Hostname: page-component-669899f699-chc8l Total loading time: 0 Render date: 2025-04-26T13:33:31.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Some aspects of the initial-value problem for the inviscid motion of a contained, rotating, weakly-stratified fluid

Published online by Cambridge University Press:  29 March 2006

J. S. Allen
J. S. Allen
Affiliation:
Department of Aerospace Engineering, The Pennsylvania State University
Get access Rights & Permissions [Opens in a new window]

Abstract

The initial-value problem for the linear, inviscid motion of a contained, rotating stratified fluid is considered in the limit of weak stratification, that is, for small values of the stratification parameter S = N2/Ω2, where N is the Brunt–Väisälä frequency and Ω is the rotational frequency. The limiting flow is of interest because, although the initial-value problem has been studied, both for the case of a homogeneous, rotating fluid and for the case of a stratified, rotating fluid, the exact relationship of the two flows, in the limit of vanishing stratification, is not straightforward. For example, the method of determining, from the initial conditions, the steady geostrophic component of the flow of a rotating, stratified fluid does not in general give a motion that reduces, in the limit S → 0, to the steady component of the flow of a homogeneous fluid. By including a consideration of slow unsteady motions that vary on a time scale dependent on the stratification parameter, the relationship of the limiting flow to the flow of a homogeneous fluid is established.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 46 , Issue 1 , 15 March 1971 , pp. 1 - 23
Copyright
© 1971 Cambridge University Press

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.)

Article purchase

Temporarily unavailable

References

Barcilon, V. 1968 Axisymmetric inertial oscillations of a rotating ring of fluid Mathematika, 15, 93–102.Google Scholar
Cole, J. D. 1968 Perturbation Methods in Applied Mathematics. Blaisdell.
Greenspan, H. P. 1965 On the general theory of contained rotating fluid motions J. Fluid Mech. 22, 449–462.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Greenspan, H. P. 1969 On the inviscid theory of rotating fluids Studies in Appl. Math. 48, 19–28.Google Scholar
Hølland, E. 1962 Discussion of a hyperbolic equation relating to inertia and gravitational fluid oscillations Geofys. Publ. 24, 211–227.Google Scholar
Howard, L. N. 1968 Notes on the 1968 Summer Program in Geophysical Fluid Dynamics, The Woods Hole Oceanographic Institution, Ref. no. 68–72, vol. I, 41–113.
Howard, L. N. & Siegmann, W. L. 1969 On the initial value problem for rotating stratified flow Studies in Appl. Math. 48, 153–169.Google Scholar
Jeffreys, H. & Jeffreys, B. S. 1966 Methods of Mathematical Physics (3rd edn.). Cambridge University Press.
Pedlosky, J. & Greenspan, H. P. 1967 A simple laboratory model for the oceanic circulation J. Fluid Mech. 27, 291–304.Google Scholar
Siegmann, W. L. 1968 Time-dependent motions in rotating stratified fluids. Ph.D. Thesis, M.I.T.