Velocity extrema in ocean gyre flows

Ocean gyres are modelled by the two-dimensional vorticity equation for inviscid flow on a rotating sphere, since their flow is governed by the tangential velocity components, whereas the vertical velocity component is negligible. From the vorticity equation we derive nonlinear elliptic equations for the square of the meridional velocity component as well as for the azimuthal velocity component. Using maximum principles we then show that, under suitable conditions on the oceanic vorticity, the velocity extrema are attained on the boundary of a subtropical gyre located in the zonal band between 15${}^{\circ }$ and 45${}^{\circ }$ Northern, respectively Southern latitude, where the five major gyres are found.