Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T11:22:02.219Z Has data issue: false hasContentIssue false
  • English
  • Français

Rotating barotropic flow over finite isolated topography

Published online by Cambridge University Press:  19 April 2006

Peter R. Bannon
Peter R. Bannon
Affiliation:
National Center for Atmospheric Research
The National Center for Atmospheric Research is sponsored by the National Science Foundation.
Boulder, Colorado 80307
Get access Rights & Permissions [Opens in a new window]

Abstract

The flow of a rotating, incompressible fluid over isolated topography whose non-dimensional height (i.e. topographic height divided by the mean fluid depth) is large compared with the Rossby number is studied. Attention is restricted to flow which is sufficiently shallow that the free-surface equations provide an adequate description. The flow is forced laterally by a specified upstream inflow (obtained from solutions of the zonally symmetric model equations) and by a prescribed surface stress. Dissipation is incorporated using a Rayleigh friction acting anti-parallel to the flow.

Steady-state solutions for uniform inflow on an f-plane are found for (a) linear viscous flow, (b) quasi-geostrophic flow with and without friction and (c) inviscid flow with and without a rigid lid. The presence of friction produces an upstream–downstream flow asymmetry over the obstacle and an associated topographic drag while inertial terms produce left-right (relative to an observer looking downstream) asymmetry. The blocking efficiency B (the percentage of the incident mass flux going around the obstacle rather than over it) of a Gaussian obstacle is largest (∼ 100%) for case (a) when viscous effects are small. In contrast quasi-geostrophic theory calculates no flow blocking (B ≡ O). For inviscid inertial theory, B ∼ 10% and is independent of the Rossby number. The presence of a free surface decreases the blocking for small-Rossby-number flow.

Numerical solutions of the appropriate initial, boundary-value problem for the complete model equations confirm these results and extend them to include the effects of (i) horizontal shear in the upstream inflow, (ii) the magnitude and shape of the topography, and (iii) variations in the Coriolis parameter (β-effect).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 101 , Issue 2 , 27 November 1980 , pp. 281 - 306
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

Arakawa, A. & Lamb, V. R. 1977 The U.C.L.A. general circulation model. In General Circulation Models of the Atmosphere, pp. 173–265. Academic.
Bannon, P. R. 1979 On the dynamics of the East African jet. Ph.D. thesis, University of Colorado, Boulder.
Buzzi, A. & Tibaldi, S. 1977 Quart. J. Roy. Met. Soc. 103, 135–150.
Charney, J. G. 1955 Proc. Nat. Acad. Sci. 41, 731–740.
Cottrell, J. R. 1970 Is the great red spot on Jupiter a Taylor column in horizontal shear flow? Woods Hole Oceanographic Institution GFD Summer Program Notes.
Edelmann, W. 1972 Beitr. z. Phys. der Atmos. 45, 196–229.
Hide, R. 1961 Nature 190, 895–896.
Hide, R. 1971 J. Fluid Mech. 49, 745–751.
Hide, R. & Ibbetson, A. 1966 Icarus 5, 279–290.
Hogg, N. G. 1973a J. Fluid Mech. 58, 517–537.
Hogg, N. G. 1973b Deep-Sea Res. 20, 449–459.
Huppert, H. E. 1975 J. Fluid Mech. 67, 397–412.
Huppert, H. E. & Bryan, K. 1976 Deep-Sea Res. 23, 655–679.
Huppert, H. E. & Stern, M. E. 1974 J. Fluid Mech. 64, 417–436.
Ingersoll, A. P. 1969 J. Atmos. Sci. 26, 744–752.
Jacobs, S. J. 1964 J. Fluid Mech. 20, 581–591.
Janowitz, G. S. 1974 J. Fluid Mech. 66, 455–464.
Johnson, E. R. 1978a J. Fluid Mech. 86, 209–224.
Johnson, E. R. 1978b Geophys. Astrophys. Fluid Dyn. 9, 327–329.
Kasahara, A. 1966 J. Atmos. Sci, 23, 259–271.
McCartney, M. S. 1975 J. Fluid Mech. 68, 71–95.
McIntyre, M. E. 1972 J. Fluid Mech. 52, 209–243.
Merkine, L. & Kalnay-Rivas, E. 1976 J. Atmos. Sci. 33, 908–922.
Miyakoda, K. 1973 Proc. Roy. Irish Acad. 73A, 99–130.
Nakamura, H. 1978 J. Meteor. Soc. Japan 56, 317–367.
Orlanski, I. 1976 J. Comput. Phys. 21, 251–269.
Piacsek, S. A. & Williams, G. P. 1970 J. Comput. Phys. 6, 392–405.
Proudman, J. 1916 Proc. Roy. Soc. A 92, 408–424.
Roberts, D. G., Hogg, N. G., Bishop, D. G. & Flewellen, D. G. 1974 Deep-Sea Res. 21, 175–184.
Smith, G. D. 1975 Numerical Solution of Partial Differential Equations. Oxford University Press.
Stevenson, J. W. & Janowitz, G. S. 1977 Dyn. Atmos. Oceans 1, 225–239.
Stewartson, K. 1957 J. Fluid Mech. 3, 17–26.
Stone, P. H. & Baker, D. J. 1968 Quart. J. Roy. Met. Soc. 94, 576–580.
Taylor, G. I. 1923 Proc. Roy. Soc. A 104, 213–218.
Taylor, G. I. 1921 Proc. Roy. Soc. A 100, 114–121.
Vaziri, A. & Boyer, D. L. 1971 J. Fluid Mech. 50, 79–95.
Vergeiner, I. & Ogura, Y. 1972 J. Atmos. Sci. 29, 270–284.
Williams, G. P. 1969 J. Fluid Mech. 37, 727–750.