Thermohaline circulation
391
1
4
2
3
Φ
Φ
T
S
b
a
c
d
Figure 16.11. Sketch of the regimes of convective and non-convective equilibria in the box model
in the (ΦT , ΦS) parameter plane. In regime 1, there are convective states, in regime 2 there are
non-convective states, whereas in regime 3 both states are present. In regime 4 no steady states
exist.
-1
-0.8
-0.6
-0.4
-0.2
0
-1
-0.8
-0.6
-0.4
-0.2
0
Φ Φ
Φ
Φ S
S
T
T, S
L 1
L 2
Figure 16.12. Diagram showing the equilibria for the box model (16.12) with ΦT =1.0, q/α =
0.5 and τ/α =2.0 and ΦS as control parameter.
temperature T = α T (T ∗ −T b ) and salinity S = α S (S ∗ −S b ) are plotted versus the
control parameter Φ S . Two saddle node bifurcations (L 1 and L 2 )occuratΦ S =
−5/7 and Φ S = −1/3. These are exactly the values −κ(τ ) and −κ(0) bounding
the regions of convective and non-convective regimes, respectively. Hence, the
high temperature and salinity states are convective and exist for Φ S > −5/7
391
1
4
2
3
Φ
Φ
T
S
b
a
c
d
Figure 16.11. Sketch of the regimes of convective and non-convective equilibria in the box model
in the (ΦT , ΦS) parameter plane. In regime 1, there are convective states, in regime 2 there are
non-convective states, whereas in regime 3 both states are present. In regime 4 no steady states
exist.
-1
-0.8
-0.6
-0.4
-0.2
0
-1
-0.8
-0.6
-0.4
-0.2
0
Φ Φ
Φ
Φ S
S
T
T, S
L 1
L 2
Figure 16.12. Diagram showing the equilibria for the box model (16.12) with ΦT =1.0, q/α =
0.5 and τ/α =2.0 and ΦS as control parameter.
temperature T = α T (T ∗ −T b ) and salinity S = α S (S ∗ −S b ) are plotted versus the
control parameter Φ S . Two saddle node bifurcations (L 1 and L 2 )occuratΦ S =
−5/7 and Φ S = −1/3. These are exactly the values −κ(τ ) and −κ(0) bounding
the regions of convective and non-convective regimes, respectively. Hence, the
high temperature and salinity states are convective and exist for Φ S > −5/7