The ‘sliced-cylinder’ laboratory model of the wind-driven ocean circulation. Part 2. Oscillatory forcing and Rossby wave resonance

Abstract

The response of the ‘sliced-cylinder’ laboratory model for the wind-driven ocean circulation is studied here in part 2 for the case of an oscillatory ‘wind’ stress. The model consists of a rapidly rotating right cylinder with a planar sloping bottom. This basin geometry contains no closed geostrophic contours, so that low frequency topographic Rossby wave modes possessing mean vorticity exist in the sliced-cylinder model by the physical analogy between topographic vortex stretching and the β effect for large-scale planetary flows. The interior flow in the laboratory model is driven by the time-dependent Ekman-layer suction produced by the periodic relative angular velocity of the upper lid. The frequency of the forcing is sufficiently small that the interior motion is quasi-geostrophic with the horizontal velocities being independent of depth. Simple two-dimensional analytic and numerical models are developed and compared very favourably with the laboratory results. The observed horizontal velocity field exhibits both (i) westward intensification and decreased horizontal scale when the forcing frequency is decreased, and (ii) a significant resonant magnification when the forcing frequency is tuned to the natural frequency of one of the lower inviscid topographic Rossby wave modes. The observed westward phase speed of the driven motion is accurately predicted and shows little dependence on the amplitude of the forcing. The instantaneous and mean Lagrangian fluid particle trajectories were measured in the laboratory model. The general derivation by Moore (1970) of the governing equations for the mean Lagrangian motion are extended to incorporate forcing and Ekman-layer dissipation. The results suggest that the mean Lagrangian flow should be significantly reduced near resonant frequencies, since the mean Eulerian motion is partially offset by the Stokes drift associated with the topographic Rossby wave modes. This result is consistent with the small observed amplitude of the mean Lagrangian motion. Also presented are the results for a laboratory experiment conducted using a combined steady and oscillatory ‘wind’ stress.