A three-dimensional model of inertial currents in a variable-density ocean

The three-dimensional equations for a general inertial ocean current are transformed so that the temperature rather than the vertical co-ordinate appears as an independent variable. A downstream power series expansion is made of the equations and boundary conditions, which involves an expansion about the mean potential vorticity. A general first-order solution is obtained for a boundary current between two level surfaces, one of no motion and one of uniform temperature. The case of constant potential vorticity is treated for arbitrary inviscid boundary conditions; it is found that the current can exist as a boundary layer only if the open ocean geostrophic drift is westward everywhere in the depth interval. This result is extended to arbitrary potential vorticity distributions by an asymptotic analysis in physical space.