OSCILLATORY FLOW PAST A CIRCULAR-CYLINDER IN A ROTATING-FRAME

Because of the importance of oscillatory components in the oncoming fl ow at certain oceanic topographic features, we investigate the oscilla tory flow past a circular cylinder in an homogeneous rotating fluid. W hen the oncoming flow is non-reversing, and for relatively low-frequen cy oscillations, the modifications to the equivalent steady flow arise principally in the 'quarter layer' on the surface of the cylinder. An incipient-separation criterion is found as a limitation on the magnit ude of the Rossby number, as in the steady-flow case. We present exact solutions for a number of asymptotic cases, at both large frequency a nd small nonlinearity. We also report numerical solutions of the nonli near quarter-layer equation for a range of parameters, obtained by a t emporal integration. Year the rear stagnation point of the cylinder, w e find a generalized velocity 'plateau' similar to that of the steady- flow problem, in which all harmonics of the free-stream oscillation ma y be present. Further, we determine that, for certain initial conditio ns, the boundary-layer flow develops a finite-time singularity in the neighbourhood of the rear stagnation point.