Numerical Simulations of the Equilibrium between Eddy-Induced Restratification and Vertical Mixing

Abstract

AbstractSubmesoscale dynamics are hypothesized to play a leading-order role in setting the stratification of the mixed layer via the interaction of submesoscale eddies and surface forcing. Previous studies of such interactions have generally focused on the time-evolving characteristics of submesoscale turbulence, such as the spindown of a baroclinically unstable front. This paper focuses instead on the equilibrium dynamics of the oceanic mixed layer, where forcing and dissipation are in balance, through a combination of scaling analysis and numerical simulations. The steady dynamics are well described by a turbulent thermal wind balance, with external forcing parameterized by a strong vertical diffusivity κ. Scaling laws are developed for the characteristic vertical length scale Lυ, ageostrophic velocity scales U and V, buoyancy frequency N2, and eddy buoyancy flux , which are appropriate for a turbulent mixed layer whose stratification is equilibrated against strong vertical mixing. A suite of numerical simulations is developed to test these scalings for different values of κ and lateral buoyancy gradient. The scaling relations are shown to be very robust across all simulations, and this allows the new scaling for to be directly compared against an extant parameterization in the forcing scenarios explored here.