The ‘sliced-cylinder’ laboratory model of the wind-driven ocean circulation. Part 1. Steady forcing and topographic Rossby wave instability

Abstract

The nonlinear response of the ‘sliced-cylinder’ laboratory model for the wind-driven ocean circulation is re-examined here in part 1 for the case of strong steady forcing. Introduced by Pedlosky & Greenspan (1967), the model consists of a rapidly rotating right cylinder with a planar sloping bottom. The homogeneous contained fluid is driven by the slow rotation of the flat upper lid relative to the rest of the basin. Except in thin Ekman and Stewartson boundary layers on the solid surfaces of the basin, the horizontal flow in the interior and western boundary layer is constrained by the rapid rotation of the basin to be independent of depth. The model thus effectively simulates geophysical flows through the physical analogy between topographic vortex stretching in the laboratory model and the creation of relative vorticity in planetary flows by the β effect.As the forcing is increased, the flow in both the sliced-cylinder laboratory and numerical models first exhibits downstream intensification in the western boundary layer. At greater forcing, separation of the western boundary current occurs with the development of stationary topographic Rossby waves in the western boundary-layer transition regions. The observed flow ultimately becomes unstable when a critical Ekman-layer Reynolds number is exceeded. We first review and compare the experimental and numerical descriptions of this low-frequency instability, then present a simple theoretical model which successfully explains this observed instability in terms of thelocalbreakdown of the finite-amplitude topographic Rossby waves embedded in the western boundary current transition region. The inviscid stability analysis of Lorenz (1972) is extended to include viscous effects, with the consequence that dissipative processes in the sliced-cylinder problem (i.e. lateral and bottom friction) are shown to inhibit the onset of the instability until the topographic Rossby wave slope exceeds a finite critical value.