Abstract
We investigate the consequence, at small Ekman number, of adding vertical mixing of momentum terms to the incompressible thermocline equations. We find that choosing the vertical eddy viscosity, ν = Af2/N2, where f is the Coriolis parameter and N is the local value of the buoyancy frequency, leads to isopycnal mixing of fQ, where Q is the reciprocal of potential vorticity, provided A is independent of the vertical coordinate. If, additionally, A is also independent of the north–south coordinate, then on a beta-plane, this implies homogenization of potential vorticity, q, within closed q-contours on isopycnal surfaces. This conclusion extends to spherical geometry if ν is also inversely proportional to β, the gradient of f with respect to latitude, i.e. ν = Af2/(N2β). The connection with the recent work of Gent and McWilliams and the consequences for coarse resolution numerical model studies are discussed.
