Numerical Simulations of Lateral Dispersion by the Relaxation of Diapycnal Mixing Events

Abstract

In this second of two companion papers, numerical simulations of lateral dispersion by small-scale geostrophic motions, or vortical modes, generated by the adjustment of mixed patches following diapycnal mixing events are examined. A three-dimensional model was used to solve the Navier?Stokes equations and an advection/diffusion equation for a passive tracer. Model results were compared with theoretical predictions for vortical mode stirring with results from dye release experiments conducted over the New England continental shelf. For ?weakly nonlinear? cases in which adjustment events were isolated in space and time, lateral dispersion in the model was consistent to within a constant scale factor with the parameter dependence predicted by Sundermeyer et al., where h and L are the vertical and horizontal scales of the mixed patches, ?N?2 is the change in stratification associated with the mixed patches, f is the Coriolis parameter, ? is the frequency of diapycnal mixing events, and ?B is the background viscosity. The associated scale factor, assumed to be of order 1, had an actual value of about 7, although this value will depend, in an unknown way, on the assumed horizontal scale of the mixed patches, which was here held constant at close to the deformation radius. A second more energetic parameter regime was also identified in which vortical mode stirring became strongly nonlinear and the effective lateral dispersion was larger. Estimates of the relevant parameters over the New England shelf suggest that this strongly nonlinear regime is more relevant to the real ocean than the weakly nonlinear regime, at least under late summer conditions. This suggests that stirring by small-scale geostrophic motion may, under certain conditions, contribute significantly to lateral dispersion on scales of 1?10 km in the ocean.