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On the Onset of Inertial Recirculation in Barotropic General Circulation Models

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  • 1 Dept. of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931
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Abstract

A nonlinear ordinary differential equation which models the western boundary layer of quasi-geostrophic barotropic models of the wind-driven circulation has been investigated by Il'in and Kamenkovich and more recently by Ierley and Ruehr. For mild nonlinearity the boundary layer model has two possible outflow solutions which match to a Sverdrup interior. For stronger nonlinearity, no solutions exist. In the weakly nonlinear case we use linear stability theory to resolve the problem of multiple solutions. A highly stretched regional model of the full quasi-geostrophic equations is used to investigate the disappearance of solutions of the boundary layer model. We find that a failure of the boundary layer model is coincident with the onset of recirculation in the solution of the partial differential equations at a sufficiently large ratio of basin scale to viscous boundary-layer scale. For less extreme ratios, the onset of recirculation is deferred, and hence its relation to a failure of the boundary layer model is obscured.

Abstract

A nonlinear ordinary differential equation which models the western boundary layer of quasi-geostrophic barotropic models of the wind-driven circulation has been investigated by Il'in and Kamenkovich and more recently by Ierley and Ruehr. For mild nonlinearity the boundary layer model has two possible outflow solutions which match to a Sverdrup interior. For stronger nonlinearity, no solutions exist. In the weakly nonlinear case we use linear stability theory to resolve the problem of multiple solutions. A highly stretched regional model of the full quasi-geostrophic equations is used to investigate the disappearance of solutions of the boundary layer model. We find that a failure of the boundary layer model is coincident with the onset of recirculation in the solution of the partial differential equations at a sufficiently large ratio of basin scale to viscous boundary-layer scale. For less extreme ratios, the onset of recirculation is deferred, and hence its relation to a failure of the boundary layer model is obscured.

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