P. Lionello et J. Pedlosky, The role of a finite density jump at the bottom of the quasi-continuous ventilated thermocline, J PHYS OCEA, 30(2), 2000, pp. 338-351
The ocean thermocline is resolved in a very large number of layers by means
of a recursive relation that extends the LPS model of the ventilated flow
from a small to an arbitrary number of layers. In order to have simplified
dynamics, the basin is semi-infinite in the zonal direction, the thermoclin
e is fully ventilated, and its thickness vanishes at the northern boundary.
In this model, the potential vorticity of each layer is shown to be invers
ely proportional to the Bernoulli function. The hi,oh vertical resolution a
dopted for the thermocline allows the study of the dependence of its motion
on the ratio between the density contrast at the sea surface and the densi
ty step separating the thermocline bottom from the underlying quiescent aby
ss. This ratio controls both the nonlinearity and the baroclinicity of the
solution. The behavior of the solution as this ratio varies from zero (line
ar and barotropic case) to infinity ("fully nonlinear" and baroclinic case)
is described. The singularity that is found in the fully nonlinear case is
discussed.