Cross-Gyre Flow
287
below this threshold value, so that the square bracket in (5.2.27) is negative, a
window is possible if (Jh < 0, i.e., if h < H west of¢ = ¢,. This implies that the
flow in the lower layer is northward in layer 3, and deep fluid moves from the
subtropical to the subpolar gyre. Figure 5.2.4 shows the right side of (5.2.22) in
the case when H2/ H is less than the critical value given by (5.2.28). If h/ H
increases above 1, the value of the right side would fall, and no solution of
(5.2.22) would occur. However, if h decreases below H, so that there is
northward flow in the lower layer a window solution is possible between
h/H= 1, and the position of the maximum of the curve at h/H == 0.94 (in this
case r 23 = 1), and thus the critical value given by (5.2.28) is 0.414 while in ¢.e
figure H/H = 0.2.
Thus the existence of the window depends only on the same combination
of factors required to produce an unventilated deep pool in the gyre as discussed in Chapters 3 and 4. However, the direction of the flow entering across
the window instead depends only on parameters reflecting the stratification of
the ocean at the intergyre boundary. The longitudinal extent of the window
depends on the stratification and the wind forcing as described by (5.2.25).
West of the point¢ = ¢2> i.e., the western limit of the window between the
gyres, the potential vorticity contours in layer 3 are still drawn around to reach
the intergyre boundary at 8 = 8o. However, west of this point the Sverdrup
advection is too strong to hold the window open, and information from the
western boundary arrives to turn off the cross-gyre flow. Flow in the subtropical
gyre in the layer 3 is thus still possible in the region west of the streamline forming the western boundary of the current crossing the gyre boundary through the
window. However, it must remain a recirculation within the subtropical gyre, as
indicated in Fig. 5.2.2. One can think of the window as now occupying an
eastern band of what would otherwise be the RhinesNoung pool, reducing that
pool in size and replacing the outer belt of the pool with a stream of water either
entering the subtropical gyre from the north or leaving it on geostrophic contours that have been reshaped by the wind to connect the two gyres.
0.22
Cr vs h2/h
0.18
0.14
0.10
0.80
0.90
1.00
Fig. 5.2.4. Right side of equation (5.2.22) for the case in which H2/ His less than the critical value
given by (5.2.28). Now at h = H the Ross by wave curve decreases with increasing h/ Hand only
northward flow in the window is allowed in the lower layer
287
below this threshold value, so that the square bracket in (5.2.27) is negative, a
window is possible if (Jh < 0, i.e., if h < H west of¢ = ¢,. This implies that the
flow in the lower layer is northward in layer 3, and deep fluid moves from the
subtropical to the subpolar gyre. Figure 5.2.4 shows the right side of (5.2.22) in
the case when H2/ H is less than the critical value given by (5.2.28). If h/ H
increases above 1, the value of the right side would fall, and no solution of
(5.2.22) would occur. However, if h decreases below H, so that there is
northward flow in the lower layer a window solution is possible between
h/H= 1, and the position of the maximum of the curve at h/H == 0.94 (in this
case r 23 = 1), and thus the critical value given by (5.2.28) is 0.414 while in ¢.e
figure H/H = 0.2.
Thus the existence of the window depends only on the same combination
of factors required to produce an unventilated deep pool in the gyre as discussed in Chapters 3 and 4. However, the direction of the flow entering across
the window instead depends only on parameters reflecting the stratification of
the ocean at the intergyre boundary. The longitudinal extent of the window
depends on the stratification and the wind forcing as described by (5.2.25).
West of the point¢ = ¢2> i.e., the western limit of the window between the
gyres, the potential vorticity contours in layer 3 are still drawn around to reach
the intergyre boundary at 8 = 8o. However, west of this point the Sverdrup
advection is too strong to hold the window open, and information from the
western boundary arrives to turn off the cross-gyre flow. Flow in the subtropical
gyre in the layer 3 is thus still possible in the region west of the streamline forming the western boundary of the current crossing the gyre boundary through the
window. However, it must remain a recirculation within the subtropical gyre, as
indicated in Fig. 5.2.2. One can think of the window as now occupying an
eastern band of what would otherwise be the RhinesNoung pool, reducing that
pool in size and replacing the outer belt of the pool with a stream of water either
entering the subtropical gyre from the north or leaving it on geostrophic contours that have been reshaped by the wind to connect the two gyres.
0.22
Cr vs h2/h
0.18
0.14
0.10
0.80
0.90
1.00
Fig. 5.2.4. Right side of equation (5.2.22) for the case in which H2/ His less than the critical value
given by (5.2.28). Now at h = H the Ross by wave curve decreases with increasing h/ Hand only
northward flow in the window is allowed in the lower layer