An analytical solution of the ideal-fluid thermocline

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 pote ntial thickness and the Bernoulli function, and for the unventilated thermo cline the potential thickness is a constant. The solution satisfies the mos t important dynamic constraints-the Sverdrup relation and other boundary co nditions. For any given Ekman pumping field, the surface density that satis fies the a priori specified potential thickness function is calculated as p art 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 thermocli ne mode that has a zero-crossing in the middle of the thermocline, resembli ng the second baroclinic mode defined in the classic stability analysis.