A Note on the Transition of the Polar Cap Flow to the Westward Flow on a Rotating Sphere

Two-dimensional flow in a circular domain on a rotating sphere is a simplest model of oceanic flows. We have studied the flow pattern in the circular domain with an inlet and an outlet on the opposite side on the domain boundary. When the domain is located in the north polar region, i.e. in a polar cap, a large polar vortex emerges with the flow going along the left boundary to the outlet. However, when the domain is outside the polar region, the westward intensified flow should prevail in the flow field. Here we study numerically the transition of the polar cap flow to the westward intensified flow, in relation to the conservation of the potential vorticity.