Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-29T12:58:23.467Z Has data issue: false hasContentIssue false
  • English
  • Français

Recycling flow over bottom topography in a rotating annulus

Published online by Cambridge University Press:  12 April 2006

M. K. Davey
M. K. Davey
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge Present address: National Centre for Atmospheric Research, Boulder, Colorado 80303.
Get access Rights & Permissions [Opens in a new window]

Abstract

Steady flow of an incompressible homogeneous fluid over shallow topography in a rotating annulus is considered. The flow is driven by a differentially rotating lid. The recycling nature of the system means that prescribed upstream conditions are not available to close the problem. Consideration of the balance of transport across streamlines for the geostrophic flow leads to a general circulation condition; namely $\Gamma(\psi) = \frac{1}{2}\Gamma_T(\psi)$, where ϕ is the stream function for the geostrophic flow, Λ is the circulation around a streamline and ΛT is the circulation around the same path calculated using the prescribed upper surface velocity. Using this condition, stream functions for the linear viscous and nonlinear quasi-inviscid flow can be found. Solutions for these two limits, and linearized perturbation solutions for the transition regime between them, are presented for flow over ridges in the annulus.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 3 , 15 August 1978 , pp. 497 - 520
Copyright
© 1978 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

Arnold, V. I. 1965 Conditions for nonlinear stability of stationary plane curvilinear flows of an ideal fluid. Dokl. Acad. Sci. USSR 162, 773–777.Google Scholar
Batchelor, G. K. 1956 On steady laminar flow with closed streamlines at large Reynolds number. J. Fluid Mech. 1, 177–190.Google Scholar
Boyer, D. L. 1971a Rotating flow over long shallow ridges. Geophys. Fluid Dyn. 2, 165–184.Google Scholar
Boyer, D. L. 1971b Rotating flow over a step. J. Fluid Mech. 50, 675–687.Google Scholar
Carrier, G. F. 1965 Some effects of stratification and geometry in rotating fluids. J. Fluid Mech. 23, 145–172.Google Scholar
Gill, A. E. & Parker, R. L. 1970 Contours of ‘h cosec tH’ for the world's oceans. Deep-Sea Res. 17, 823–824.Google Scholar
Hart, J. E. 1977 A note on quasi-geostrophic flow over topography in a bounded basin. J. Fluid Mech. 79, 657–668.Google Scholar
Huppert, H. E. & Stern, M. E. 1974a Ageostrophic effects in rotating stratified flow. J. Fluid Mech. 62, 369–385.Google Scholar
Huppert, H. E. & Stern, M. E. 1974b The effect of side walls on homogeneous rotating flow over two-dimensional obstacles. J. Fluid Mech. 62, 417–436.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 SSR Inst. Okean. Trudy 56, 241–293.Google Scholar
Maxworthy, T. 1977 Topographic effects in rapidly rotating fluids: flow over a transverse ridge. Z. angew. Math. Phys. 28, 853–864.Google Scholar
Stewartson, K. 1957 On almost rigid rotations. J. Fluid Mech. 3, 17–26.Google Scholar