A two‐dimensional model of mesoscale frontogenesis in the ocean

Abstract

AbstractA two‐dimensional primitive equation model conserving potential vorticity is used to simulate the effect of a horizontal barotropic deformation field on a pre‐existing isopycnic potential vorticity gradient. The novel feature of the prognostic model is that it accurately describes the development of the density and velocity distributions up to local Rossby number 0.5 and beyond. The model coordinates are based in the vertical on quasi‐isopycnic vertical coordinates and in the horizontal on geostrophic coordinates. The model is integrated forward in time for three days creating a density front and a jet of 0.4 m s−1 in the surface layers. Cross‐jet velocities are one order of magnitude smaller. Conservation of potential vorticity leads to a modulation of spacing between isopycnals as both the cyclonic and anticyclonic vorticity associated with the horizontal shear of the accelerating jet increase. Vortex stretching and compression sustain a strong vertical circulation. The paper shows how the jet kinetic energy is limited by the amount of available potential energy in a catchment area defined by the extent of the region of confluence. The jet becomes shallower as frontogenesis approaches this limit.The model is also applicable to the development of permanent streams in the large‐scale circulation of the upper ocean, by slow (order one month) frontogenesis due to gyre‐scale deformation acting on an isopycnic potential vorticity gradient in the seasonal thermocline.The vigorous upwelling on the anticyclonic side of the jet raises nutrients through the euphotic zone, increasing primary productivity. This explains observed meoscale modulations of biomass.