The distribution of the geostrophic flow in a stratified surface layer

We consider the drainage of a low-density surface layer from a semi-enclosed deep basin. The flow is geostrophically controlled and occurs in a frontal region where the isopycnals bend upwards to meet the surface. A useful fact for modellers is that the total volume flow in the frontal region is completely determined from the stratification inside the region covered by the surface layer. In this paper, we will discuss how the geostrophic flow is divided between different parts of the surface layer. Such information is needed for the calculation of the flow of heat, salt and chemical constituents that are not well mixed within the surface layer. For this purpose, the structure of the front has to be considered. A general formula for the distribution of the flow with respect to density is derived, and some useful qualitative properties are demonstrated which may be helpful for modelling purposes. The distribution of the flow depends first on the density stratification of the undisturbed surface layer inside the basin. Secondly, it depends on how the separation of the isopycnals vary through the front. If, e.g. the isopycnals converge as they reach the surface, the flow of the uppermost part of the surface layer is favoured. The distribution of the flow, however, does not depend on the width of the front. Nor does it depend on the shape of the isopycnals as long as the vertical distance between the isopycnals does not vary through the front. Assuming a standard, or close to standard, behaviour of the front, we derive certain simplified formulas for the calculation of the distribution of the flow with density.