Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-19T04:00:27.014Z Has data issue: false hasContentIssue false

On the algebraic decay of disturbances in a stratified linear shear flow

Published online by Cambridge University Press:  19 April 2006

S. N. Brown
Affiliation:
Department of Mathematics, University College, London
K. Stewartson
Affiliation:
Department of Mathematics, University College, London

Abstract

In this note we confirm the time dependence of the decay of disturbances in a stratified linear shear flow found by Eliassen, Høiland & Riis (1953) and by Booker & Bretherton (1967). The result differs from those of Case (1960b) and of Chimonas (1979) which are incorrect.

Type
Research Article
Copyright
© 1980 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.)

References

Booker, J. R. & Bretherton, F. P. 1967 Internal gravity waves in a shear flow. J. Fluid Mech. 27, 513539.Google Scholar
Brown, S. N. & Stewartson, K. 1978 The evolution of the critical layer of a Rossby wave. II. Geophys. Astrophys. Fluid Dyn. 10, 124.Google Scholar
Case, K. M. 1960a Stability of inviscid plane Couette flow. Phys. Fluids 3, 143148.Google Scholar
Case, K. M. 1960b Stability of an idealized atmosphere. I. Discussion of results. Phys. Fluids 3, 149154.Google Scholar
Chimonas, G. 1979 Algebraic disturbances in stratified shear flows. J. Fluid Mech. 90, 119.Google Scholar
Eliassen, A., Høiland, E. & Riis, E. 1953 Two-dimensional perturbation of a flow with constant shear of a stratified fluid. Inst. Weather & Climate Res. Norwegian Acad. Sci. & Lett., Publ. no. 1.Google Scholar
Engevik, L. 1966 On the stability of plane inviscid Couette flow. Dept. of Appl. Math., Univ. Bergen, Rep. no. 12.Google Scholar
Orr, W. McF. 1907 Stability or instability of the steady motions of a perfect liquid. Proc. Roy. Irish Acad. 27, 969.Google Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.