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Showing papers in "Annual Review of Fluid Mechanics in 1974"



Journal ArticleDOI
TL;DR: In this article, it has been shown that the simultaneous presence of two components with different diffusivities can lead to a whole range of new phenomena, and these form the subject of the present review.
Abstract: The study of convective motions produced by unstable density distributions in a fluid is now highly developed. Most attention has been given to the case of a thin horizontal layer of fluid, heated below and cooled above, and results obtained using a combination of Boussinesq theory and laboratory experiments have been success­ fully applied in many contexts (Chandrasekhar 1961, Spiegel 1971). The problem of buoyant convection from isolated sources has also been extensively studied (Turner 1969). Though the effect of adding other processes, such as rotation and magnetic fields, to the buoyant motion has been considered (Spiegel 1972), it has been assumed that the driving density differences are produced by the spatial variations of a single diffusing property (such as heat or a solute). Comparatively recently it has been shown that the simultaneous presence of two components with different diffusivities can lead to a whole range of new phenomena, and these form the subject of the present review. A striking feature of many systems of interest is that instabilities can develop even when the net density decreases upwards. Diffusion, which is generally stabilizing in a fluid containing a single solute, can now act so as to allow the release of the potential energy in the component that is heavy at the top. Much of this work was initiated with an application to the ocean in mind, and because heat and salt (or some other dissolved substance) are then important, the process has been called thermohaline (or thermosolutal) convection. Related effects have now been observed in other contexts, to be described below, and the name double-diffusive convection has been used to encompass this wider range of phenomena. The minimum requirements for the occurrence of double-diffusive convection, in the sense implied here, are the following: (i) The fluid must contain two or more components having different molecular diffusivities. It is the differential diffusion that produces the density differences required to drive the motion. (ii) The components must make opposing contributions to the vertical density gradient. (It is assumed throughout that the fluids are completely miscible, so that surface-tension effects do not arise. Some of the motions produced by the Marangoni

410 citations


Journal ArticleDOI
TL;DR: There has been extensive work in the development of turbulence models, particularly for use in boundary layer calculations as mentioned in this paper, and substantial advances made over the past decade in the prediction of turbulent flows are discussed.
Abstract: Substantial advances made over the past decade in the prediction of turbulent flows are discussed. There was extensive work in the development of turbulence models, particularly for use in boundary layer calculations. Basic aspects of several important methods based on partial differential equations for the mean velocity field and turbulence quantities, including the relationship between the methods and suggestions for future development were reviewed. Work on three-dimensional time-dependent large eddy simulations is discussed. The emphasis is on the hydrodynamics of incompressible flows, but sources for consideration of heat transfer and compressibility are mentioned.

383 citations




Journal ArticleDOI
TL;DR: In this paper, the Navier-Stokes equations have been put to a very severe test in the experiments of Poiseuille and others, and the results showed that they are the law of the fourth power for the discharge of an incompressible fluid of shear viscosity from a circular pipe of radius R through which it is driven by a pressure gradient.
Abstract: Of the Navier-Stokes equations Lamb (1895, §326) wrote that they embodied "the simplest hypothesis we can frame" and, citing the authority of Reynolds, that "this hypothesis has been put to a very severe test in the experiments of Poiseuille and others, [so that] we can hardly hesitate to accept the equations in question as a complete statement of the laws of viscosity." The particular consequence of the Navier-Stokes theory which "the experiments of Poiseuille and others" tested under a "very wide range of values of the rates of distortion" is the "law of the fourth power" for the discharge D of an incompressible fluid of shear viscosity J1 from a circular pipe of radius R through which it is driven by a pressure gradient a:

57 citations


Journal ArticleDOI
TL;DR: In this article, the authors show that the need for and increasing emphasis on vertical and short takeoff and landing aircraft, however, demand additional lift and higher wing loadings at the lowest possible thrust-to-weight ratios.
Abstract: Mechanical high-lift systems of various degrees of sophistication are used on most production aircraft today. These systems of flaps located at the leading and trailing edges of wings are known to generate remarkable gains in lift, leading to lower direct operating costs, increased payload capacity, and higher revenues. Although lift coefficients of the order of 3 have been achieved, boundary-layer separation at large flap deflections and angles of attack limits further increase. Today's need for and increasing emphasis on vertical and short takeoff and landing aircraft, however, demand additional lift and higher wing loadings at the lowest possible thrust-to-weight ratios, in order to reduce takeoff and landing distances below 2500 ft, and through high values of eLm" to achieve low approach speeds. This additional lift requirement can be best satisfied by so-called "powered high-lift systems." The flight trajectory of a conventional takeoff and landing aircraft (CTOL) is, in Figure 1, compared with the trajectories for short (STOL) and vertical (VTOL) takeoff and landing aircra,ft. The greater demand for lift and power of V jSTOL aircraft is self-evident and demonstrated furthermore by some characteristic values of the ratio of engine thrust to aircraft gross weight of TjW = OJ, 0.6, and 1.2 for CTOL, STOL, and VTOL aircraft, respectively. There are, however, designs that significantly deviate from these ratios. Whereas the CTOL aircraft for approach, or getting off the ground, depends on flap-augmented wing lift alone, the STOL aircraft requires that its basic wing lift be augmented by engine power. This wing-lift augmentation can fundamentally be obtained by various degrees of integration of the lifting and the propulsive systems, whereby the lifting effectiveness of the wing can be substantially increased. This may be achieved, e.g., by means of propeller slipstream deflectors, externally blown flaps, boundary-layer control (BLC), supercirculation, jet flap or jet-augment or wing, etc, or by vectoring part of the engine power into the lift direction by means of jet deflector flaps, slotted flaps, shrouded fans, etc. Tilt wings, helicopter rotors, wing fans, and other devices, which generate the still higher lift values required

