An Advective Model of the Ocean Thermocline

A theoretical study is made of the density field and the associated velocity field produced in an unlimited ocean by a prescribed density distribution at the surface. It is assumed that all motions take place under geostrophic and hydrostatic balance, and that the density is simply advected by the motions occurring. The computation is carried out for a spherical earth. The theory gives a depth of penetration of the surface disturbances of the order of 1000 m, if one assumes a relative density variation of the order 10−3 and a characteristic velocity below the boundary layer of the order 1 cm. sec−1. The depth of penetration is proportional to the sine of the latitude. Assuming a stable ocean with a surface density increasing from the equator to the pole the theory gives a meridional distribution of density of the form observed in the real oceans. The associated zonal velocities are westerlies at high latitudes, easterlies near the equator.

To permit a more precise check of the theory by laboratory experiments the corresponding solution is derived for a rotating “dishpan”. The solution is found to be of the same type as the one studied in the spherical case, but it is pointed out that fundamental differences between the spherical and parabolic cases are likely to occur in more general solutions than those studied here.