Showing papers in "Annual Review of Fluid Mechanics in 1980"

Particle Motions in a Viscous Fluid

Abstract: The motion of small particles, drops, and bubbles in a viscous fluid at low Reynolds number is one of the oldest classes of problems in theoretical fluid mechanics, dating at least to Stokes’s (1851) analysis of the translation of a rigid sphere through an unbounded quiescent fluid at zero Reynolds number.

Models of Wind-Driven Currents on the Continental Shelf

Abstract: Adjacent to the ocean shoreline, the continental shelves form regions of relatively shallow water for offshore distances that vary with geographical location, but are typically the order of 50-150 km. The sea floor slopes gently across the continental shelf from the coast to water depths of about 200 m, where an abrupt increase in slope generally occurs at the so-called shelf break. Seaward of the break, the continental slope extends down­ ward to the deep ocean floor over an additional horizontal distance of the order of 100 km. The motion of the oceanic waters over the continental shelf and slope is influenced by the earth's rotation, the density stratification, the offshore current regime, the sloping bottom topography, and the presence of a coastline. In particular, the topographic constraints of the coastline and shallow sloping bottom give the shelf flow field certain characteristics that differ from those typical of the deep ocean. 111 many instances, flow over the shelf may be considered independent of motions farther offshore. The physical oceanographic conditions on the shelf influence several important oceanic processes. For example, most of the biological primary productivity of the world's oceans takes place in the relatively fertile surface waters over the continental shelves. The biological phenomena involved there are highly dependent on the fluid mechanical processes on the shelf. Sediment transport and pollutant dispersion are other processes occurring over the shelf that are strongly affected by the properties of the fluid motion. Observational information on the nature of shelf flow fields has increased tremendously since the early 1970s with the development and

Water Transport in Soils

Abstract: Newer approaches and recent developments on the topic of water movement in soil are discussed. Static issues include thermodynamic potential and hysteresis, and dynamic considerations include horizontal water movement, horizontal air and water movement, and gravity effects. Solute transport dynamics also are described, such as variable infiltration rates, stagnant phase effects, and dynamic instability and fingering. Sample examples are used to illucidate the concepts of water transport in soils. 65 references.

Continuous drawing of liquids to form fibers

Abstract: The continuous stretching of viscous liqu ids to form fibers is a primary manufacturing process in the textile industry. The mechanics of certain sheet formation and sheet and wire coating operations are quite similar, as are the mechanics of the formation of glass fibers. Most published experimental and theoretical work has been motivated by applications using polymeric liquids, where the interactions between processing conditions and the complex fluid rheology are of particular interest. The melt spinning process for the manufacture of textile fibers is shown schematically in Figure 1. Molten polymer is extruded through a small hole into cross-flowing ambient air at a temperature below the solidifica­ tion temperature of the polymer. The solidified polymer is taken up at a higher speed than the mean extrusion velocity, resulting in drawing of the filament. The steady-state ratio of extrusion to takeup area is known as the draw ratio (DR); the draw ratio is also equal to the steady-state ratio of takeup to extrusion velocity (to within the approximation that polymer density is independent of temperature). Typical processing variables for the manufacture of poly (ethylene terephthalate) (PET) fiber are shown in Table 1. Commercial PET, a polyester sold under such trade names as Dacron, Terylene, and Fortrel, is a nearly amorphous material as spun, although PET with forty percent crystalline polymer can be produced. Other commercially important melt-spun polymers include Nylon-6, Nylon-66, and polypropylene. The solidified filament is typically subjected

Instabilities of Waves on Deep Water

Abstract: Waves on deep water provide one of the most vivid examples of wave motion found in nature and men have long sought to understand this familiar yet complex phenomenon. It is not surprising, therefore, that the problem of the generation of deep-water waves by a local disturbance was the first hydrodynamic problem to be investigated systematically through the general equations of fluid motion; it was posed as a prize topic by the French Academy in 1816, and solved in the same year by Poisson and Cauchy. The Cauchy-Poisson solution describing the radia­ tion of waves from a local source served as one of the most outstanding examples of mathematics applied to a widely observed physical process. A comprehensive treatise on the general subject of waves on deep water was published by Stokes in 1849. The mathematical techniques introduced therein became the cornerstone for modern theories of linear and nonlinear dispersive waves. It is noteworthy that this pioneering theoretical study was motivated by physical observations (Russell 1844). The continued close coupling between experimental and theoretical efforts is probably most responsible for the widespread interest and significant progress in the subject over the past century. For some, the novelty of the Stokes expansion raised questions of convergence in the mathematical sense (Burnside 1916, Nekrasov 1919, Levi-Civita 1925), while for others (Michell 1893, Wilton 1913, Rayleigh 1917), the existence of finite-amplitude steady periodic waves seemed practically certain, and determining the profiles of very steep waves presented the real challenge. Until recently, the stability of a train of steady periodic deep-water waves, regardless of steepness, remained unquestioned. Thus, the theoretical discovery by Lighthill (1965) using

