332
Equatorial Dynamics of the Thermocline: The Equatorial Undercurrent
This solution is not presented as a realistic model of the equatorial zone,
but it does contain all the elements of the verbal argument that has been
proposed above as an "explanation" of the undercurrent. It fails to produce an
undercurrent because at every level in z the eastward pressure force is balanced
by a frictional stress, and there is no eastward acceleration. The value of the
solution in the current discussion is its demonstration that it is the vertical
distribution of pressure that matters. In particular, what is required for the
undercurrent is the penetration to depths below the surface of an unbalanced
pressure gradient available to drive an eastward flow.
An "explanation" for the undercurrent can not logically start with an
unbalanced pressure force as if it were an externally imposed force. It is part of
the solution to be determined. Appealing to an unbalanced pressure force at
the equator to explain the EUC would be no different than an "explanation" of
the subtropical gyre which presents it as a response to a high pressure center in
the ocean produced by the wind. The theory must, first of all, explain the
distribution of the pressure field, and then the velocity field follows. Indeed, in
midlatitudes the theory for the circulation is a theory for the height, or pressure
fields. Such a theory in midlatitudes comes from uniting the geostrophic relation with potential vorticity dynamics. An analogous development must
occur at the equator in order to derive the pressure field that is consistent with
the undercurrent although at the equator the geostrophic approximation is no
longer relevant.
An illuminating discussion of the way in which potential vorticity dynamics could explain the undercurrent was first presented by Fofonoff and
Montgomery (1955). They suggested that columns of fluid in subsurface layers
approach the equator to replace flow driven away from the equator in the
surface mixed layer, and that the fluid approaching the equator conserves its
potential vorticity. If a fluid column starts its journey to the equator at a
latitude 80 where relative vorticity is unimportant, for each fluid column:
f+(
fo
h
ho
(6.2.11)
where the 0 subscript refers to variables evaluated at 8 = 80 . In the region of
the undercurrent the zonal velocity is many times greater than the meridional
velocity, and the latitude scale is very small compared to the zonal scale, so that
momentarily using Cartesian coordinates:
(6.2.12)
and we will also define the parameter yo by the relation f o = f3 Yo.
Although it is certainly not actually true for fluid columns approaching the
equator in the ocean, Fofonoff and Montgomery examined the simple case in
which the layer thickness is constant for a fluid column along its path to the
equator so that h = h 0 • Then (6.2.12) reduces to:
Equatorial Dynamics of the Thermocline: The Equatorial Undercurrent
This solution is not presented as a realistic model of the equatorial zone,
but it does contain all the elements of the verbal argument that has been
proposed above as an "explanation" of the undercurrent. It fails to produce an
undercurrent because at every level in z the eastward pressure force is balanced
by a frictional stress, and there is no eastward acceleration. The value of the
solution in the current discussion is its demonstration that it is the vertical
distribution of pressure that matters. In particular, what is required for the
undercurrent is the penetration to depths below the surface of an unbalanced
pressure gradient available to drive an eastward flow.
An "explanation" for the undercurrent can not logically start with an
unbalanced pressure force as if it were an externally imposed force. It is part of
the solution to be determined. Appealing to an unbalanced pressure force at
the equator to explain the EUC would be no different than an "explanation" of
the subtropical gyre which presents it as a response to a high pressure center in
the ocean produced by the wind. The theory must, first of all, explain the
distribution of the pressure field, and then the velocity field follows. Indeed, in
midlatitudes the theory for the circulation is a theory for the height, or pressure
fields. Such a theory in midlatitudes comes from uniting the geostrophic relation with potential vorticity dynamics. An analogous development must
occur at the equator in order to derive the pressure field that is consistent with
the undercurrent although at the equator the geostrophic approximation is no
longer relevant.
An illuminating discussion of the way in which potential vorticity dynamics could explain the undercurrent was first presented by Fofonoff and
Montgomery (1955). They suggested that columns of fluid in subsurface layers
approach the equator to replace flow driven away from the equator in the
surface mixed layer, and that the fluid approaching the equator conserves its
potential vorticity. If a fluid column starts its journey to the equator at a
latitude 80 where relative vorticity is unimportant, for each fluid column:
f+(
fo
h
ho
(6.2.11)
where the 0 subscript refers to variables evaluated at 8 = 80 . In the region of
the undercurrent the zonal velocity is many times greater than the meridional
velocity, and the latitude scale is very small compared to the zonal scale, so that
momentarily using Cartesian coordinates:
(6.2.12)
and we will also define the parameter yo by the relation f o = f3 Yo.
Although it is certainly not actually true for fluid columns approaching the
equator in the ocean, Fofonoff and Montgomery examined the simple case in
which the layer thickness is constant for a fluid column along its path to the
equator so that h = h 0 • Then (6.2.12) reduces to: