Quasi-Geostrophic Model with Continuous Stratification
155
1.0
+
1
0.8
+
t
I
++
0.6
++++
++
+
+
+
+
0.4
+
+
+
+
0.2
Fig. 3.10.5c
0 0
0.2
0.4
0.6
0.8
1.0
at each depth the lateral extent of the pool varies becoming more restricted
with depth. Figure 3.10.5 shows a sequence of streamline patterns. Panel a
shows the circulation at the surface. Note that it covers the entire basin. This
can be anticipated from (3.9.5) in the limit where the layer thicknesses, and
thus H, go to zero. Although the pool covers the basin, it is infinitesimally thin
on the eastern boundary and only skims the surface of the fluid. At greater
depth where the bowl has a finite thickness the domain of motion becomes
restricted to the familiar northwest pool, as shown in Fig. 3.10.5b, which is at
zjd = -1. At even greater depth the pool shaped zone of moving fluid is even
more restricted as in panel c, in which the circulation at z = - 2d is shown and
is nearly indistinguishable in structure from the predictions of the layer model
(Fig. 3.9.2b) even with the very low resolution 2! layer model.
The disturbed density field can be found from (3.10.19). Panel a of
Fig. 3.10.6 shows the density surface in a meridional cross section and panel b
a zonal cross section. Each case uses the parameter setting PL/ fo = 0.3.
Careful inspection of panel a shows the slight spreading of the isopycnals for
increasing y to offset the increase in f so as to keep the potential vorticity
constant. As the bowl rises to the surface at x = Xe, the isopycnals outside the
bowl become flat on the eastern boundary except for the near surface
isopycnals that form a wedge near x = Xe and z = 0. In fact at z = 0 the density
anomaly is proportional to:
8t{!
[
] 1/3 (
) 1/3
2/3
Bz (x, y, 0) = 6(xe- x)
- WE(Y)
(1 - y) .
(3.10.26)
Although the density is finite on the eastern boundary, its derivative with
respect to x is not. Strong meridional velocities are predicted by the model since
the pool must carry the nonzero southward Sverdrup transport at x = Xe in a
155
1.0
+
1
0.8
+
t
I
++
0.6
++++
++
+
+
+
+
0.4
+
+
+
+
0.2
Fig. 3.10.5c
0 0
0.2
0.4
0.6
0.8
1.0
at each depth the lateral extent of the pool varies becoming more restricted
with depth. Figure 3.10.5 shows a sequence of streamline patterns. Panel a
shows the circulation at the surface. Note that it covers the entire basin. This
can be anticipated from (3.9.5) in the limit where the layer thicknesses, and
thus H, go to zero. Although the pool covers the basin, it is infinitesimally thin
on the eastern boundary and only skims the surface of the fluid. At greater
depth where the bowl has a finite thickness the domain of motion becomes
restricted to the familiar northwest pool, as shown in Fig. 3.10.5b, which is at
zjd = -1. At even greater depth the pool shaped zone of moving fluid is even
more restricted as in panel c, in which the circulation at z = - 2d is shown and
is nearly indistinguishable in structure from the predictions of the layer model
(Fig. 3.9.2b) even with the very low resolution 2! layer model.
The disturbed density field can be found from (3.10.19). Panel a of
Fig. 3.10.6 shows the density surface in a meridional cross section and panel b
a zonal cross section. Each case uses the parameter setting PL/ fo = 0.3.
Careful inspection of panel a shows the slight spreading of the isopycnals for
increasing y to offset the increase in f so as to keep the potential vorticity
constant. As the bowl rises to the surface at x = Xe, the isopycnals outside the
bowl become flat on the eastern boundary except for the near surface
isopycnals that form a wedge near x = Xe and z = 0. In fact at z = 0 the density
anomaly is proportional to:
8t{!
[
] 1/3 (
) 1/3
2/3
Bz (x, y, 0) = 6(xe- x)
- WE(Y)
(1 - y) .
(3.10.26)
Although the density is finite on the eastern boundary, its derivative with
respect to x is not. Strong meridional velocities are predicted by the model since
the pool must carry the nonzero southward Sverdrup transport at x = Xe in a