444
Abyssal Circulation
(7.7.45)
and fo is a characteristic value of the Coriolis parameter in the basin (Io- 4 s- 1 )
while L = Xe - xw, is the width of the basin. In terms of oc:
(7.7.46)
In their calculations Edwards and Pedlosky chose rx = 0.0 1.
Note that the Rossby modes corresponding to higher n are trapped near
the eastern boundary, and therefore the baroclinic modes with low n will
dominate in the western basin. With rx = 0.01 the gravest modes reach across
the basin with little damping.
Figure 7.7.2 shows the meridional velocity in the interior solution driven
by a source distribution, S(z), shown in panel a. S(z) has the form:
(7.7.47)
so that the fluid entering the basin enters at middepth in the abyss in the
perimeter average and contains Fourier harmonic content in only the zero and
second Fourier modes. Panel b shows the meridional velocity profiles at nine
zonal locations on the line y = 0.5L. At each location a solid vertical line
represents the zero line for v. The origin of the x coordinate, corresponding to
xw is placed at x = 0 while xis scaled with Lin the figure. In the example shown
in panel b the upwelling velocity is spatially uniform, and we can see that the
result of (7.7.43) obtains. The vertical structure of the meridional velocity is
precisely the same as that of the source with a maximum of v at middepth. The
scale of the velocity in the figure is fKL/fJH where K, in (7.7.44), is chosen to
satisfy the overall mass balance (7.7.40). The only structural reflection of the
Rossby wave dynamics is the slight decay in the amplitude of the response in
the west with respect to the eastern basin. In panel c there is instead a
substantial variation of the upwelling with x such that sL = 2. Now the
meridional velocity profiles are no longer similar to the source structure.
Instead there is a progression of the structure from east to west. In the east,
where there is strong upwelling, the meridional velocity is strongly positive
near the surface, reflecting the vortex tube stretching there. There is a minimum
at z ~ H /4 corresponding to the decay of that stretching. At middepth the
effect of the source again becomes important, and the meridional velocity
shows a secondary maximum. In the west the meridional velocity changes sign
in the upper part of the water column, and the flow is directed equatorward.
Since the signal of the upward vertical velocity produced in the east propagates
westward, in the west there is a positive w in the body of the fluid. However,
since w is very small at the upper boundary of the abyss due to the exponential
decay of w0 , with increasing distance westward, the vertical velocity must
Abyssal Circulation
(7.7.45)
and fo is a characteristic value of the Coriolis parameter in the basin (Io- 4 s- 1 )
while L = Xe - xw, is the width of the basin. In terms of oc:
(7.7.46)
In their calculations Edwards and Pedlosky chose rx = 0.0 1.
Note that the Rossby modes corresponding to higher n are trapped near
the eastern boundary, and therefore the baroclinic modes with low n will
dominate in the western basin. With rx = 0.01 the gravest modes reach across
the basin with little damping.
Figure 7.7.2 shows the meridional velocity in the interior solution driven
by a source distribution, S(z), shown in panel a. S(z) has the form:
(7.7.47)
so that the fluid entering the basin enters at middepth in the abyss in the
perimeter average and contains Fourier harmonic content in only the zero and
second Fourier modes. Panel b shows the meridional velocity profiles at nine
zonal locations on the line y = 0.5L. At each location a solid vertical line
represents the zero line for v. The origin of the x coordinate, corresponding to
xw is placed at x = 0 while xis scaled with Lin the figure. In the example shown
in panel b the upwelling velocity is spatially uniform, and we can see that the
result of (7.7.43) obtains. The vertical structure of the meridional velocity is
precisely the same as that of the source with a maximum of v at middepth. The
scale of the velocity in the figure is fKL/fJH where K, in (7.7.44), is chosen to
satisfy the overall mass balance (7.7.40). The only structural reflection of the
Rossby wave dynamics is the slight decay in the amplitude of the response in
the west with respect to the eastern basin. In panel c there is instead a
substantial variation of the upwelling with x such that sL = 2. Now the
meridional velocity profiles are no longer similar to the source structure.
Instead there is a progression of the structure from east to west. In the east,
where there is strong upwelling, the meridional velocity is strongly positive
near the surface, reflecting the vortex tube stretching there. There is a minimum
at z ~ H /4 corresponding to the decay of that stretching. At middepth the
effect of the source again becomes important, and the meridional velocity
shows a secondary maximum. In the west the meridional velocity changes sign
in the upper part of the water column, and the flow is directed equatorward.
Since the signal of the upward vertical velocity produced in the east propagates
westward, in the west there is a positive w in the body of the fluid. However,
since w is very small at the upper boundary of the abyss due to the exponential
decay of w0 , with increasing distance westward, the vertical velocity must