Vortex motion in a rotating barotropic fluid layer

Abstract

To study vortex motion and the mechanisms of geostrophic adjustment (i.e. the equilibrium between pressure gradient and Coriolis force, which leads to the weakening of inertio-gravity waves) in large scale geophysical flows, we simulate the dynamics of a shallow-water layer in uniform rotation, without any forcing other than the initial injection of energy and potential enstrophy. Such a flow generates inertio-gravity waves which interact with the rotational eddies. We found that both inertio-gravity waves and rotation reduce the non-linear interactions between vortices, namely the condensation of the vorticity field into isolated coherent vortices, corresponding to the inverse rotational energy cascade, and the associated production of vorticity filaments, due to the direct potential enstrophy cascade. Rotation also inhibits the direct inertio-gravitational energy cascade for scales larger than the Rossby deformation radius. Therefore, if inertio-gravity waves are initially excited at large enough scales, they will remain trapped there due to rotation and there will be no geostrophic adjustment. On the contrary, if inertio-gravity waves are only present at scales smaller than the Rossby deformation radius, which are insensitive to the effect of rotation, they will non-linearly interact and cascade towards the dissipative scales, leaving the flow in geostrophic equilibrium.