Temporal evolution of vorticity staircases in randomly strained two-dimensional vortices

Abstract

The evolution of a Gaussian vortex subject to a weak-external-random n-fold multipolar strain field is examined using fully nonlinear simulations. The simulations show that at large Reynolds numbers, fine scale steps form at the periphery of the vortex, before merging, generally leaving one large step, which acts as a barrier between the vorticity within the coherent core and the surrounding, well mixed, “surf zone.” It is shown for n = 2 that the width and the number of fine scale steps which initially form at the periphery of the vortex is dependent on the strain parameters, but that the range of radial values for which steps initially occur is only dependent on n and the amplitude of the strain field. A criteria is developed which can predict this range of radial values using the linear stability results of Le Dizès [“Non-axisymmetric vortices in two-dimensional flows,” J. Fluid Mech. 406, 175 (2000)]. This criteria is based upon the perturbation vorticity needing to be larger than some fraction of the vorticity gradient to flatten the vortex profile. For n = 3 and 4, the radial step range is again predicted, and it is observed that for these higher wavenumbers the long lasting steps are narrower than the n = 2 case. For n = 4 the steps which form are so narrow that they do not persist very long before they are destroyed by the strain field and viscosity.