Effect of Ridges and Gaps
415
Fig. 7.5.2. Curve ofy(x1, y) as a function ofy. The horizontal line labeled 1J!1 is the constant value of
the streamfunction on the ridge. The stagnation points of the boundary layer flow occur at Yi and
y;
negative and has a single minimum, representing a cyclonic cell that would fill
the basin with an unbroken Stommel-Arons gyre if there were no ridge. The
constant 'P1 is determined by the integral condition (7.5.14), and its value is
indicated by the horizontal line in the figure which intersects the curve of
'P1 (x1, y) at two locations. These correspond to the latitudes Yt and Yi which
are the stagnation points of the flow along the ridge.
In Fig. 7.5.3 the streamline pattern is shown for this ridge system for the
case where:
f
fo
. ( Y)
PH wo = PoH Wo sm n Yn
(7.5.20)
and where the ongm in y has been placed at Ys· The geostrophic
streamfunction in the figure has been scaled with foWoxefP 0 H. The ridge is
placed at x1 = 0.5lxe. For this configuration the value of the streamfunction on
the ridge, given by (7.5.14) is 'P1 :::::! -0.34. This yields two stagnation points at
y"" 0.24 Yn andy"" 0.76 Yn· These points are labeled y! and yf respectively,
and are shown in the figure. The streamline in the interior which corresponds
to the value 'P1 joins the two stagnation points and encloses a region in which
the flow is completely encircled by this streamline and recirculates in a pool
anchored to the eastern side of the ridge as shown in Fig. 7.5.3. Fluid in this
pool does not communicate with the fluid in the western basin but remains in
the recirculating pool driven by the local upwelling into the thermocline. A
small flux, of order (Pxe/ f)t/1 1 enters the pool to replace the fluid entering the
thermocline, but this is negligible within the P-plane quasi-geostrophic
approximation.
In the solution east of the ridge (7.5.5) in this case yields:
415
Fig. 7.5.2. Curve ofy(x1, y) as a function ofy. The horizontal line labeled 1J!1 is the constant value of
the streamfunction on the ridge. The stagnation points of the boundary layer flow occur at Yi and
y;
negative and has a single minimum, representing a cyclonic cell that would fill
the basin with an unbroken Stommel-Arons gyre if there were no ridge. The
constant 'P1 is determined by the integral condition (7.5.14), and its value is
indicated by the horizontal line in the figure which intersects the curve of
'P1 (x1, y) at two locations. These correspond to the latitudes Yt and Yi which
are the stagnation points of the flow along the ridge.
In Fig. 7.5.3 the streamline pattern is shown for this ridge system for the
case where:
f
fo
. ( Y)
PH wo = PoH Wo sm n Yn
(7.5.20)
and where the ongm in y has been placed at Ys· The geostrophic
streamfunction in the figure has been scaled with foWoxefP 0 H. The ridge is
placed at x1 = 0.5lxe. For this configuration the value of the streamfunction on
the ridge, given by (7.5.14) is 'P1 :::::! -0.34. This yields two stagnation points at
y"" 0.24 Yn andy"" 0.76 Yn· These points are labeled y! and yf respectively,
and are shown in the figure. The streamline in the interior which corresponds
to the value 'P1 joins the two stagnation points and encloses a region in which
the flow is completely encircled by this streamline and recirculates in a pool
anchored to the eastern side of the ridge as shown in Fig. 7.5.3. Fluid in this
pool does not communicate with the fluid in the western basin but remains in
the recirculating pool driven by the local upwelling into the thermocline. A
small flux, of order (Pxe/ f)t/1 1 enters the pool to replace the fluid entering the
thermocline, but this is negligible within the P-plane quasi-geostrophic
approximation.
In the solution east of the ridge (7.5.5) in this case yields: