Numerical calculations of coastal flow with turbulent dynamics

Abstract

A two-dimensional numerical model of coastal flow, in which the eddy fluxes are computed by a second-order turbulence model, has been developed. The behaviour of the inertial oscillations due to an impulsive start is in excellent agreement with the analytical solution of Kundu et al. ( Deep-Sea Research, 30, 1059–1082, 1983). Much of the inertial energy gain in the deep ocean is due to the downward leakage from the coast-surface corner and is accompanied by an upward phase propagation. The low-frequency upwelling solutions develop gravitationally unstable regions in the surface layer, even in the presence of realistic surface heating. But the thickness of the surface layer without surface cooling is never very large, so the analytical models driven by a sink at the coast-surface corner give realistic subsurface solutions. The upwelling solutions generate flow reversal across a strong thermocline, but no ‘closed’ double cells. Frictional turning, as suggested by several workers, is responsible for the flow reversal. These open double cell persist in the presence of surface heating but not in the presence of an alongshore pressure gradient, p γ = τ γ ( maximum depth) . The imposition of p γ creates a poleward undercurrent on a flat shelf but not on a sloping shelf. The alongshore jet moves offshore due to the nonlinear advection of the thermocline, so that the width of the jet is larger than the Rossby radius. An approximate expression has been derived for predicting the offshore frontal location; the numerical calculation is in fair agreement with it.