343
.
2 So
S = --'YT - 21q1S.
cw D
(28)
The coupled model has been reduced to two prognostic equations, (21) and
(28), for the meridional temperature and salinity differences, respectively.
Inserting the hydraulic flow law, eq. (5), gives
T = >.(TE - T) - 2klaT - {3SIT,
(29)
S = c~ t'YT - 2klaT - {3SIS.
(30)
Note that eq. (30) for the salinity contrast is homogeneous; the meridional salinity gradient is forced by the temperature gradient, which itself
is maintained by solar radiation and eroded by longwave radiation and
meridional atmospheric transports [implicit in the definitions for TE and
>., eqs. (18) and (20), respectively], and by oceanic transports. The heat
and salt budgets are coupled not only through the oceanic flow, q, but also
through the temperature-driven freshwater flux.
2.4 Equilibrium solutions
The structure of the equilibrium solutions is best displayed graphically.
Fig. 2 shows the T -8 phase space between the origin and a little beyond
{3S = aTE, aT = aTE, for the choice of parameters of Table 1. The main
diagonal (dashed line) marks {3S = aT where the influences oftemperature
and salinity gradients on density gradients exactly cancel, and there is no
flow (q = 0). To the left of the diagonal, the flow is temperature dominated
(thermally direct), with near-surface flow toward high latitudes. The heavy
and thin solid curves represent, respectively, the equations S = 0 and
T = O. The curves intersect at the solution points; solutions A and C
are stable to infinitesimal perturbations, while the other is unstable. The
equilibrium curves are now discussed for q > O.
The shape of the temperature equilibrium curve, which is not a straight
line, is readily understood as follows. It meets the main diagonal at
(aTE, aTE) where the flow vanishes; hence, T = Tg Generally, a smaller
salinity gradient causes stronger flow, which in turn leads to a stronger
reduction of the temperature gradient. Hence, T deviates more from TE
along the T = 0 curve as one moves to the left in Fig. 2. For the parameters used here, the ocean circulation can further reduce the meridional
temperature gradient by up to 10 c e.
.
2 So
S = --'YT - 21q1S.
cw D
(28)
The coupled model has been reduced to two prognostic equations, (21) and
(28), for the meridional temperature and salinity differences, respectively.
Inserting the hydraulic flow law, eq. (5), gives
T = >.(TE - T) - 2klaT - {3SIT,
(29)
S = c~ t'YT - 2klaT - {3SIS.
(30)
Note that eq. (30) for the salinity contrast is homogeneous; the meridional salinity gradient is forced by the temperature gradient, which itself
is maintained by solar radiation and eroded by longwave radiation and
meridional atmospheric transports [implicit in the definitions for TE and
>., eqs. (18) and (20), respectively], and by oceanic transports. The heat
and salt budgets are coupled not only through the oceanic flow, q, but also
through the temperature-driven freshwater flux.
2.4 Equilibrium solutions
The structure of the equilibrium solutions is best displayed graphically.
Fig. 2 shows the T -8 phase space between the origin and a little beyond
{3S = aTE, aT = aTE, for the choice of parameters of Table 1. The main
diagonal (dashed line) marks {3S = aT where the influences oftemperature
and salinity gradients on density gradients exactly cancel, and there is no
flow (q = 0). To the left of the diagonal, the flow is temperature dominated
(thermally direct), with near-surface flow toward high latitudes. The heavy
and thin solid curves represent, respectively, the equations S = 0 and
T = O. The curves intersect at the solution points; solutions A and C
are stable to infinitesimal perturbations, while the other is unstable. The
equilibrium curves are now discussed for q > O.
The shape of the temperature equilibrium curve, which is not a straight
line, is readily understood as follows. It meets the main diagonal at
(aTE, aTE) where the flow vanishes; hence, T = Tg Generally, a smaller
salinity gradient causes stronger flow, which in turn leads to a stronger
reduction of the temperature gradient. Hence, T deviates more from TE
along the T = 0 curve as one moves to the left in Fig. 2. For the parameters used here, the ocean circulation can further reduce the meridional
temperature gradient by up to 10 c e.