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The slow motion of a flat plate in a viscous stratified fluid

Published online by Cambridge University Press:  28 March 2006

Seelye Martin  and
Robert R. Long
Seelye Martin
Affiliation:
Department of Mechanics, The Johns Hopkins University, Baltimore, Maryland
Robert R. Long
Affiliation:
Department of Mechanics, The Johns Hopkins University, Baltimore, Maryland
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Abstract

The existence of a ‘wake’ upstream of an obstacle moving slowly through a stratified fluid has been known for some time. The present study shows that a thin, flat plate moving slowly and horizontally through a linearly stratified salt-water mixture has, in addition, a boundary layer over the plate whose thickness increases upstream from the back of the plate.

The theory assumes that the ratio of diffusivity to viscosity is small, and that the plate moves so slowly that inertia forces are negligible; under these conditions, a similarity solution is derived describing the boundary layer over the plate. The study also shows that salt diffusion is important in a second, thinner boundary layer whose thickness increases from the front of the plate.

In the experiment, a plate was towed through a tank of linearly stratified salt water. From streak photographs of the boundary layer over the plate, it was possible to confirm quantitatively the similarity solution and to infer at very slow velocities the presence of the thin diffusion boundary layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 31 , Issue 4 , 18 March 1968 , pp. 669 - 688
Copyright
© 1968 Cambridge University Press

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