A one-dimensional model of the seasonal thermocline: II. The general theory and its consequences

TLDR

The authors develop a general theory of thermocline layer formation driven by surface processes, extending the framework of their preceding paper. The theory incorporates depth heating, surface cooling, wind‑induced stirring, and arbitrary heating patterns, and yields an analytic solution for the case studied in paper I. The model reproduces realistic layer depths from measured heating rates, links surface stress to turbulent kinetic energy, shows depth heating can rival wind stirring, and indicates winter surface cooling dominates layer deepening.

Abstract

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.