38 citations


Journal ArticleDOI
TL;DR: In the early 1960s, it became clear that some contemplated experiments were so extremely complex, costly, difficult to repeat, or basically of such an un­ conventional nature, that high-resolution digital sampling and analysis were either a good investment or absolutely necessary.
Abstract: a turbulent fluid have not changed fundamentally in the last ten years. In contrast, the methodology of extracting information from turbulent signals has evolved rapidly, bringing new life and interest to the study of many aspects of fluid turbulence. Before modern high-speed digital computers became generally accessible to experimentalists , most statistical measurements in turbulent flows consisted of time averages obtained with analog devices operating continuously on the fluctuating electrical sigilals. Special circuits were constructed for measuring mean squares, cubes, and higher powers of the fluctuating random variables and their derivatives, correlation functions, energy spectra, triple correlations, intermittency factors, and other statistical quantities. Discretized values of the instantaneous fluctuations were rarely measured, and their determination from chart or oscillograph records was very laborious. Severe limitations on accuracy and useful dynamic range often arose from the approximation of exact mathematical operations by imperfect analog approxima­ tions. The development of specialized analog equipment to perform certain kinds of correlation and spectral analysis was in some cases sufficiently difficult to force postponement or abandonment of key scientific objectives in some potentially very significant studies. These and other factors precipitated the increased employment of discretized data, using more recently developed types of analog sampling devices, digitized data, and computer analysis. In the early 1960s, it became clear that some contemplated experiments were so extremely complex, costly, difficult to repeat, or basically of such an un­ conventional nature, that high-resolution digital sampling and analysis were either a good investment or absolutely necessary. In some experiments it was necessary to calculate various quantities by making many different computing passes with exactly the same samples of data; this made digital recording and analysis the only realizable

37 citations


Journal ArticleDOI

31 citations


Journal ArticleDOI
TL;DR: In this article, the velocity of flow in a steady-state system is altered at any cross section, and an hydraulic transient is initiated by an unbalanced pressure impulse, which is transmitted through the system at the acoustic speed a of the liquid in the system.
Abstract: When the velocity of flow in a steady-state system is altered at any cross section, an hydraulic transient is initiated. The alteration of velocity requires that an un­ balanced pressure impulse be applied, which is· transmitted through the system at the acoustic speed a of the liquid in the system. The magnitude of the pressure pulse may be attenuated due to the action of fluid friction, or it may be changed due to changes in cross-sectional area of the conduit. For a frictionless liquid in a horizontal, prismatic, elastic tube, the application of a pressure differential Ap would result in a change in liquid velocity Av given by Ap = pa Av. in which p is the density. This Av and Ap would be transmitted unchanged throughout the length of the tube at speed a. This relation is a consequence of the impulse-momentum principle. The acoustic speed is determined by the bulk modulus of the liquid, Young's modulus for the pipe wall material, pipe wall thickness, pipe diameter, and method of supporting the pipe. An additional complication is that the bulk modulus of the liquid changes greatly with very small amounts of entrained gases or air. In the simple case of a reservoir, a pipe of length L. and a downstream valve, we can see how pressure waves are transmitted and reflected through the system. If the frictional effects are neglected and the valve is suddenly closed during a steady uniform flow of velocity Vo. the pressure suddenly jumps by Ap = paVo' This wave travels upstream, bringing the velocity to zero and raising the pressure by Ap. At instant L/a. the liquid in the pipe is at rest, the pipe diameter is enlarged, and the liquid is compressed. An unbalanced force exists on the segment of liquid at the upstream end of the pipe, causing it to be set in motion with speed Vo upstream and causing the pressure to drop to reservoir pressure. This wave arrives at the valve at 2L/a sec, at which time all the liquid is moving upstream at speed Vo. with pressure throughout at reservoir pressure. An un­ balanced condition exists at the closed valve, however, as the liquid cannot move away from the valve without causing a drop in pressure. In fact (if the transient isn't too strong and vapor pressure is not attained), the layer of liquid at the gate is held at zero velocity by a drop in pressure at the gate. This pressure drop

30 citations