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Wave-vortex dynamics in rotating shallow water

Published online by Cambridge University Press:  26 April 2006

Marie Farge  and
Robert Sadourny
Marie Farge
Affiliation:
Laboratoire de Météorologie Dynamique du CNRS, 24, rue Lhomond, 75231 Paris Cedex 05, France
Robert Sadourny
Affiliation:
Laboratoire de Météorologie Dynamique du CNRS, 24, rue Lhomond, 75231 Paris Cedex 05, France
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Abstract

We investigate how two-dimensional turbulence is modified when the incompressibility constraint is removed, by numerically integrating the full Saint-Venant (shallow-water) equations. In the case of small geopotential fluctuations considered here, we find no energy exchange between the inertio-gravitational and the potentio-vortical components of the flow. At small scales, the potentio-vortical component behaves as if the flow were incompressible, while we observe an intense direct energy cascade within the inertio-gravitational component. At large scales, the reverse potentio-vortical energy cascade is reduced when the level of inertio-gravitational energy is high. Looking at the effect of rotation, we find that a fast rotation rate tends to inhibit all three cascades. In particular, the inhibition of the inertio-gravitational energy cascade towards small scales implies that the geostrophic adjustment process is hindered by an increase of rotation. Concerning the structure of the coherent vortices emerging out of these decaying turbulent flows, we observe that the smallest scales are concentrated inside the vortex cores and not on their periphery.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 206 , September 1989 , pp. 433 - 462
Copyright
© 1989 Cambridge University Press

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