Quasi-geostrophic stratified flow over isolated finite amplitude topography |
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| Authors: | Christoph Schr Huw C Davies |
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| Institution: | Christoph Schär,Huw C. Davies |
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| Abstract: | The quasi-geostrophic response of a stratified stream incident upon isolated finite amplitude topography on a f-plane is examined in the limit of a Boussinesq, incompressible, inviscid fluid. Compact solutions are derived subject to the following stipulations: uniform upstream velocity and stratification, a circular obstacle and an entirely isentropic/isopycnic lower surface.It is shown that for a semi-infinite flow domain the criterion for Taylor cap formation (i.e., a region of closed streamlines) is
. However, for the isentropic lower boundary condition the solutions exist (i.e., have physical validity) only if R0F−1 < 0.5. (Here R0 and F refer to the Rossby and Froude numbers defined respectively in terms of the mountain half-width and height.) Also considered are the modifications both to the flow response and to the foregoing existence criterion that are induced by the introduction of an upstream profile comprising two layers of uniform but different stratification. In addition, the relationship of the derived solutions to the results obtained in previous studies is explored, and in particular an outline is given of the impact of adopting the ‘traditional’ simplified lower boundary condition. |
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