199
zontal effects that might come into play when the state of the stratification
changes. Note from Fig. 14a that thermal advection is dominantly vertical
at low latitude and horizontal at high latitude. Fig. 14b shows the upward
heat flux with F = 0 for steady states with P = 0.1 and P = 1. In the
P = 1 case the temperature of the convecting layers is effectively pinned at
the overlying reference temperature. Since the reference profile is a halfcosine curve, its meridional derivative goes to zero at y = 1 (the "northern" boundary). Near y = 1, the flow is predominantly meridional, and so
the convergence of the heat transport and the surface heat flux go to zero.
With the smaller surface restoring coefficient, heat is released through the
surface more "frugally", and the water sinks with a temperature above the
coldest reference temperature. This excess heat may be thought of as left
over convecting capacity and these considerations highlight the importance
of accurately modeling the temperature of the deepwater when the issue
of thermohaline stability is being addressed.
Fig. 14c shows the surface heat flux for the P = 1 case with F = 2,
just below the critical level of freshening. The small amount of freshening
is able to dominate the upward heat flux and stratify the water column at
the y = 1 boundary. With slightly larger freshening (F = 3), freshwater
pools at the surface and continually interferes with the sinking branch of
the circulation to the south. The sinking moves to lower latitudes and
ventilates shallower depths as the halo cline expands. This process has
been termed a "halo cline catastrophe". It should be pointed out that
the two-dimensional model, particularly this one with isotropic diffusion,
exaggerates the sensitivity to freshening because of the neglect of horizontal
plane motions that can provide an alternative outlet for freshening aside
from incorporation into deepwater [see Winton and Sarachik (1993) for
a comparison of the sensitivity of similarly formulated two- and threedimensional models].
The sensitivity described above is associated with the flattening of the
reference temperature profile as the y=l boundary is approached. This
might be thought a rather artificial aspect of the forcing. However, it
might also be argued that the thermal boundary condition seen by the
actual ocean flattens near the poles due to the fact that seawater does not
go below freezing and the thermal buoyancy flux associated with a given
heat flux decreases at low temperatures due to the temperature dependence of the thermal expansion coefficient. Beyond the latitude where the
water column, or perhaps a substantial portion thereof, is brought to near
zontal effects that might come into play when the state of the stratification
changes. Note from Fig. 14a that thermal advection is dominantly vertical
at low latitude and horizontal at high latitude. Fig. 14b shows the upward
heat flux with F = 0 for steady states with P = 0.1 and P = 1. In the
P = 1 case the temperature of the convecting layers is effectively pinned at
the overlying reference temperature. Since the reference profile is a halfcosine curve, its meridional derivative goes to zero at y = 1 (the "northern" boundary). Near y = 1, the flow is predominantly meridional, and so
the convergence of the heat transport and the surface heat flux go to zero.
With the smaller surface restoring coefficient, heat is released through the
surface more "frugally", and the water sinks with a temperature above the
coldest reference temperature. This excess heat may be thought of as left
over convecting capacity and these considerations highlight the importance
of accurately modeling the temperature of the deepwater when the issue
of thermohaline stability is being addressed.
Fig. 14c shows the surface heat flux for the P = 1 case with F = 2,
just below the critical level of freshening. The small amount of freshening
is able to dominate the upward heat flux and stratify the water column at
the y = 1 boundary. With slightly larger freshening (F = 3), freshwater
pools at the surface and continually interferes with the sinking branch of
the circulation to the south. The sinking moves to lower latitudes and
ventilates shallower depths as the halo cline expands. This process has
been termed a "halo cline catastrophe". It should be pointed out that
the two-dimensional model, particularly this one with isotropic diffusion,
exaggerates the sensitivity to freshening because of the neglect of horizontal
plane motions that can provide an alternative outlet for freshening aside
from incorporation into deepwater [see Winton and Sarachik (1993) for
a comparison of the sensitivity of similarly formulated two- and threedimensional models].
The sensitivity described above is associated with the flattening of the
reference temperature profile as the y=l boundary is approached. This
might be thought a rather artificial aspect of the forcing. However, it
might also be argued that the thermal boundary condition seen by the
actual ocean flattens near the poles due to the fact that seawater does not
go below freezing and the thermal buoyancy flux associated with a given
heat flux decreases at low temperatures due to the temperature dependence of the thermal expansion coefficient. Beyond the latitude where the
water column, or perhaps a substantial portion thereof, is brought to near