Adiabatic behavior of an elliptical vortex in a time-dependent external strain flow

When vortex patches are subjected to externally imposed strain flows where the strain rate grows slowly in time, the system approximately preserves an adiabatic invariant related to oscillatory elliptical deformations of the vortices. Formulae are derived for the breaking of this invariant with respect to the rate and functional form of the strain ramp. The analytical results are compared to experimental data acquired using magnetized pure electron plasmas, which provide a close laboratory realization of the motion of two-dimensional ideal vortices.