The wall jet in a rotating fluid

Abstract

The previously observed spatial evolution of the two-dimensional turbulent flow from a source on the vertical wall of a shallow layer of rapidly rotating fluid is strikingly different from the non-rotating three-dimensional counterpart, insofar as the instability eddies generated in the former case cause the flow to separate completely from the wall at a finite downstream distance. In seeking an explanation of this, we first compute the temporal evolution of two-dimensional finite-amplitude waves on an unstable laminar jet using a finite difference calculation at large Reynolds number. This yields a dipolar vorticity pattern which propagates normal to the wall, while leaving some of the near-wall vorticity (negative) of the basic flow behind. The residual far-field eddy therefore contains a net positive circulation and this property is incorporated in a heuristic point-vortex model of the spatial evolution of the instability eddies observed in a laboratory experiment of a flow emerging from a source on a vertical wall in a rotating tank. The model parameterizes the effect of Ekman bottom friction in decreasing the circulation of eddies which are periodically emitted from the source flow on the wall. Further downstream, the point vortices of the model merge and separate abruptly from the wall; the statistics suggest that the downstream separation distance scales with the Ekman spin-up time (inversely proportional to the square root of the Coriolis parameter f) and with the mean source velocity. When the latter is small and f is large, qualitative support is obtained from laboratory experiments.