Stokeslets and Eddies in Creeping Flow

Abstract: Flow at low Reynolds number Re = pUL//1 is characterized by the small­ ness of representative quantities in the flow, i.e. the density p, the velocity U, and the length L, as well as by large values of the viscosity J.l. If we let Re --+ 0 and neglect the molecular structure of the fluid that is studied in rarefied fluid dynamics as well as the Brownian motions that appear for extremely small p and L, we are led to a universal feature of a real fluid. We have a perfectly laminar creeping flow governed by the Stokes equations of motion, which are linear and reversible, and contain no parameters to complicate the structure of the flow field. The most essential factor is the geometry of the flow. As is well known, the Stokes equations are not uniformly valid in an unbounded fluid, leading to various paradoxes, which however are remedied by matching to an outer region where the neglected inertia terms are dominant. Further, in real situations, the flow is usually bounded and is dominated by the so-called Stokes regions if we let pU //1 be sufficiently small. In this review certain limited aspects of creeping flow will be surveyed, since extensive surveys before 1964 are found in Happel & Brenner's treatise (1965) and in several articles in the Annual Review of Fluid Mechanics (Cox & Mason 1971, Brennen & Winet 1977). First, we neglect unsteady effects on the assumption that the typical frequency is not larger than U /L, as well as the effect of free surfaces such as bubbles and suspensions. In Section 2 Stokes flow and various singularities are introduced as factors as free of geometries as possible, leading to general solutions of the Stokes equations proposed by Imai (1973). In Section 3 two-dimensional solutions of the Stokes equations are discussed as the inner solutions near a cyiindrical body. The complex velocity at a distance is characterized by the logarithmic term and constants depend­ ing on the size and ellipticity of the cylinder. In Section 4 typical stokeslet constants depending on the geometry of a particle, i.e. the

Coastal circulation and wind-induced currents

Abstract: Coastal circulation has been a subject for inquiry by marine scientists since the earliest days of fishing and shipping. The two most easily distinguishable causes for coastal motion are winds and tides, but the response of coastal waters to these forces varies widely, influenced by climate, geomorphology, and stratification. The last decade has seen a veritable explosion of field studies of coastal circulation, made possible by the development of recording current meters which, deployed in arrays over the shelf, provide long time series of horizontal currents, temperature, and, in some instances, salinity. Results from some of these studies are reviewed here, with emphasis on the wind-driven circulation, which until now has been the primary focus of attention.

Fluid Mechanics of the Duodenum

Abstract: Throughout the duodenum (the first 30 em or so of the small intestine), the smooth muscle lies in two layers. In the outer layer, the muscle cells lie with their long axis parallel to the axis of the intestinal tube while the long axis of the cells of the inner layer lies along the circumference of the tube. The two layers are of nearly equal thickness and, together, are called the muscularis propria, or simply, the duodenal musculature. Although bound together, the longitudinal and the circular layers seem to be able to contract independently. These contractions produce quite different deformations of the tube: contractions of the outer longitudimil muscle shorten the tube locally, while contractions of the inner circular layer of muscle reduce its diameter. The muscularis propria is lined on the outside by the serosa and on the inside by the mucosa. This mucosa contains another muscle layer, the muscularis mucosae. This muscle layer is separated from the inner circular layer of the muscularis propria by a layer of loose fibrous tissue so that, presumably, considerable movement may occur between the mucosa and the muscularis propria. It is not known what kind of movement actually occurs here. The mucosa is not uniformly applied to the inner surface of the muscularis propria. Instead, it lies in folds, called the folds of Kerkring or the valvulae conniventes. The innermost lining of the duodenum, the epithelium, constitutes finger­ like projections called villi. Each villus contains, at its core, a bundle of muscle connected to the muscularis mucosae. The cells of the intestinal

Scientific Progress on Fire

Abstract: ly unwanted-of some oxid izable struc­ ture or material in air. This review will be limited to fires in buildings. In this case the need to know is the desire to design buildings and their contents such that 1. persons in the building will be warned of a fire in time to get out, and 2. the building itself has a low probability of ignition and/or fire spread so as to keep life and property lo sses lo w. Many of the present fire safety procedures-as embodied in city fire codes for example-are purely empirical and contain obvious contradic­ tions as disclosed, for example, by some round-robin flammability tests (Emmons 1967, 1974). Such failures of a practical safety system can best and most rapidly be corrected by developing an understanding of the fundamental phenomena, in this case the "Science of Fire."