Showing papers in "Annual Review of Fluid Mechanics in 1976"

Boundary layer stability and transition

Abstract: : A review is given of boundary layer stability and transition. The normal modes procedures as they apply to boundary layers are briefly reviewed and the mechanism of instability is discussed. It is shown how normal modes results may be used to give guidance regarding the factors affecting transition. Some remarks are made about the prediction of transition and about the fixing of transition. It is concluded that the process of transition from laminar to turbulent flow remains unsolved. However, significant inroads into inroads into the understanding of transition are now possible because of our ability to do sophisticated theoretical and experimental studies of the stability of laminar boundary layers.

The Stability of Time-Periodic Flows

Abstract: The stability of periodic states of mechanical systems has long been an object of study. Dynamic stabilization and destabilization can lead to dramatic modifications of behavior depending on the proper tuning of the amplitude and frequency of the modulation. It has only been in the recent past that attention has been focused on such possibilities in hydrodynamics. The interest lies not only with the mechanics of this new class of problems but with the possibilities for applications. If an imposed modulation can destabilize an otherwise stable state, then there can be a major enhancement of heat/mass/momentum transport. If an imposed modulation can stabilize an otherwise unstable state, then higher efficiencies can be attained in various processing techniques. The aim here is to give reviews of three prototypal problems having sinusoidal time variation: parallel shear flows, convective instabilities, and centrifugal insta­ bilities.1 These will be used as vehicles for a discussion of scale analysis, a procedure which is crucial to the understanding of these as well as more general flows. Before proceeding with the examination of periodic basic states, a word must be said in reference to the definition of stability. Since the basic state is unsteady, it seems natural to compare the disturbance growth rate with the rate of change of the basic state (Shen 1961). However, in periodic states the repeating sequence of basic-state acceleration followed by basic-state deceleration leads to ambiguities in interpretation. As a result, there is fairly common agreement to follow Rosenblat (1968) and term a basic periodic state unstable if there exists a disturbance that experiences net growth over each modulation cycle. A state on which every disturbance decays at every instant is called stable. namely, monotonically stable. It may happen that a state is neither unstable nor stable, i.e. the basic state is subject

Mixing and Dispersion in Estuaries

Abstract: Prior to 1950, studies of estuaries were primarily observational. Rhodes ( 1950), for instance, described velocities and salinities in several estuaries along the eastern coast of the United States. Stommel & Farmer (1952) compiled data from 20 world­ wide estuaries, ranging in size from the Moros in France (2.3 km long and a few meters deep) to the Straits of Juan de Fuca (100 km long and 350 m deep). Their report, although more than 20 years old, remains one of the more extensive compilations of salinity and velocity data in existence and, in addition, shows the wide range of water bqdies we call estuaries. Since the appearance in the early 1950s of Ketchum's work (1951a,b, 1955), of the unpublished manuscript On the Nature of Estuarine Circulation by Stommel & Farmer (1952), and of Pritchard's analyses of the salt balance in the James (1952 and later), researchers have used more analytic techniques to try to understand the process of mixing in estuaries and to quantify such aspects as residence times and pollutant concentrations. It is not easy to agree on what an estuary is. Schubel (1971) listed 10 earlier definitions each of which he found unacceptable for some reason and settled on an eleventh definition by Pritchard (1967): "An estuary is a semi-enclosed coastal body of water which has a free connection with the open sea and within which sea water is measurably diluted with fresh water derived from land drainage. " Even this definition is inadequate for our purpose, because it excludes such estuaries as San Diego Bay where the fresh-water flow is less than the evaporation, but which can be treated like other estuaries with respect to mixing problems. For our purposes it may be more appropriate to say that estuaries are something like pornography­ hard to define exactly, but we know one when we see one. A number of writers (Stommel & Farmer 1952, Bowden 1967, Pritchard 1967, Schubel 1971, Dyer 1973) have given classification schemes for estuaries. In hydro­ dynamic terms all the schemes distinguish three major categories: sharply stratified estuaries, such as fjords and salt-wedge estuaries; partially stratified estuaries, in which there is a significant vertical-density gradient and vertical mixing is inhibited;

