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

The motion of a two-dimensional (2D) elliptical vortex in an external strain flow can be complicated when the strain rate varies in time. However, when the external flow changes slowly, adiabatic theory can be employed. We present analytical calculations and experimental measurements of the adiabatic behavior of elliptical vortices in external strain flows where the strain rate is ramped upward in time [N. C. Hurst et. al., Phys. Rev. Fluids 6, 054703 (2021)]. The theoretical work uses a Hamiltonian elliptical vortex patch model, where the adiabatic invariant is interpreted as the amplitude of an oscillation about a stable equilibrium. It is shown that both a driving term and frequency variation contribute to adiabatic breaking, where a WKB method is used to evaluate the latter effect. The experimental work uses pure electron plasmas, which have been shown to closely follow the 2D Euler equations describing ideal fluids. One conclusion is that the adiabatic breaking depends in complicated ways on the time-dependence of the strain rate, with linear ramps resulting in periodically-modulated power-law breaking. Another is that the experimental vortices experience critical-layer damping due to their smooth edges, which decreases the oscillation amplitude. Work supported by US DOE.