Dynamical aspects of shallow sea fronts

Abstract

We examine the role of internal friction in the evolution of a two-dimensional front in a rotating stratified fluid. For a two-layer fluid with interfacial friction the depth of the frontal interface satisfies a diffusion equation with respect to time and the cross-frontal coordinate. Similarity solutions are used to compare the behaviour of the front for linear and quadratic interfacial friction laws. For a continuously stratified front a simple formula is derived for the cross-frontal flow induced by friction, parametrized in terms of an eddy viscosity coefficient Av, provided that the Rossby and Ekman numbers are small. Outside surface and bottom Ekman layers the deptht) of an isopycnal with density p satisfies the diffusion equation z t — [(A 1 2/ / 2) where are the Väisälä and Coriolis frequencies, x is the cross-frontal coordinate and t is time. The consequences of this for the evolution and maintenance of a front are discussed. The circulation in tidal mixing fronts is examined, with results being presented for a semi-analytic diagnostic model, which is fitted to two particular continental shelf fronts. A prominent feature is a two-cell circulation pattern in the plane normal to the front. A variety of cross-frontal transfer mechanisms are discussed, with order-of-magnitude comparisons of their importance being made. Transfer by the mean flow appears to be more important than either shear flow dispersion or the flux associated with baroclinic eddies, but the results are sensitive to the parametrization of vertical mixing of momentum.