Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-08T22:10:43.044Z Has data issue: false hasContentIssue false
  • English
  • Français

A quasi-linear theory for rotating flow over topography. Part 2. Beta-plane annulus

Published online by Cambridge University Press:  20 April 2006

Michael K. Davey
Michael K. Davey
Affiliation:
The Joint Institute for the Study of the Atmosphere and Ocean. University of Washington, Seattle, Washington 98195 U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

An obstacle in westerly flow on a periodic β-plane can generate resonant Rossby waves and cause large perturbations to the flow field. The pattern and strength of the flow can vary markedly in response to relatively small changes in the forces driving the system. The aim of this paper is to develop a simple theory valid in these circumstances. Such a theory has application to the dynamics of planetary scale quasi-steady perturbations in the atmosphere.

A series of models for barotropic quasi-geostrophic flow in an annulus is presented. An implicit quasi-linear model, with zonally averaged flow parametrized in terms of topography shape and net zonal mass transport, gives good agreement with nonlinear calculations. In one case stable multiple equilibria are predicted and confirmed, but the multiplicity regime is small.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 103 , February 1981 , pp. 297 - 320
Copyright
© 1981 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

Charney, J. G. & DeVore, J. G. 1979 Multiple flow equilibria in the atmosphere and blocking. J. Atmos. Sci. 36, 1205–1216.Google Scholar
Davey, M. K. 1978 Recycling flow over bottom topography in a rotating annulus. J. Fluid Mech. 87, 497–520.Google Scholar
Davey, M. K. 1980 A quasi-linear theory for rotating flow over topography. Part 1: Steady β-plane channel. J. Fluid Mech. 99, 267–292.Google Scholar
Frenzen, P. 1955 Westerly flow past an obstacle in a rotating hemispherical shell. Bull. Am. Met. Soc. 36, 204–210.Google Scholar
Fultz, D. & Frenzen, P. 1955 A note on certain interesting ageostrophic motions in a rotating hemispherical shell. J. Met. 12, 332–338.Google Scholar
Fultz, D. & Long, R. R. 1951 Two-dimensional flow around a circular barrier in a rotating spherical shell. Tellus 3, 61–68.Google Scholar
Hart, J. E. 1979 Barotropic quasi-geostrophic flow over anisotropic mountains. J. Atmos. Sci. 36, 1736–1746.Google Scholar
Haurwitz, B. 1940a The motion of atmospheric disturbances. J. Mar. Res. 3, 35–50.Google Scholar
Haurwitz, B. 1940b The motion of atmospheric disturbances on the spherical earth. J. Mar. Res. 3, 254–267.Google Scholar
Holton, J. R. 1971 An experimental study of forced barotropic Rossby waves. Geophys. Fluid Dyn. 2, 323–341.Google Scholar
Johnson, J. A. & Hill, R. B. 1975 A three-dimensional model of the Southern Ocean with bottom topography. Deep-Sea Res. 22, 745–752.Google Scholar
Kamenkovich, V. M. 1962 On the theory of the Antarctic Circumpolar Current. Akad. Nauk. S.S.R. Inst. Okean. Trudy 56, 241–293.Google Scholar
Long, R. R. 1952 The flow of a liquid past a barrier in a rotating spherical shell. J. Met. 9, 187–199.Google Scholar
Phillips, N. A. 1965 Elementary Rossby waves. Tellus 17, 295–301.Google Scholar