The Influence of Ocean Mixing on the Absolute Velocity Vector

Abstract

Abstract The potential vorticity equation has been vertically differentiated and used with the thermal wind equation to obtain the following expression for the absolute horizontal Eulerian velocity vector, where where ϕz is the rate of turning with height of the epineutral q contours, ∇nq is the gradient of potential vorticity in the neutral surface, k is the unit vector antiparallel to gravity, and ∇2ρ is the horizontal gradient of in situ density in the geopotential surface; ϵz, is the vertical derivative of the dianeutral velocity plus the effective vortex stretching due to unsteadiness and the lateral mixing of potential vorticity and V⊥ is the horizontal velocity component normal to the epineutral contours of potential vorticity. A new finding is that the velocity component that mixing induces along the epineutral q contours, V⊥z/ϕz, is equal to the rate of change of the V⊥ component up the cast per unit change in ϕ (measured in radians). The equation for the absolute velocity vector V is used to exp...