The behavior of an anticyclonic coherent eddy in a barotropic strain field is examined using a shallow water equation model. The ''lens equation'' model, a set of eight nonlinear ordinary differential equations, was first exploited by Cushman-Roisin et al. <1985> and Ripa <1987> to examine the behavior and stability of isolated vortices. In this paper we expand the application to include the effect of external fields on the vortex, in particular, an external barotropic strain field. The equilibrium solutions to the equations are found to be elliptical lenses aligned along the high-pressure axis of the strain field (up to a rate of strain of 0.1f), and an aphysical rain gutter aligned along the strain field outflow axes. The linear stability of the elliptical solutions is explored, and it is found that regardless of the rate of strain, vortices with ellipticities (E) greater than ~2 are unstable to lens-like and higher order perturbations, and that this value of E corresponds to a maximum in the conservative lens quantity Potential Vorticity (PV). Time dependent integrations of the model confirm the results of the instability analysis: lenses with Es or PVs greater than the stable maxima integrate toward the rain gutter solution. The initial growth rates (O~f/20) correspond to the linear analysis, but once the perturbations are finite, the growth rate is superexponential. Numerical experiments with a time dependent external strain field show that lens PV can be used a a predictor of stability, and a general stability diagram for a lens in an external strain field is constructed. Laboratory experiments confirm some of the results of the theoretical model and also reveal its weaknesses. ¿ American Geophysical Union 1990 |