THE WALL-JET IN A ROTATING FLUID

The previously observed spatial evolution of the two-dimensional turbu lent flow from a source on the vertical wall of a shallow layer of rap idly rotating fluid is strikingly different from the non-rotating thre e-dimensional counterpart, insofar as the instability eddies generated in the former case cause the flow to separate completely from the wal l at a finite downstream distance. In seeking an explanation of this, we first compute the temporal evolution of two-dimensional finite-ampl itude waves on an unstable laminar jet using a finite difference calcu lation at large Reynolds number. This yields a dipolar vorticity patte rn 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 prop erty is incorporated in a heuristic point-vortex model of the spatial evolution of the instability eddies observed in a laboratory experimen t of a flow emerging from a source on a vertical wall in a rotating ta nk, The model parameterizes the effect of Ekman bottom friction in dec reasing 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 s uggest that the downstream separation distance scales with the Ekman s pin-up time (inversely proportional to the square root of the Coriolis parameter f) and with the mean source velocity. When the latter is sm all and f is large, qualitative support is obtained from laboratory ex periments.