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The stability of vortices in a rotating, stratified fluid

Published online by Cambridge University Press:  20 April 2006

R. W. Griffiths  and
P. F. Linden
R. W. Griffiths
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge
P. F. Linden
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge
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Abstract

Axisymmetric flows with a two-layer density stratification are produced by releasing either a constant flux of fluid from a point source or a constant volume of fluid into a rotating environment with a different density. In both experiments the density interface intersects one horizontal boundary, forming a front. Transition to non-axisym-metric flow is observed and can be described by two parameters: θ, the square of the ratio of the internal Rossby radius of deformation to the horizontal length scale of the flow, and δ, the fraction of the total fluid depth occupied by the layer inside the front. For θ [Lt ] 1 and δ > 10−1 unstable disturbances obtain most of their energy from the potential energy of the flow, whilst for δ < 10−1 extraction of kinetic energy from the basic shear becomes the dominant driving mechanism. When the front intersects the free surface, n = 2 is the minimum azimuthal wavenumber for an unstable disturbance. At large amplitude of the growing waves, baroclinic and barotropic processes combine to form n vortex dipole structures which entrain buoyant fluid from the original vortex and propagate radially over the free surface. Vortices are also produced by the continuous release of fluid from a confined source at its own density level in a region of constant density gradient. As in the two-layer case the axisymmetric vortex grows to a critical size and then becomes unstable to a disturbance with wavenumber n = 2, producing, at large amplitude, two vortex pairs.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 105 , April 1981 , pp. 283 - 316
Copyright
© 1981 Cambridge University Press

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