On the Validity of Sverdrup Theory
21
=
+
Fig. 1.4.2. Schematic presentation of the way in which the observed distribution of transport with
depth can be considered a sum of a net component plus an internal mode. The Sverdrup balance
should apply only to the net component, i.e., the vertical average over the total water column
give us the transport of the wind-driven portion as shown on the left of the
second panel. If the Sverdrup balance is applied to only a portion of the water
column, the vertical velocity in (1.2.15) at the "bottom" of the range of
integration is not zero, and the connection of the transport to the wind driving
will be lost. Unless a deep level can be determined where w is zero, the Sverdrup
balance must be applied to the whole water column.
Much of the disagreement in the literature over the validity of the Sverdrup
balance is in fact connected to such attempts to apply the relation to only a
portion of the water column. Wunsch and Roemmich (1985) have criticized
earlier attempts to make such applications and present compelling arguments
for the fragility of currently available supporting evidence beyond the overall
transport balance previously noted. In particular they argue, as described
above, that the integrated Sverdrup balance, as opposed to the Sverdrup
relation, i.e., the approximate vorticity equation, is vulnerable to the effects of
even small velocities interacting with the bottom slope.
Calculations of the pattern of Sverdrup transport more modern than
W dander's nevertheless give rather good agreement with the overall pattern of
flow deduced from hydrography (see Fig. 1.4.3, for example, which should be
compared with Fig. 1.1.1a). However, in spite of this apparent agreement the
reader must remain aware that even to this day precise, incontrovertible
observational evidence for the validity of either the Sverdrup vorticity equation
or the Sverdrup balance is lacking although the evidence in its favor is
compelling. Nevertheless, the Sverdrup relation and balance are employed
throughout this book. It currently forms the basis for all our present theories
for the circulation.
There is even a more subtle issue associated with the validity of the
Sverdrup balance. Let us even suppose that observational evidence clearly
supports its validity. Could we maintain that we can theoretically justify or
explain the Sverdrup balance even assuming, for example, that there were no
interaction with the bottom? One might suppose that for a given wind stress we
could calculate the velocity from Sverdrup theory and then verify a posteriori
21
=
+
Fig. 1.4.2. Schematic presentation of the way in which the observed distribution of transport with
depth can be considered a sum of a net component plus an internal mode. The Sverdrup balance
should apply only to the net component, i.e., the vertical average over the total water column
give us the transport of the wind-driven portion as shown on the left of the
second panel. If the Sverdrup balance is applied to only a portion of the water
column, the vertical velocity in (1.2.15) at the "bottom" of the range of
integration is not zero, and the connection of the transport to the wind driving
will be lost. Unless a deep level can be determined where w is zero, the Sverdrup
balance must be applied to the whole water column.
Much of the disagreement in the literature over the validity of the Sverdrup
balance is in fact connected to such attempts to apply the relation to only a
portion of the water column. Wunsch and Roemmich (1985) have criticized
earlier attempts to make such applications and present compelling arguments
for the fragility of currently available supporting evidence beyond the overall
transport balance previously noted. In particular they argue, as described
above, that the integrated Sverdrup balance, as opposed to the Sverdrup
relation, i.e., the approximate vorticity equation, is vulnerable to the effects of
even small velocities interacting with the bottom slope.
Calculations of the pattern of Sverdrup transport more modern than
W dander's nevertheless give rather good agreement with the overall pattern of
flow deduced from hydrography (see Fig. 1.4.3, for example, which should be
compared with Fig. 1.1.1a). However, in spite of this apparent agreement the
reader must remain aware that even to this day precise, incontrovertible
observational evidence for the validity of either the Sverdrup vorticity equation
or the Sverdrup balance is lacking although the evidence in its favor is
compelling. Nevertheless, the Sverdrup relation and balance are employed
throughout this book. It currently forms the basis for all our present theories
for the circulation.
There is even a more subtle issue associated with the validity of the
Sverdrup balance. Let us even suppose that observational evidence clearly
supports its validity. Could we maintain that we can theoretically justify or
explain the Sverdrup balance even assuming, for example, that there were no
interaction with the bottom? One might suppose that for a given wind stress we
could calculate the velocity from Sverdrup theory and then verify a posteriori