Ekman layers and two‐dimensional frontogenesis in the upper ocean

Abstract

A two‐dimensional modified semi geostrophic model is used to study the evolution of oceanic fronts in the presence of vertical mixing. The parameterization used for mixing is an elevated constant value of vertical viscosity and friction; hence the Ekman layer acts as a surrogate mixed layer, with, however, vertical shear allowed everywhere. An initial condition representative of the observed fields in Frontal Air‐Sea Interaction Experiment (FASINEX) is used, and its modification in the presence of vertical mixing alone is investigated. Without external forcing an Ekman layer results because of the presence of vertical geostrophic shear at the surface. The maximum density gradient moves toward the dense side of the front driven by this flow. Convergence of Ekman flow results in downward bowing of the isopycnals beneath the surface expression of the front, a feature reminiscent of density sections taken during FASINEX. This feature is not evident when a barotropic convergence field is applied in the absence of mixing or in fully nonlinear simulations of the evolution of fronts with baroclinic instability. An analytic theory suggests that the maximum density gradient will increase over time when vertical mixing alone is present. In the presence of negative uniform wind stress in the direction opposite to the surface geostrophic flow the front moves toward the denser water, and the jet uniformly decreases in strength. In the presence of a positive uniform wind in the direction of the surface geostrophic flow the surface jet initially weakens but then strengthens again as the wind‐driven Ekman flow opposes the frictionally driven Ekman flow and the cross‐front density gradient increases.