Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-19T06:11:44.619Z Has data issue: false hasContentIssue false
  • English
  • Français

A quasi-linear theory for rotating flow over topography. Part 1. Steady β-plane channel

Published online by Cambridge University Press:  19 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

Steady rotating flow over topography in a periodic channel is examined, with emphasis on the interaction of waves, topography and mean flow. A simple quasi-linear theory is presented that features an implicit equation relating the net zonal flow to the forcing and topography. A good description of the dynamics is obtained, even when resonant Rossby waves appear. Multiple solutions for given external parameters are predicted in some cases, and confirmed by comparison with a fully nonlinear numerical model.

The nonlinear results also indicate that the zonally averaged shear can be important when topographic effects or Rossby numbers are large. With this factor taken into account the theory gives good agreement with the fully nonlinear model, as long as eddy–eddy interactions are minor.

The theory is relevant to the dynamics of planetary waves in the atmosphere, and may also be applied to some oceanic problems.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 99 , Issue 2 , 25 July 1980 , pp. 267 - 292
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

Charney, J. G. & DeVore, J. G. 1979 Multiple flow equilibria in the atmosphere and blocking. J. Atmos. Sci. 36, 1205–1216.Google Scholar
Charney, J. G. & Eliassen, A. 1949 A numerical method for predicting the perturbations of the middle latitude westerlies. Tellus 1, 38–54.Google Scholar
Clarke, R. A. & Fofonoff, N. P. 1969 Oceanic flow over varying bottom topography. J. Mar. Res. 27, 226–240.Google Scholar
Davey, M. K. 1978 Recycling flow over bottom topography in a rotating annulus. J. Fluid Mech. 87, 497–520.Google Scholar
Egger, J. 1978 Dynamics of blocking highs. J. Atmos. Sci. 35, 1788–1801.Google Scholar
Gordon, A. L. & Bye, J. A. T. 1972 Surface dynamic topography of Antarctic waters. J. Geophys. Res. 77, 5993–5999.Google Scholar
Grose, W. L. & Hoskins, B. J. 1979 On the influence of orography on large-scale atmospheric flow. J. Atmos. Sci. 36, 223–234.Google Scholar
Hart, J. E. 1979 Barotropic geostrophic flow over anisotropic mountains: multiequilibria and bifurcations. J. Atmos. Sci. (to appear.)Google Scholar
McIntyre, M. E. 1968 On stationary topography-induced Rossby wave patterns in a barotropic zonal current. Dt. Hydrogr. Z. 21, 203–214.Google Scholar
Manabe, S. & Terpstra, T. B. 1974 The effect of mountains on the general circulation of the atmosphere as identified by numerical experiments. J. Atmos. Sci. 31, 3–42.Google Scholar
Neumann, G. 1960 On the effect of bottom topography on ocean currents. Dt. Hydrogr. Z. 13, 132–141.Google Scholar
Pedlosky, J. 1971 Geophysical fluid dynamics. In Mathematical Problems in Geophysical Sciences (ed. W. H. Reid), Lectures in Applied Mathematics vol. 13, pp. 1–60. Providence, Rhode Island: American Mathematical Society.
Smagorinsky, J. 1953 The dynamical influence of large-scale heat sources and sinks on the quasistationary mean motions of the atmosphere. Quart. J. Roy. Met. Soc. 79, 342–366.Google Scholar
Smith, N. R. & Fandry, C. B. 1978 Combined effects of wind stress and topography in a two-layer model of the Southern Ocean. Deep-Sea Res. 25, 371–390.Google Scholar
Thompson, R. O. R. Y. & Luyten, J. R. 1976 Evidence for bottom-trapped topographic Rossby waves from single moorings. Deep-sea Res. 23, 629–635.Google Scholar