to stored chemical energy). A biofluid-mechanical overview of a typical green plant is shown in Figure 1. See Nobel (1974) for an extensive self-contained quantitative introduction and order-of-magnitude analysis; for a shorter quantitative introduction, see Merva (1975). Meidner & Sheriff (1976) have written a short introduction that uses engineering concepts with a minimum of mathematics, and Canny (1977) has written a brief nonmathematical introduction for fluid mechanicians. The leaves are the site of photosynthesis. This process requires sunlight, CO2 , and water, and produces glucose (a simple sugar) and oxygen. Sugars manufactured in the leaves are translocated to other parts of the plant via the vascular phloem tissue. Water and minerals absorbed in the roots are brought up to the leaves via the vascular xylem tissue. The upward xylem flow (called the transpiration stream) is driven by evapora­ tion at the leaves, while the largely downward phloem flow is thought to be driven by concentration differences created locally by active transport (e.g. the Munch hypothesis; see Bidwell 1974). Studies of each of these parts of the plant have involved special fluid mechanics problems based on the particular physiological function and geometry. This article introduces the reader to the concepts and problems