302
Buoyancy Forced Circulation and Cross-Gyre Flow
region of cooling and is converted to cold water by flowing nearly horizontally
across the steeply sloping interface between the two layers.
The difference in the behavior in the eastern and western regimes can be
traced to the characteristic equations for the pressure fields in the two layers,
i.e., (5.3.15c) and (5.3.22). Since the ratio of the Ekman velocity to the crossisopycnal velocity is a constant, as we step along a characteristic curve the ratio
of the change in upper layer pressure compared to the change in the lower layer
pressure is proportional to:
(5.3.28)
On or near the eastern boundary the ratio of the layer depths is a constant due
to the boundary conditions. Thus the pressure changes in the two layers tend to
advance in synchrony in the eastern region, resulting in aligned isobars and a
thermally direct circulation. It is quite different in the western regime where
each of the layer thicknesses on the western wall varies quite differently with
latitude as fluid exits in the upper layer in the western boundary current. This
results in a spiral of the velocity vector with depth and strong horizontal flow
across the interface between the layers.
Example 2: Subtropical Gyre with Heating
The effect of heating and cooling on the circulation of the subtropical gyre can
be examined in fundamentally the same way as has been done for the subpolar
gyre. There are, however, several interesting dynamical issues which distinguish
the two domains. As we saw in Chapter 4 for the adiabatic model, the circulation in the subtropical gyre contains different subregions of the flow such as
the shadow zone and the ventilated region. The delineation of these zones in
the adiabatic theory depends on the position of critical streamlines which carve
out the various subdomains. When the motion is no longer conservative, the
streamlines lose this privileged function, and we expect it to be the characteristic curves that carry the information to determine the subdomains.
The presence of outcropping presents an apparent difficulty in the characteristic formulation. If there is an outcrop line, say, along the latitude circle
e = e2, the upper layer thickness vanishes there. It also vanishes at this latitude
at the eastern boundary, and if the zonal flow vanishes at the eastern boundary,
the layer thicknesses must be constant there so that h1 is thus zero for all
latitudes along tfJ = tPe· This implies that the Ross by wave speed c, is zero on the
eastern boundary. Certainly Us is also zero there. It would appear from a
superficial examination of (5.3.15a,b) that the characteristics from the eastern
boundary can not enter the basin in the region south of the outcrop line.
This is, however, not the case. Consider the neighborhood of the eastern
boundary where h1 goes to zero. Although both the Sverdrup zonal velocity
Buoyancy Forced Circulation and Cross-Gyre Flow
region of cooling and is converted to cold water by flowing nearly horizontally
across the steeply sloping interface between the two layers.
The difference in the behavior in the eastern and western regimes can be
traced to the characteristic equations for the pressure fields in the two layers,
i.e., (5.3.15c) and (5.3.22). Since the ratio of the Ekman velocity to the crossisopycnal velocity is a constant, as we step along a characteristic curve the ratio
of the change in upper layer pressure compared to the change in the lower layer
pressure is proportional to:
(5.3.28)
On or near the eastern boundary the ratio of the layer depths is a constant due
to the boundary conditions. Thus the pressure changes in the two layers tend to
advance in synchrony in the eastern region, resulting in aligned isobars and a
thermally direct circulation. It is quite different in the western regime where
each of the layer thicknesses on the western wall varies quite differently with
latitude as fluid exits in the upper layer in the western boundary current. This
results in a spiral of the velocity vector with depth and strong horizontal flow
across the interface between the layers.
Example 2: Subtropical Gyre with Heating
The effect of heating and cooling on the circulation of the subtropical gyre can
be examined in fundamentally the same way as has been done for the subpolar
gyre. There are, however, several interesting dynamical issues which distinguish
the two domains. As we saw in Chapter 4 for the adiabatic model, the circulation in the subtropical gyre contains different subregions of the flow such as
the shadow zone and the ventilated region. The delineation of these zones in
the adiabatic theory depends on the position of critical streamlines which carve
out the various subdomains. When the motion is no longer conservative, the
streamlines lose this privileged function, and we expect it to be the characteristic curves that carry the information to determine the subdomains.
The presence of outcropping presents an apparent difficulty in the characteristic formulation. If there is an outcrop line, say, along the latitude circle
e = e2, the upper layer thickness vanishes there. It also vanishes at this latitude
at the eastern boundary, and if the zonal flow vanishes at the eastern boundary,
the layer thicknesses must be constant there so that h1 is thus zero for all
latitudes along tfJ = tPe· This implies that the Ross by wave speed c, is zero on the
eastern boundary. Certainly Us is also zero there. It would appear from a
superficial examination of (5.3.15a,b) that the characteristics from the eastern
boundary can not enter the basin in the region south of the outcrop line.
This is, however, not the case. Consider the neighborhood of the eastern
boundary where h1 goes to zero. Although both the Sverdrup zonal velocity