| description 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, ? = 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 ? is also inversely proportional to ?, the gradient of f with respect to latitude, i.e. ? = Af2/(N2?). The connection with the recent work of Gent and McWilliams and the consequences for coarse resolution numerical model studies are discussed. | |
