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Instability of a periodic boundary layer in a stratified fluid

Published online by Cambridge University Press:  29 March 2006

R. M. Robinson  and
A. D. McEwan
R. M. Robinson
Affiliation:
CSIRO, Division of Atmospheric Physics, Aspendale, Victoria 3195, Australia
A. D. McEwan
Affiliation:
CSIRO, Division of Atmospheric Physics, Aspendale, Victoria 3195, Australia
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Abstract

It has been found that the periodic boundary layer formed on a vertically oscil-lating vertical wall bounding a stratified fluid is liable to two distinct modes of wavelike instability. In the first, which arises when the oscillation frequency ω is lower than 0·7 times the buoyancy frequency N, the phase lines are aligned horizontally. The second mode, in which the phase lines are aligned at 45° or more to the horizontal, becomes dominant as ω is increased above 0·9 N.

In distinction from the unstratified periodic Stokes layer, there appears to be, for ω in the vicinity of N, a definite low threshold to the boundary-layer Stokes-Reynolds number (defined as Wo/(2ων)½, where Wo is the maximum vertical wall velocity and v is the kinematic viscosity) above which the instability is sustained a t a detectable level.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 68 , Issue 1 , 11 March 1975 , pp. 41 - 48
Copyright
© 1975 Cambridge University Press

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