The instability of lenticular vortices

We examine the stability of lenticular vortices or lenses using a two-layer shallow water model. The simplest configuration is one in which the lenses overlay a deep layer and have a free surface, and this can be studied using a two-layer model. We report results from laboratory experiments and high-resolution direct numerical simulations of the destabilization of vortices with constant potential vorticity, and compare these to a linear stability analysis. The stability properties of the system are governed by two parameters: the typical upper-layer potential vorticity and the size of the vortex. Good agreement is found between analytical, numerical and experimental results for the growth rate and wavenumber of the instability. The nonlinear saturation of the instability is associated with conversion from potential to kinetic energy and weak emission of gravity waves, giving rise to the formation of coherent vortex multipoles with trapped waves. The impact of flow in the lower layer is examined, in particular its effect on the growth rate of the instability.