Eigenanalysis of the two-dimensional wind-driven ocean circulation problem

A barotropic model of the wind-driven circulation in the subtropical region of the ocean is considered. A no-slip condition is specified at the coasts and slip at the fluid boundaries. Solutions are governed by two parameters: inertial boundary-layer width; and viscous boundary-layer width. Numerical computations indicate the existence of a wedge-shaped region in this two-dimensional parameter space, where three steady solutions coexist. The structure of the steady solution can be of three types: boundary-layer, recirculation and basin-filling-gyre. Compared to the case with slip conditions (Ierley and Sheremet, 1995) in the no-slip case the wedge-shaped region is displaced to higher Reynolds numbers. Linear stability analysis of solutions reveals several classes of perturbations: basin modes of Rossby waves, modes associated with the recirculation gyre, wall-trapped modes and a resonant mode. For a standard subtropical gyre wind forcing, as the Reynolds number increases, the wall-trapped mode is the first one destabilized. The resonant mode associated with disturbances on the southern side of the recirculation gyre is amplified only at larger Reynolds number, nonetheless this mode ultimately provides a stronger coupling between the mean circulation and Rossby basin modes than do the wall-trapped modes.

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