The fate of pancake vortices

Abstract

Nonlinear evolution of pancake-like vortices in a uniformly rotating and stratified fluid is studied using a 3D Boussinesq numerical model at large Rossby numbers. After the initial stage of viscous decay, the simulations reveal exponential growth of toroidal circulation cells (aka Taylor vortices) at the peripheral annulus with a negative Rayleigh discriminant. At the nonlinear stage, these thin cells redistribute the angular momentum and density differently at the levels of radial outflow and inflow. Resulting layering, with a vertical stacking of sharp variations in velocity and density, enhances small-scale mixing and energy decay. Characteristic detectable stretching patterns are produced in the density field. The circulation patterns, induced by centrifugal instability, tend to homogenize the angular momentum in the vicinity of the unstable region. We demonstrate that the peak intensity of the cells and the vortex energy decay are dramatically reduced by the earth’s rotation due to conservation of total absolute angular momentum. The results have important implications for better understanding the fate of pancake vortices and physical mechanisms of energy transfer in stratified fluids.