Frontogenesis in an Advective Mixed-Layer Model

Abstract

Through an analysis of a multi-dimensional extension of the bulk mixed layer model of Kraus and Turner (1967) it is shown how, even under spatially uniform atmospheric conditions, an initially smooth horizontal temperature gradient in the surface mixed layer can still develop into a front. For this to occur, it is essential that the net downward heat flux at the air-water interface be related to the difference between the mixed layer temperature T and an apparent atmospheric temperature TA (Haney, 1971), so that the initial horizontal gradient in T corresponds to a horizontal variation in the surface buoyancy flux. As a result the mixed layer depth also differs from place to place. Depending on the direction of the wind-driven transport, this produces either a steepening or a flattening of the initial temperature profile. A lower bound condition for the initial horizontal advective heat flux is derived in terms of the initial surface heat flux, the stirring by the wind, and the time rate of chance of the apparent atmospheric temperature. If that condition is satisfied, a front develops. If not, then frontogenesis is prevented by the damping effect of the local atmospheric heating. It is shown that the condition can be satisfied on the scales of lakes (or small seas) and in near-equatorial oceanic regions. Mathematically, the physical process can be described by a first-order quasilinear hyperbolic partial differential equation that is solved exactly by the method of characteristics.