Vortex Dynamics of Geostrophically Adjusted Density Perturbations in Triply-Periodic Models of Stratified Incompressible Fluids

Abstract

A model exploring contributions to lateral dispersion in the oceanic submesoscale is presented. Well-mixed patches of uid, produced by turbulent mixing events, are geostrophically adjusted to create compound vortices. The dynamics of these vortices are investigated for their contributions to inverse cascades of kinetic energy and to the lateral dispersion of a passive tracer in numerical simulations. When perturbed by the proximity of another vortex, these vortices break down into propagating dipole forms, contributing to the dispersion of tracers. A memory e ect for the locations of well-mixed patches is explored for its e ect on dispersion dynamics. The vertical periodicity of triply-periodic numeric domains is found to be a source of weakly dissipated, slowly accumulated, barotropic mode kinetic energy and increased tracer dispersion. The two dimensionality of the barotropic mode is found to be the source for observed inverse cascades of kinetic energy in viscous simulations of anisotropic domains. Signatures of inverse cascades in nearly equilibrated simulations are found to strongly contribute to the lateral dispersion of a passive tracer. Additional techniques are proposed to evaluate lateral dispersion relevant to the ocean.