Thermally Driven Circulations in Small Oceanic Basins*
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A linear, steady model of the circulation of a small (f plane) oceanic basin driven by heating or cooling at the surface is considered in order to examine the partition of upwelling (heating) or downwelling (cooling) between the basin’s interior and its boundary layers on the sidewall in which frictional dissipation and lateral temperature diffusion are dominant. The basin is rectangular in plan form. On three of its lateral sides the basin is insulated to heat exchange; on the fourth side the heat added at the surface is shown to be removed through a thin sublayer that also closes the mass balance. The temperature is linearized about a basic linear stratification. The analytical solution shows that in the case of heating (cooling) in the basin interior, most of the resulting upwelling (downwelling) near the upper surface actually occurs in narrow boundary layers, whose width is on the order of the deformation radius, rather than in the interior directly. This nonintuitive result is consistent with numerical calculations recently performed by Spall and suggests the distribution of vertical motion between interior and boundary layers is a robust one that is not dependent on particular parameterizations of eddy fluxes of heat.