The long-time decay of rotating homogeneous flows over variable topography

The long-time decay of rotating, homogeneous flows over variable topography is analyzed by means of laboratory experiments and numerical simulations. The influence of the topography on the flow evolution is associated with stretching and squeezing effects on fluid columns as they experience changes in depth, and with viscous effects produced by the boundary condition at the solid bottom of the tank. In particular, experiments with a sine-shaped topography in one of the horizontal directions are analyzed by using two different basic flows. First, the evolution of dipolar vortices drifting across the topography while slowly decaying, is examined. The second set of experiments considers the evolution and decay of an initially circular vortex transforming into a tripolar structure. The experiments are well represented by numerical simulations based on a quasi-two-dimensional formulation with variable topography.The main result is that the long-term evolution of the flow (one or two Ekman periods, which are much longer than the rotation period of the system) is characterized by the alignment of the flow along the topographic contours. It is shown that the key process that leads to this phenomenon takes place as cyclonic (anticyclonic) structures are cleaved in two parts over crests (troughs) of the topography. As a result, positive relative vorticity is distributed on deep regions, while anticyclonic vorticity spreads over shallow parts of the domain. In addition, it is numerically found that the dipole speed is somewhat slower than for the flat bottom case, due to a more effective Ekman decay over variable topography. For circular, unstable vortices where the horizontal length scale of the topography is comparable with the vortex diameter, the formation of tripolar structures might be inhibited.