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.