A LABORATORY STUDY OF THE EFFECTS OF A SLOPING SIDE BOUNDARY ON WIND-DRIVEN CIRCULATION IN A HOMOGENEOUS OCEAN MODEL

A laboratory model is used to investigate the effects of sloping bound aries on homogeneous wind-driven beta-plane circulation. The very gent le slopes of real oceanic boundaries raise the possibility that dissip ation by lateral diffusion of vorticity to the boundary is largely rem oved, leaving dissipation only in bottom Ekman layers. The laboratory model is a modification of the rotating 'sliced-cylinder' introduced b y Pedlosky and Greenspan (1967) and Beardsley (1969) and in which how is driven by a differentially rotating lid. The vertical wall is repla ced with a side wall having a uniform 45 degrees slope around the enti re perimeter. This sloping boundary, like a continental slope, tends t o steer the flow along the slope. In the geometry chosen for this stud y it also provides closed potential vorticity contours through every p oint in the basin, thus removing the blocked contours of the experimen ts with a vertical wall and the open contours of ocean basins that app roach the equator. For cyclonic forcing there is a northward (Sverdrup ) flow in the interior superimposed on a zonal flow so that a particle starts out at the southwest, enters the slope region in the northwest , circles cyclonically along a circle of constant radius (and depth) t o a point on the southeast where it crosses constant depth contours an d rejoins the original point. The direction of flow is reversed for an ticyclonic forcing. The main dissipation of vorticity takes place in t he southeast where the flow crosses constant depth contours. For cyclo nic forcing the how is stable and steady under all conditions achieved . For anticyclonic forcing the laboratory flow is unsteady under all c onditions attainable and unstable to eddy shedding at sufficiently lar ge Rossby or Reynolds numbers. At large Ekman numbers the onset of ins tability corresponds to shedding of cyclonic eddies in the region wher e the boundary current enters the interior, whereas at small Ekman num bers it corresponds to periodic breakup of an anticyclonic gyre in the 'northwest' and the formation of anticyclonic eddies. Eddies of bath sign are shed when the forcing is sufficiently supercritical and the E kman number small. A simple, qualitative argument explains why the cyc lonic flow is stable and the anticyclonic Bow is unstable when the sys tem is nonlinear.