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A theory of the layer formation due to surface processes is presented, which is more general than that used in the preceding paper I. Convection due to heating at depth and cooling at the surface is included, as well as the mechanical stirring due to wind action. The theory is applicable to arbitrary forms of heating, including intermittent or continuous processes, and could be used to investigate diurnal as well as seasonal effects. A detailed application is made to the case treated approximately in I, for which a solution is now obtained in analytic form. The results obtained allow a quantitative, as well as qualitative, comparison with the ocean. It is found that reasonable layer depths are predicted using measured heating rates, and a value of the turbulent kinetic energy input to the water deduced from the mean surface stress. The effects of heating at depth can be comparable with wind stirring, even when the temperature of the upper layer is increasing. During the winter, convection due to surface cooling dominates the processes which deepen the layer.
Kraus et al. (Sun,) studied this question.