TEARING OF AN ALIGNED VORTEX BY A CURRENT DIFFERENCE IN 2-LAYER QUASI-GEOSTROPHIC FLOW

A study of two-layer quasi-geostrophic vortex flow is performed to det ermine the effect of a current difference between the layers on a vort ex initially extending through both layers. In particular, the conditi ons under which the vortex can resist being torn by the current differ ence are examined. The vortex evolution is determined using versions o f 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 layer s is maintained. In the first set of flows studied, the current differ ence is generated by a (stronger) third vortex in the upper layer loca ted at a large distance from the (weaker) vortex under study. Flows of this type are important for understanding the interactions of vortice s of different sizes in geophysical turbulence. A set of flows is also considered in which an ambient geostrophic current difference is prod uced by a non-uniform background potential vorticity field. In this ca se, an additional (secondary) flow field about the vortex patch in eac h layer is generated by redistribution of the ambient potential vortic ity field. It is found that a vortex that initially extends through bo th layers will undergo a periodic motion, in which the two parts of th e initial vortex in the different layers (called the 'upper' and 'lowe r' vortices) oscillate about each other, provided that the current dif ference between the layers is less than a critical value. When the cur rent difference exceeds this critical value, the upper and lower vorti ces separate permanently and the initial vortex is said to 'tear'. The effects of various dimensionless parameters that characterize the flo w are considered, including the ratio of core radius to internal Rossb y radius, the ratio of layer depths and the ratio of the strengths of the upper and lower vortices. These parameters affect both the critica l current difference for tearing and the deformation of the vortex cor es by their interaction. It is found that for small values of inverse internal Rossby deformation radius, calculations with circular non-def ormable vortices (convected at their centrepoints) give results in goo d agreement with the contour dynamics simulations, since the vortex de formation is small. The results of the study will be useful in determi ning the conditions under which large geophysical vortex structures, s uch as cyclones and ocean rings, can extend to large heights (depths) even though the mean winds (currents) in the ambient flow change signi ficantly along the vortex length.