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The Rayleigh problem for a slightly diffusive density-stratified fluid

Published online by Cambridge University Press:  29 March 2006

R. G. Standing
R. G. Standing
Affiliation:
Department of the Mechanics of Fluids, University of Manchester
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Abstract

A doubly-infinite sloping flat plate, initially at rest in a slightly diffusive viscous density-stratified fluid, starts to move impulsively with a constant velocity along the line of greatest slope. The resulting flow is found to be an unsteady motion superimposed on a steady diffusion-induced flow, which is present throughout. Laplace transform methods give solutions which are valid either in an essentially non-diffusive outer layer or in a diffusive inner layer. The impulsive start sets up oscillations in the outer layer. These gradually die out, and a steady diffusive flow develops.

A glass plate was towed vertically through stratified brine, into which aluminium particles were introduced. The flow velocities deduced from the particle motions confirmed the theoretical predictions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 48 , Issue 4 , 27 August 1971 , pp. 673 - 688
Copyright
© 1971 Cambridge University Press

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