388
Abyssal Circulation
scale motion in the abyssal interior. This forms a fundamental presumption of
the development which follows.
It is important to note that the theory developed earlier in Chapters 3 and
4 for the dynamics of the thermocline assumes that the effect of the abyssal
motion is negligible. The weak velocity of the abyssal motion was neglected in
calculating the slope of the deep density surfaces in the thermocline. In
addition, the Sverdrup balance was applied to only the depth interval of the
thermocline. This is equivalent to the condition that W 00 is negligible compared
to W£ so that the Sverdrup condition can be applied to only the thermocline,
and this seems apt on the basis of the above estimates. As noted in Chapter 1,
this is also equivalent to assuming that the characteristic transport of the abyss
is locally small compared to the wind-driven transport, and it is certainly not
clear from observations that this is true. If the vertically integrated transports
in the oceanic abyssal interior were of the same order as the wind-driven
transports, the separation of the dynamics of the abyss and the thermocline
become problematic, and the two regions must then be considered
simultaneously. The theory for such a combined dynamics is currently lacking.
Instead, in most of this chapter the thermocline-induced, deep vertical velocity
is assumed to be determined only by the thermocline's dynamics, independently
of the abyssal motion, and is responsible for driving the interior abyssal
motion. Furthermore, it has recently been suggested that the upwelling into the
thermocline may indeed be geographically limited. Observations of uniformly
low values of the mixing coefficient over most of the oceanic interior are
matched by observations of very strong mixing near deep topographic features
(Toole et al.1994). It is quite possible then that the overall balance suggested by
Stommel and Arons is valid, only that w00 is in fact geographically limited.
Note that this would imply a generally weak interaction between the dynamics
of the abyss and thermocline dynamics over that broad part of the interior
where w00 is negligible. The effect of such a geographically limited W 00 is taken
up in Section 7.7.
7.2 The Stommel, Arons, and Faller Experiment
The theoretical consequences of the application of Sverdrup theory to source
driven flow, as would be relevant for the abyss, seemed so nonintuitive to
Stommel and Arons themselves that they, in collaboration with Faller, carried
out an elegant laboratory experiment to check some of the more surprising
results. We invert the process here for didactic purposes and start with an
analysis of the experiment (Stommel et. al. 1958).
The experimental situation is shown schematically in Fig. 7 .2.1. A pieshaped basin contains water, and it is spun about a vertical axis at a rate Q
which was about 1.05 s- 1 in the experiment. The basin has an apex angle, 8o,
which in the actual experiments was 60°. The water, of density p 0 , has a depth
Abyssal Circulation
scale motion in the abyssal interior. This forms a fundamental presumption of
the development which follows.
It is important to note that the theory developed earlier in Chapters 3 and
4 for the dynamics of the thermocline assumes that the effect of the abyssal
motion is negligible. The weak velocity of the abyssal motion was neglected in
calculating the slope of the deep density surfaces in the thermocline. In
addition, the Sverdrup balance was applied to only the depth interval of the
thermocline. This is equivalent to the condition that W 00 is negligible compared
to W£ so that the Sverdrup condition can be applied to only the thermocline,
and this seems apt on the basis of the above estimates. As noted in Chapter 1,
this is also equivalent to assuming that the characteristic transport of the abyss
is locally small compared to the wind-driven transport, and it is certainly not
clear from observations that this is true. If the vertically integrated transports
in the oceanic abyssal interior were of the same order as the wind-driven
transports, the separation of the dynamics of the abyss and the thermocline
become problematic, and the two regions must then be considered
simultaneously. The theory for such a combined dynamics is currently lacking.
Instead, in most of this chapter the thermocline-induced, deep vertical velocity
is assumed to be determined only by the thermocline's dynamics, independently
of the abyssal motion, and is responsible for driving the interior abyssal
motion. Furthermore, it has recently been suggested that the upwelling into the
thermocline may indeed be geographically limited. Observations of uniformly
low values of the mixing coefficient over most of the oceanic interior are
matched by observations of very strong mixing near deep topographic features
(Toole et al.1994). It is quite possible then that the overall balance suggested by
Stommel and Arons is valid, only that w00 is in fact geographically limited.
Note that this would imply a generally weak interaction between the dynamics
of the abyss and thermocline dynamics over that broad part of the interior
where w00 is negligible. The effect of such a geographically limited W 00 is taken
up in Section 7.7.
7.2 The Stommel, Arons, and Faller Experiment
The theoretical consequences of the application of Sverdrup theory to source
driven flow, as would be relevant for the abyss, seemed so nonintuitive to
Stommel and Arons themselves that they, in collaboration with Faller, carried
out an elegant laboratory experiment to check some of the more surprising
results. We invert the process here for didactic purposes and start with an
analysis of the experiment (Stommel et. al. 1958).
The experimental situation is shown schematically in Fig. 7 .2.1. A pieshaped basin contains water, and it is spun about a vertical axis at a rate Q
which was about 1.05 s- 1 in the experiment. The basin has an apex angle, 8o,
which in the actual experiments was 60°. The water, of density p 0 , has a depth