Currents in Submarine Canyons: An Air-Sea-Land Interaction

Abstract: x8090 Submarine canyons serve as active conduits joining the shallow waters of the shelf to the deeper waters offshore. Canyon currents are generated by many forces, including those related to wind, surface waves, internal waves, tides, and suspended sediment. Studies of canyon currents indicate that submarine canyons can generally be divided into deep- and shallow-water regimes that are dominated by specific driving forces. The deep-water regime is generally exposed to energy from tides, intern al waves, and spin-off eddies from large-scale current systems, whereas the shallow-water areas are dominated by currents related to surface waves and wind. Strong down-canyon currents appear to be caused by a unique combination of air-sea-Iand interactions consisting of 1. a pile-up of water along the shoreline caused by strong onshore winds; 2. down-canyon pulses of water associated with groups of high incident waves; 3. excitation of standing edge waves that produce longer-period up-and down-canyon oscillations; and finally, 4. the formation of discrete pulses of down-canyon motion, which become more intense and lead to sustained down-canyon currents, as the weight of the sediment suspended by the currents overcomes the density stratification of the deeper water. Simultaneous measurements of currents and pressure in Scripps Submarine Canyon, and of winds, waves, and pressure over the adjacent shelf have been made for several years, with the strongest down-canyon current measured, 1.9 m sec-1 at a depth of 44 m, being recorded during the

Useful Non-Newtonian Models

Abstract: Here 1t is the total momentum flux (or stress tensor), defined in such a way that the force transmitted from the negative side of a surface element of unit area and normal vector n is [n· 1t] (Bird, Stewart & Lightfoot 1960). The symbol b stands for the unit tensor, , is the extra stress tensor, p is the isotropic pressure, and y = (Vv) + (Vv)t is the rate-of-strain tensor; the viscosity Il depends on temperature, pressure, and concentration, but not on the time t or on any kinematic quantities such as y. It is well known that liquids with complex structure, such as macromolecular fluids, soap solutions, and two-phase fluids are not described by (1). The following are some of the "non-Newtonian" effects that have been observed:

Multiphase Fluid Flow Through Porous Media

Abstract: As is frequently the case in topics related to fluid mechanics, the field of muItiphase flow in porous media embraces highly diverse phenomena, ranging from the motion of immiscible fluids, through interaction with the medium via the exchange of heat and/or soluble mass and the exchange between phases, to fluid-solid-phase flows accompanied by colmatage (clogging) and suffusion (leaching). The latter area, which includes the whole field of filtration (Davies 1973, Polubarinova-Kochina 1969), is a topic in itself and cannot be considered in the present survey, which is limited to the discussion of immiscible-fluid phases, usually in two-phase flow. Again, while heat or solute may be regarded as an additional phase and may significantly affect mass flow and phase exchange, the transport of these quantities is generally outside the scope of the present discussion. Superficially, flow through porous media appears to offer the possibility of two alternative analytical approaches, based upon either the scale of pore dimensions or the scale of the macroscopic system. The former approach would be expected to lead to detailed boundary-value problems, would incorporate physicochemical properties, and should, in principle, lead to exact solutions from which numerical coefficients can be evaluated. Unfortunately, such a procedure is not fully practicable owing to the geometric complexity of porous media, although valuable qualitative models have been obtained. Usually, authors abandon the capillary scale and take Darcy's law, involving an undetermined constant-the permeability-as the basis of an axiomatic, macroscale approach (Philip 1970, 1973a, 1974). However, in the field of mUltiphase flow many important questions remain unanswered. For example, what factors affect the flow regime and hence the pore distributions of immiscible fluids, with effects of pressure gradient, etc? In immiscible displacement, what proportion is recovered of a fluid initially in the