Rw. Griffiths et G. Veronis, A LABORATORY STUDY OF THE EFFECTS OF A SLOPING SIDE BOUNDARY ON WIND-DRIVEN CIRCULATION IN A HOMOGENEOUS OCEAN MODEL, Journal of marine research, 55(6), 1997, pp. 1103-1126
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.