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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

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