Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-17T23:23:18.250Z Has data issue: false hasContentIssue false
  • English
  • Français

Barotropic flow over finite isolated topography: steady solutions on the beta-plane and the initial value problem

Published online by Cambridge University Press:  26 April 2006

Luanne Thompson  and
Glenn R. Flierl
Luanne Thompson
Affiliation:
School of Oceanography WB-10, University of Washington, Seattle, WA 98195, USA
Glenn R. Flierl
Affiliation:
Massachussetts Institute of Technology, 54-1426, Cambridge, MA 02139, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Solutions for inviscid rotating flow over a right circular cylinder of finite height are studied, and comparisons are made to quasi-geostrophic solutions. To study the combined effects of finite topography and the variation of the Coriolis parameter with latitude a steady inviscid model is used. The analytical solution consists of one part which is similar to the quasi-geostrophic solution that is driven by the potential vorticity anomaly over the topography, and another, similar to the solution of potential flow around a cylinder, that is driven by the matching conditions on the edge of the topography. When the characteristic Rossby wave speed is much larger than the background flow velocity, the transport over the topography is enhanced as the streamlines follow lines of constant background potential vorticity. For eastward flow, the Rossby wave drag can be very much larger than that predicted by quasi-geostrophic theory. The combined effects of finite height topography and time-dependence are studied in the inviscid initial value problem on the f-plane using the method of contour dynamics. The method is modified to handle finite topography. When the topography takes up most of the layer depth, a stable oscillation exists with all of the fluid which originates over the topography rotating around the topography. When the Rossby number is order one, a steady trapped vortex solution similar to the one described by Johnson (1978) may be reached.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 250 , May 1993 , pp. 553 - 586
Copyright
© 1993 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

Bannon, P. R. 1980 Rotating barotropic flow over finite isolated topography. J. Fluid Mech. 101, 281–306.Google Scholar
Boyer, D. L., Davies, P. A. & Holland, W. R. 1984 Rotating flow past disks and cylindrical depressions. J. Fluid Mech. 141, 67–95.Google Scholar
Hide, R. 1961 Origin of Jupiter's Great Red Spot. Nature 190, 895–896.Google Scholar
Huppert, H. E. 1975 Some remarks on the initiation of inertial Taylor Columns. J. Fluid Mech. 67, 397–412.Google Scholar
Huppert, H. E. & Bryan, K. 1976 Topographically generated eddies. Deep-Sea Res. 23, 655–697.Google Scholar
Ingersoll, A. P. 1969 Inertial Taylor Columns and Jupiter's Great Red Spot. J. Atmos. Sci. 26, 744–752.Google Scholar
James, I. N. 1980 The forces due to geostrophic flows over shallow topography. Geophys. Astrophys. Fluid Dyn. 9, 159–177.Google Scholar
Janowitz, G. S. 1975 The effect of bottom topography on a stratified flow in the beta plane. J. Geophys. Res. 80, 4163–4168.Google Scholar
Johnson, E. R. 1977 Stratified Taylor columns on a beta-plane. Geophys. Astrophys. Fluid Dyn. 9, 159–177.Google Scholar
Johnson, E. R. 1978 Trapped vortices in rotating flow. J. Fluid Mech. 86, 209–224.Google Scholar
Johnson, E. R. 1979 Finite depth stratified flow over topography on a beta-plane. Geophys. Astrophys. Fluid Dyn. 12, 35–43.Google Scholar
Johnson, E. R. 1983 Taylor columns in a horizontally sheared flow. Geophys. Astrophys. Fluid Dyn. 24, 143–164.Google Scholar
Johnson, E. R. 1984 Starting flow for an obstacle moving transversely in a rapidly rotating fluid. J. Fluid Mech. 149, 71–88.Google Scholar
Kozlov, V. F. 1983 The method of contour dynamics in model problems of the ocean topographysical cyclogenesis. Izv. Atmos. Ocean Phys. 635–640.
Meacham, S. P. 1991 Meander evolution on quasi-geostrophic jets. J. Phys. Oceanogr. 21, 1139–1170.Google Scholar
McCartney, M. S. 1975 Inertial Taylor columns on a beta plane. J. Fluid Mech. 68, 71–95.Google Scholar
McKee, J. W. 1971 Comments on ‘A Rossby wake due to an island on an eastward current.’ J. Phys. Oceanogr. 1, 287.Google Scholar
Miles, J. W. & Huppert, H. E. 1968 Lee waves in a stratified flow. Part 2. Semi-circular obstacle. J. Fluid Mech. 33, 803–814.Google Scholar
Polvani, L. M. Geostrophic vortex dynamics. Ph.D thesis, MIT/WHOI, WHOI-88-48.
Rhines, P. B. 1969 Slow oscillations in an ocean of varying depth. Part 2. Islands and seamounts. J. Fluid Mech. 37, 191–205.Google Scholar
Taylor, G. I. 1917 Motion of solids in fluids when the flow is not irrotational. Proc. R. Soc. Lond A 93, 99–113.Google Scholar
Taylor, G. I. 1923 Experiments on the motion of solid bodies in rotating fluids. Proc. R. Soc. Lond A 104, 213–218.Google Scholar
Thompson, L. 1990 Flow over finite isolated topography. PhD thesis, MIT-WHOI, WHOI-91-05.
Verron, J. & Le Provost, C. 1985 A numerical study of quasi-geostrophic flow over isolated topography. J. Fluid Mech. 154, 231–252.Google Scholar