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On oscillatory flow over topography in a rotating fluid

Published online by Cambridge University Press:  26 April 2006

J. E. Hart
J. E. Hart
Affiliation:
Department of Astrophysical, Planetary and Atmospheric Sciences, Campus Box 391, University of Colorado, Boulder, CO 80309, USA
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Abstract

Quasi-geostrophic β-plane motion of a homogeneous liquid over topography is considered for situations in which there is a time-periodic forcing of a zonal current. Such an oscillatory current generates a topographic Rossby wave response that has a complicated, but periodic, temporal structure. The linear solution shows resonances at all integer values of the β-parameter. The nonlinear analysis demonstrates that for weak friction and forcing, the resonances are bent and multiple equilibria of the time-dependent Rossby wave states are possible in certain parameter ranges. While the basic forced flow in the absence of topography has no time-mean, the nonlinear amplitude equations show that a mean retrograde (westward) Eulerian zonal flow is generated in the interactions of the forced flow with the topography. This result is in agreement with a previous theory of Samelson & Allen, constructed for strongly nonlinear flow over a series of asymptotically long ridges. However, in contrast to the behaviour of their amplitude equations for certain parameter settings, the nearresonant weakly nonlinear model for more or less isotropic bottom topography appears non-chaotic for all accessible parameter values.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 214 , May 1990 , pp. 437 - 454
Copyright
© 1990 Cambridge University Press

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References

Bell, T. H. 1975 Lee waves in stratified flow with simple harmonic time dependence. J. Fluid Mech. 67, 705–722.Google Scholar
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. 1980a A quasi-linear theory for rotating flow over topography. Part 1. Steady β-plane channel. J. Fluid Mech. 99, 267–292.Google Scholar
Davey, M. K. 1980b A quasi-linear theory for rotating flow over topography. Part 2. β-plane annulus. J. Fluid Mech. 103, 297–320.Google Scholar
Hart, J. E. 1972 A laboratory study of baroclinic instability. Geophys. Fluid Dyn. 3, 181–209.Google Scholar
Hart, J. E. 1979 Barotropic quasi-geostrophic flow over anisotropic mountains: multi-equilibria and bifurcations. J. Atmos. Sci. 36, 1736–1746.Google Scholar
Hart, J. E. 1981 Experiments on rapidly rotating recycling flow over topography. Tellus 33, 597–603.Google Scholar
Pedlosky, J. 1981 Resonant topographic waves in barotropic and baroclinic flows. J. Atmos. Sci. 12, 2626–2641.Google Scholar
Samelson, R. M. & Allen J. S. 1987 Quasi-geostrophic topographically generated mean flow over a continental margin. J. Phys. Oceanogr., 17, 2043–2064.Google Scholar