THE INFLUENCE OF OCEAN MIXING ON THE ABSOLUTE VELOCITY VECTOR

The potential vorticity equation has been vertically differentiated an d used with the thermal wind equation to obtain the following expressi on for the absolute horizontal Eulerian velocity vector, [GRAPHICS] wh ere [GRAPHICS] where phi(z) is the rate of turning with height of the epineutral q contours, del(n)q is the gradient of potential vorticity in the neutral surface, k is the unit vector antiparallel to gravity, and del(2)p is the horizontal gradient of in situ density in the geopo tential surface; epsilon(z) is the vertical derivative of the dianeutr al velocity plus the effective vortex stretching due to unsteadiness a nd the lateral mixing of potential vorticity and V perpendicular to is the horizontal velocity component normal to the epineutral contours o f potential vorticity. A new finding is that the velocity component th at mixing induces along the epineutral a contours, V1/2/phi(z), is equ al to the rate of change of the V perpendicular to component up the ca st per unit change in phi(measured in radians). The equation for the a bsolute velocity vector V is used to explore the conditions required-f or V = 0. In the absence of mixing processes, V = 0 occurs only where the epineutral gradient of potential vorticity is zero; however, with mixing processes, the lateral velocity can be arrested by mixing witho ut requiring this condition on the gradient of potential vorticity. Co nversely, in the presence of mixing, the flow is nonzero at points whe re del(n)q = 0, and it is shown that at these points the lateral veloc ity is determined by the epineutral gradient of q epsilon(z). A zero o f the lateral Eulerian velocity will occur only at isolated points on any particular surface. Similarly, points of zero three-dimensional ve locity will be so rare that one may never expect to encounter such a p oint on any particular surface. Mesoscale eddy activity is assumed to transport potential vorticity q in a downgradient fashion along neutra l; surfaces, and this leads directly to a parameterization of this con tribution to the lateral Stokes drift. This extra lateral velocity is typically 1 mm s(-1) in the direction toward greater \q\ along neutral surfaces, that is, broadly speaking, in the direction away from the e quator and toward the poles. This Stokes drift will often make a large contribution to the tracer conservation equations.