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Tearing of an aligned vortex by a current difference in two-layer quasi-geostrophic flow

Published online by Cambridge University Press:  26 April 2006

J. S. Marshall  and
B. Parthasarathy
J. S. Marshall
Affiliation:
Department of Ocean Engineering, Florida Atlantic University, Boca Raton, FL 33431, USA
B. Parthasarathy
Affiliation:
Department of Ocean Engineering, Florida Atlantic University, Boca Raton, FL 33431, USA
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Abstract

A study of two-layer quasi-geostrophic vortex flow is performed to determine the effect of a current difference between the layers on a vortex initially extending through both layers. In particular, the conditions under which the vortex can resist being torn by the current difference are examined. The vortex evolution is determined using versions of the contour dynamics and discrete vortex methods which are modified for two-layer quasi-geostrophic flows. The vortex response is found to depend upon the way in which the current difference between the layers is maintained. In the first set of flows studied, the current difference is generated by a (stronger) third vortex in the upper layer located at a large distance from the (weaker) vortex under study. Flows of this type are important for understanding the interactions of vortices of different sizes in geophysical turbulence. A set of flows is also considered in which an ambient geostrophic current difference is produced by a non-uniform background potential vorticity field. In this case, an additional (secondary) flow field about the vortex patch in each layer is generated by redistribution of the ambient potential vorticity field.

It is found that a vortex that initially extends through both layers will undergo a periodic motion, in which the two parts of the initial vortex in the different layers (called the ‘upper’ and ‘lower’ vortices) oscillate about each other, provided that the current difference between the layers is less than a critical value. When the current difference exceeds this critical value, the upper and lower vortices separate permanently and the initial vortex is said to ‘tear’. The effects of various dimensionless parameters that characterize the flow are considered, including the ratio of core radius to internal Rossby radius, the ratio of layer depths and the ratio of the strengths of the upper and lower vortices. These parameters affect both the critical current difference for tearing and the deformation of the vortex cores by their interaction. It is found that for small values of inverse internal Rossby deformation radius, calculations with circular non-deformable vortices (convected at their centrepoints) give results in good agreement with the contour dynamics simulations, since the vortex deformation is small. The results of the study will be useful in determining the conditions under which large geophysical vortex structures, such as cyclones and ocean rings, can extend to large heights (depths) even though the mean winds (currents) in the ambient flow change significantly along the vortex length.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 255 , October 1993 , pp. 157 - 182
Copyright
© 1993 Cambridge University Press

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