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Slow time-dependent motion of a hemisphere in a stratified fluid

Published online by Cambridge University Press:  26 February 2010

R. Grimshaw
Affiliation:
The University of Melbourne, Australia.
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Abstract

A hemisphere, resting on a horizontal plane, is initially at rest relative to an incompressible, inviscid, non-diffusive fluid whose density is vertically stratified. The hemisphere is then given, impulsively, a small constant horizontal velocity which is maintained thereafter. Assuming that the Froude number is small, and using the Boussinesq approximation, the equations of motion are linearised and solved using a Laplace transform. The disturbance in the fluid is analysed for large times and is found to contain a steady component of purely horizontal flow, an internal wave field and internal oscillations at the Brunt-Väisälä frequency, together with their various interactions. The effects of viscosity and diffusivity are discussed qualitatively by considering their effects on an internal wave.

Type
Research Article
Copyright
Copyright © University College London 1969

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