196
Now consider a non-rotating, two-dimensional, viscous model with convective adjustment. Models of this sort make a considerable step in the
direction of realism by forming their own thermocline through advectivediffusive processes and modeling the important nonlinear dependence of
vertical mixing upon vertical density gradient (convection). A version of
this model without salinity effects was used by Winton (1995b). Here we
restore surface temperatures to a half-cosine reference profile, with coefficient P, and apply a half-cosine shaped salt flux pattern with magnitude, F.
Fig.13 shows the result of a series of experiments designed to determine the
maximum freshwater forcing that could be sustained by a steady thermally
direct cell over a range of thermal restoring coefficients. Although, P in
this model is not entirely analogous to P in the two-box model since only
the surface temperature gradient is directly under its influence, it is rather
surprising to see that this model becomes more susceptible to freshwater
forcing with stronger clamping to the reference temperature profile over
most of the range of P. For each experiment we have noted the percentage
reduction in overturning magnitude from F = 0 to F = Fcrit, the point
where the cell breaks down. In the low P range where Fcrit is increasing
with P, there is a substantial reduction indicating a role for advective instability of the type characterizing the two-box model. In the region where
Ferit is decreasing with P, the reduction goes to zero. In this region, another kind of instability must be responsible for the breakdown of steady,
thermally direct overturning. We will argue that this is a convective instability.
One piece of evidence for convective instability comes from applying
a different values of P over the two halves of the basin. When this is
done, it is found that the critical level of freshwater forcing is not sensitive
to the value of P in the warm, "low-latitude", half of the basin. This is
consistent with the time scales involved in the problem. In the low-latitude
half, heat penetrates diffusively through the thermocline. The time scale
for this process is the flushing time by the thermal overturning (Winton,
1995b). This is long compared to the time scales of the processes that
control surface, or equivalently, mixed layer temperature: months for airsea exchange processes to several years for the top of atmosphere radiative
balance. Notice that, starting near mid basin, shallow convective layers are
found; these deepen moving toward the cold end, finally striking the bottom
at the boundary (Fig. 14a). Convection is modeled as an instantaneous
process; so in this convecting region, the heat balance is affected by the
strength of the surface temperature restoring.
Now consider a non-rotating, two-dimensional, viscous model with convective adjustment. Models of this sort make a considerable step in the
direction of realism by forming their own thermocline through advectivediffusive processes and modeling the important nonlinear dependence of
vertical mixing upon vertical density gradient (convection). A version of
this model without salinity effects was used by Winton (1995b). Here we
restore surface temperatures to a half-cosine reference profile, with coefficient P, and apply a half-cosine shaped salt flux pattern with magnitude, F.
Fig.13 shows the result of a series of experiments designed to determine the
maximum freshwater forcing that could be sustained by a steady thermally
direct cell over a range of thermal restoring coefficients. Although, P in
this model is not entirely analogous to P in the two-box model since only
the surface temperature gradient is directly under its influence, it is rather
surprising to see that this model becomes more susceptible to freshwater
forcing with stronger clamping to the reference temperature profile over
most of the range of P. For each experiment we have noted the percentage
reduction in overturning magnitude from F = 0 to F = Fcrit, the point
where the cell breaks down. In the low P range where Fcrit is increasing
with P, there is a substantial reduction indicating a role for advective instability of the type characterizing the two-box model. In the region where
Ferit is decreasing with P, the reduction goes to zero. In this region, another kind of instability must be responsible for the breakdown of steady,
thermally direct overturning. We will argue that this is a convective instability.
One piece of evidence for convective instability comes from applying
a different values of P over the two halves of the basin. When this is
done, it is found that the critical level of freshwater forcing is not sensitive
to the value of P in the warm, "low-latitude", half of the basin. This is
consistent with the time scales involved in the problem. In the low-latitude
half, heat penetrates diffusively through the thermocline. The time scale
for this process is the flushing time by the thermal overturning (Winton,
1995b). This is long compared to the time scales of the processes that
control surface, or equivalently, mixed layer temperature: months for airsea exchange processes to several years for the top of atmosphere radiative
balance. Notice that, starting near mid basin, shallow convective layers are
found; these deepen moving toward the cold end, finally striking the bottom
at the boundary (Fig. 14a). Convection is modeled as an instantaneous
process; so in this convecting region, the heat balance is affected by the
strength of the surface temperature restoring.