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The slow transverse motion of a flat plate through a non-diffusive stratified fluid

Published online by Cambridge University Press:  29 March 2006

G. S. Janowitz
G. S. Janowitz
Affiliation:
Division of Fluid and Thermal Sciences Case Western Reserve University, Cleveland, Ohio
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Abstract

We consider the two-dimensional flow produced by the slow horizontal motion of a vertical plate of height 2b through a vertically stratified (ρ = ρ0(1 - βz)) non-diffusive viscous fluid. Our results are valid when U2 [Lt ] Ub/ν [Lt ] 1, where U is the speed of the plate and ν the kinematic viscosity of the fluid. Upstream of the body we find a blocking column of length 10−2b4/(Uν/βg. This column is composed of cells of closed streamlines. The convergence of these cells near the tips of the plate leads to alternate jets. The plate itself is embedded in a vertical shear layer of thickness (Uν/βg)1/3. In the upstream portion of this layer the vertical velocities are of order U and in the downstream portion of order Ub/(Uν/βg)1/3 ([Gt ] U). The flow is uniform and undisturbed downstream of this layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 47 , Issue 1 , 14 May 1971 , pp. 171 - 181
Copyright
© 1971 Cambridge University Press

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References

Bretherton, F. P. 1967 The time-dependent motion due to a cylinder in an unbounded rotating or stratified fluid J. Fluid Mech. 28, 545.Google Scholar
Janowitz, G. S. 1968 On wakes in stratified fluids J. Fluid Mech. 33, 417.Google Scholar
Long, R. R. 1953 Some aspects of the flow of stratified fluids. I. A theoretical investigation Tellus, 5, 42.Google Scholar
Martin, S. & Long, R. R. 1968 The slow motion of a flat plate in a stratified fluid J. Fluid Mech. 31, 669.Google Scholar
Titchmarsh, E. C. 1937 Introduction to the theory of Fourier Integrals. Oxford: Clarendon.
Tricomi, F. G. 1957 Integral Equations. New York: Interscience.