Finite amplitude stability of the wind-driven ocean circulation

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Abstract
The stability of the wind-driven ocean circulation to finite amplitude perturbations is explored. Sufficient conditions for stability, in the kinetic energy norm, are determined for steady solutions of the quasi-geostrophic barotropic vorticity equation on a midlatitude β-plane. In addition, the spatial pattern of the perturbation which is able to extract energy from the flow just above criticality is determined (the most energetic disturbance). The energy stability bounds are computed numerically, by using a continuation method to follow branches of steady states in parameter space, energy identities and calculus of variations. It is found that wind-driven single gyre flows are more stable than double gyre flows. For zero bottom friction and slip meridional boundaries, the most energetic disturbance is a single cell basin-wide flow. No-slip conditions at the meridional boundaries stabilize the double gyre flow and modify the structure of the most energetic disturbance to a multicellular one. Bottom friction further stabilizes the flows and its presence may strongly localize the spatial pattern of the most energetic disturbance.