The evolution of a front in turbulent thermal wind balance. Part 1. Theory

Abstract

Here, we examine the influence of small-scale turbulence on the evolution of fronts in the ocean and atmosphere. Specifically, we consider the evolution of an initially balanced density front subject to an imposed viscosity and diffusivity as a simple analogue for small-scale turbulence. At late times, the dominant balance is found to be the quasisteady turbulent thermal wind balance with time evolution due to an advection–diffusion balance in the buoyancy equation. We use the leading-order balance to determine analytical similarity solutions for the spreading of a front and find that the spreading rate is maximum for an intermediate value of the Ekman number, with the spreading resulting from shear dispersion associated with the cross-front flow and vertical diffusion of density. In response to shear dispersion, the front evolves towards a density profile that is nearly linear in the cross-front coordinate. At the edges of the frontal zone, the density field develops large curvature, and these regions are associated with narrow bands of intense vertical velocity.