An Analytical Solution of the Ideal-Fluid Thermocline

Abstract

An exact analytical solution for the ideal-fluid thermocline is discussed. The solution is calculated from the specified functional relations: for the ventilated thermocline it is a linear functional relation between the potential thickness and the Bernoulli function, and for the unventilated thermocline the potential thickness is a constant. The solution satisfies the most important dynamic constraints?the Sverdrup relation and other boundary conditions. For any given Ekman pumping field, the surface density that satisfies the a priori specified potential thickness function is calculated as part of the solution. Climate variability induced by surface cooling/heating is inferred from the construction of the Green function. It is shown that for the model based on the special functional form discussed in this paper, the cooling-induced anomaly is in the form of the second dynamic thermocline mode that has a zero-crossing in the middle of the thermocline, resembling the second baroclinic mode defined in the classic stability analysis.