Hostname: page-component-7c8c6479df-ph5wq Total loading time: 0 Render date: 2024-03-28T16:35:27.433Z Has data issue: false hasContentIssue false

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bretherton, F. P., J. Fluid Mech., 28 (1967), 545570.CrossRefGoogle Scholar
Drazin, P. G., Tellus, 13 (1961), 239251.CrossRefGoogle Scholar
Phillips, O. M., Dynamics of the upper ocean (Cambridge, 1966).Google Scholar
Stewartson, K., Proc. Camb. Phil. Soc, 48 (1952), 168177.CrossRefGoogle Scholar
Stewartson, K., Quart. J. Mech. Appl. Math., 6 (1953), 141162.CrossRefGoogle Scholar
Yih, C. S., Dynamics of nonhomogeneous fluids (Macmillan, 1965).Google Scholar