20
Sverdrup Theory
interior geostrophic transport, calculated from hydrographic data, for the
region above the ao = 27.4 density surface (at about 900 min depth) with the
Sverdrup transport. The agreement is quite good in the eastern basin, i.e., east
of 55°W, but the calculated transport is spatially quite variable to the west of
that longitude. Only an extrapolation of the trend of the geostrophic transport
yields the 30 Sverdrups that would balance the Florida Current transport and
match the calculation of Sverdrup transport. The issue of this extrapolation
and the question of whether the wind-driven Sverdrup transport is sufficient to
explain the observed transports has led to considerable controversy. If only the
region east of 55°W is used as a reliable region for the calculation of the winddriven circulation by the Sverdrup theory, the total transport that results is
only about 17 Sverdrups, much less than the 30 Sverdrups needed. Wunsch and
Roemmich (1985) have suggested, partly as a consequence of this imbalance,
that the evidence for the agreement between the geostrophic wind-driven
transport and the Sverdrup transport is fundamentally lacking. Schmitz et al.
(1992) and Schmitz and McCartney (1993) have made an alternative suggestion
in which only 17 Sverdrups of the Florida Current are wind driven while 13
Sverdrups flow northward in the current in compensation for a deep southward
flow in the interior driven by deep water formation in the northern North
Atlantic. Thus they suggest that actually only 17 Sverdrups need be acounted
for by the Sverdrup transport and consider this evidence of the validity of the
Sverdrup balance. However, unless the southward flowing transport of 13
Sverdrups occurs in a deep western boundary layer, east of the Florida current
but exempt from Sverdrup dynamics because it forms part of the general western
boundary current system, the total interior transport in the interior would still
have to account for 30 sverdrups, in agreement with the direct calculation using
(1.2.22).
The total circulation can be driven by both wind stress and heating and
cooling at the surface (or within the fluid). The virtue of the Sverdrup balance
is that, if it is true, it tells us that the net vertically averaged transport must be
due only to the wind stress curl, and that any other part of the motion must
have a zero vertical average. Unless the total flow vanishes below a certain
depth, it is problematic to attempt to apply the Sverdrup relation to only a
portion of the water column in the belief that it will capture only the winddriven portion of the flow. Figure 1.4.2 shows a schematic of the problem. On
the left is a schematic presentation of the velocity distribution in the interior.
The upper fifth of the water column possesses a strong southward flow, and
beneath it is a fairly weak flow which, however, distributed over the water
column, has about the same transport. We can consider the flow as made up, as
shown on the right of the figure, of a part that has a net transport (and is here
arbitrarily limited to the upper part of the water column) and another part
which is a purely internal mode, i.e., a part that has no net- transport. If we
attempt to identify the Sverdrup relation with the transport in the upper part of
the water column, as shown on the left, we would seriously underestimate the
transport. The Sverdrup balance should apply to the whole column and would
Sverdrup Theory
interior geostrophic transport, calculated from hydrographic data, for the
region above the ao = 27.4 density surface (at about 900 min depth) with the
Sverdrup transport. The agreement is quite good in the eastern basin, i.e., east
of 55°W, but the calculated transport is spatially quite variable to the west of
that longitude. Only an extrapolation of the trend of the geostrophic transport
yields the 30 Sverdrups that would balance the Florida Current transport and
match the calculation of Sverdrup transport. The issue of this extrapolation
and the question of whether the wind-driven Sverdrup transport is sufficient to
explain the observed transports has led to considerable controversy. If only the
region east of 55°W is used as a reliable region for the calculation of the winddriven circulation by the Sverdrup theory, the total transport that results is
only about 17 Sverdrups, much less than the 30 Sverdrups needed. Wunsch and
Roemmich (1985) have suggested, partly as a consequence of this imbalance,
that the evidence for the agreement between the geostrophic wind-driven
transport and the Sverdrup transport is fundamentally lacking. Schmitz et al.
(1992) and Schmitz and McCartney (1993) have made an alternative suggestion
in which only 17 Sverdrups of the Florida Current are wind driven while 13
Sverdrups flow northward in the current in compensation for a deep southward
flow in the interior driven by deep water formation in the northern North
Atlantic. Thus they suggest that actually only 17 Sverdrups need be acounted
for by the Sverdrup transport and consider this evidence of the validity of the
Sverdrup balance. However, unless the southward flowing transport of 13
Sverdrups occurs in a deep western boundary layer, east of the Florida current
but exempt from Sverdrup dynamics because it forms part of the general western
boundary current system, the total interior transport in the interior would still
have to account for 30 sverdrups, in agreement with the direct calculation using
(1.2.22).
The total circulation can be driven by both wind stress and heating and
cooling at the surface (or within the fluid). The virtue of the Sverdrup balance
is that, if it is true, it tells us that the net vertically averaged transport must be
due only to the wind stress curl, and that any other part of the motion must
have a zero vertical average. Unless the total flow vanishes below a certain
depth, it is problematic to attempt to apply the Sverdrup relation to only a
portion of the water column in the belief that it will capture only the winddriven portion of the flow. Figure 1.4.2 shows a schematic of the problem. On
the left is a schematic presentation of the velocity distribution in the interior.
The upper fifth of the water column possesses a strong southward flow, and
beneath it is a fairly weak flow which, however, distributed over the water
column, has about the same transport. We can consider the flow as made up, as
shown on the right of the figure, of a part that has a net transport (and is here
arbitrarily limited to the upper part of the water column) and another part
which is a purely internal mode, i.e., a part that has no net- transport. If we
attempt to identify the Sverdrup relation with the transport in the upper part of
the water column, as shown on the left, we would seriously underestimate the
transport. The Sverdrup balance should apply to the whole column and would