Application of the Theory to the Subtropical Gyre
y/L
0.4
0.2
141
Fig. 3.9.1c o~~~~~~~~~~~~~=====::~J -1
-0.5
0
0.5
alpha= 1
x/L
lies within the basin, a region in the northwest corner of the gyre in layer 2 can
be set into motion. The condition (3.9.8) can be rewritten:
(3.9.9)
The left side of (3.9.9) can be recognized as the barotropic zonal velocity at
the point (x" L) if we refer to (3.9.3). The condition that closed geostrophic
contours appear in the gyre is equivalent to the statement (3.9.9) that there
exists a point Xr on the northern boundary of the gyre (where the eastward
barotropic velocity is strongest) such that this barotropic velocity is large
enough to arrest the westward propagating Rossby wave that would otherwise
turn off the flow in layer 2. This is precisely the heuristic result of (3.4.11 ). The
stronger the forcing, the further eastward this point is. For weak forcing the
point is driven westward and outside of the basin, i.e,. west of the western
boundary. The critical point is found at the northern boundary because the
eastward barotropic flow is strongest there, and the Rossby wave is arrested in
its most eastward point there. If there is no position at this latitude where the
Rossby wave can be arrested, there can be no other position where it can
happen in the basin, and layer 2 is at rest. As we see from Fig. 3.9.1, the pool of
closed geostrophic contours is broadest at the gyre's northern boundary.
To find the flow in layer 2 in the pool region which is shielded from the
baroclinic Rossby waves requires a choice for the dissipation parameterization. We follow Young and Rhines (1982) and imagine that the dissipation can
be modeled as a diffusion of potential vorticity. We saw in Section 3.8 that
under the proper conditions this would lead to homogenization of potential
y/L
0.4
0.2
141
Fig. 3.9.1c o~~~~~~~~~~~~~=====::~J -1
-0.5
0
0.5
alpha= 1
x/L
lies within the basin, a region in the northwest corner of the gyre in layer 2 can
be set into motion. The condition (3.9.8) can be rewritten:
(3.9.9)
The left side of (3.9.9) can be recognized as the barotropic zonal velocity at
the point (x" L) if we refer to (3.9.3). The condition that closed geostrophic
contours appear in the gyre is equivalent to the statement (3.9.9) that there
exists a point Xr on the northern boundary of the gyre (where the eastward
barotropic velocity is strongest) such that this barotropic velocity is large
enough to arrest the westward propagating Rossby wave that would otherwise
turn off the flow in layer 2. This is precisely the heuristic result of (3.4.11 ). The
stronger the forcing, the further eastward this point is. For weak forcing the
point is driven westward and outside of the basin, i.e,. west of the western
boundary. The critical point is found at the northern boundary because the
eastward barotropic flow is strongest there, and the Rossby wave is arrested in
its most eastward point there. If there is no position at this latitude where the
Rossby wave can be arrested, there can be no other position where it can
happen in the basin, and layer 2 is at rest. As we see from Fig. 3.9.1, the pool of
closed geostrophic contours is broadest at the gyre's northern boundary.
To find the flow in layer 2 in the pool region which is shielded from the
baroclinic Rossby waves requires a choice for the dissipation parameterization. We follow Young and Rhines (1982) and imagine that the dissipation can
be modeled as a diffusion of potential vorticity. We saw in Section 3.8 that
under the proper conditions this would lead to homogenization of potential