On a differential equation arising in geophysics

We investigate a recently derived model for arctic gyres by showing the existence of non-trivial solutions with a vanishing azimuthal velocity in the case of linear vorticity functions. Our approach consists in deriving an equivalent differential equation on a semi-infinite interval, with suitable asymptotic conditions for the unknown stream function. A qualitative study reveals that, given the linear vorticity function, the value assigned to the stream function at the North Pole determines uniquely the flow throughout the gyre. We also provide some explicit solutions.