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circulation associated with a warm pool. It should be noted that this is
a consistent picture with the advective and convective mechanism (Yin
and Sarachik, 1995), in which at the weak phase of convection, there is an
anomalous warm water, anomalous high overturning, and anomalous high
surface pressure related to anomalous surface divergence, so an anticyclonic
horizontal circulation.
7 Sudden Transitions
Perhaps the simplest model of the counteracting effects of thermal and
haline forcing on the control of the buoyant overturning is the Stommel
two-box model (Stommel, 1961; Marotzke, 1989). Here we use a variant
of this model that, after non-dimensionalizing, has two free parameters: F,
the magnitude of the salt flux from the high-latitude to the low latitude
box, and P, a coefficient for restoring the thermal difference between the
boxes to a reference value (Fig. 12a). This model is identical to that of
Marotzke except that we allow the temperature difference to deviate from
its reference value. The equations for the differences in salinity, 6.S, and
temperature, b.T, between the low and high latitude boxes are:
db.S
dt = -2116.T - 6.SII . 6.S + 2F
and
d6.T
dt = -2116.T - 6.SII· 6.T + P(l- 6.T).
Fig. 12b shows the magnitude of the overturning, 6.T - 6.S, normalized
by its magnitude with the same thermal restoring, P, but with no freshwater forcing (F=O) in the region of the parameter space with a stable, thermally dominated equilibrium. The portion of the solution space without
such an equilibrium is shaded. Two aspects of this figure are noteworthy:
(1) With stronger thermal restoring, more freshening can be sustained by a
thermally dominated equilibrium; (2) A substantial reduction of the overturning (more than 40%) occurs before the thermally dominated solution
becomes untenable. Both of these properties are evidence of an advective instability: the salinity gradient retards the overturning, increasing
the influence of the freshwater flux boundary condition relative to internal
mixing, thereby further increasing the salinity gradient. Thus the advective
instability works by countering the effect of the thermal torque upon the
overturning. With stronger thermal restoring, a larger freshwater flux is
required to retard the overturning and obtain significant positive feedback
from the salinity boundary condition.
circulation associated with a warm pool. It should be noted that this is
a consistent picture with the advective and convective mechanism (Yin
and Sarachik, 1995), in which at the weak phase of convection, there is an
anomalous warm water, anomalous high overturning, and anomalous high
surface pressure related to anomalous surface divergence, so an anticyclonic
horizontal circulation.
7 Sudden Transitions
Perhaps the simplest model of the counteracting effects of thermal and
haline forcing on the control of the buoyant overturning is the Stommel
two-box model (Stommel, 1961; Marotzke, 1989). Here we use a variant
of this model that, after non-dimensionalizing, has two free parameters: F,
the magnitude of the salt flux from the high-latitude to the low latitude
box, and P, a coefficient for restoring the thermal difference between the
boxes to a reference value (Fig. 12a). This model is identical to that of
Marotzke except that we allow the temperature difference to deviate from
its reference value. The equations for the differences in salinity, 6.S, and
temperature, b.T, between the low and high latitude boxes are:
db.S
dt = -2116.T - 6.SII . 6.S + 2F
and
d6.T
dt = -2116.T - 6.SII· 6.T + P(l- 6.T).
Fig. 12b shows the magnitude of the overturning, 6.T - 6.S, normalized
by its magnitude with the same thermal restoring, P, but with no freshwater forcing (F=O) in the region of the parameter space with a stable, thermally dominated equilibrium. The portion of the solution space without
such an equilibrium is shaded. Two aspects of this figure are noteworthy:
(1) With stronger thermal restoring, more freshening can be sustained by a
thermally dominated equilibrium; (2) A substantial reduction of the overturning (more than 40%) occurs before the thermally dominated solution
becomes untenable. Both of these properties are evidence of an advective instability: the salinity gradient retards the overturning, increasing
the influence of the freshwater flux boundary condition relative to internal
mixing, thereby further increasing the salinity gradient. Thus the advective
instability works by countering the effect of the thermal torque upon the
overturning. With stronger thermal restoring, a larger freshwater flux is
required to retard the overturning and obtain significant positive feedback
from the salinity boundary condition.