Stommel-Arons Theory: Abyssal Flow on the Sphere
395
a geostrophic zonal flow to match the source input. Since n is independent of(),
it follows that when S = 0 the zonal velocity independent of e. Fluid can
proceed across the sector only as shown in Fig. 7 .2.3d. After reaching the
western boundary it can travel along the western boundary to the radius of the
sink, and retracing its path in azimuth, it leaves the sector by flowing eastward
at constant radius to the sink. This is perhaps the most bizarre of all the cases.
The constraints placed on the motion by the potential vorticity dynamics in the
interior and the absence of an eastern boundary layer forces the flow into an
immensely indirect and intricate path to flow from source to sink.
It is even now astonishing to realize that these dynamical ideas achieved
full confirmation in the experiments of Stommel, Arons, and Faller (1958), and
the reader is referred to their original paper both for a complete discussion of
the experimental evidence and for the original sense of wonder at the power of
the constraint imposed by the ambient potential vorticity gradient which yields
such remarkable flow patterns.
With this experimental confirmation in hand Stommel and Arons were
emboldened to apply their ideas to planetary motions in the ocean's abyss.
7.3 Stommel-Arons Theory: Abyssal Flow on the Sphere
Stommel and Arons (1960 a,b) extended the dynamical ideas of the previous
section to describe a theory for the abyssal motion on a spherical earth. They
envisioned the entire ocean as a two-layer model with localized sinking at both
poles from the upper to lower layer and a widespread return flow from the
lower layer, which represents the abyss, into the upper layer, which is meant to
represent the thermocline driven by the wind. The return flow has a vertical
velocity, w0, specified over the area of the ocean basin at the interface between
the two layers, i.e., at the top of the abyssal layer. This distributed sink acting
on the abyss provides the driving mechanism for the interior flow. As in the
analysis of the Stommel, Arons, and Faller experiment, western boundary
currents are added as needed to satisfy mass balance considerations.
In this form the abyss is represented as a single layer, and therefore at each
geographical location the abyss moves in a single direction. As we have noted
above, the evidence from tracer and hydrographic data implies that motion in
the abyss is strongly baroclinic, with interleaving of water masses moving in
quite different directions. The Stommel-Arons model is clearly unable to deal
with this vertical structure and should be considered as a model only for the
vertical average of the abyssal flow. The authors themselves were concerned
about this restriction. (I am indebted to Arnold Arons for a fascinating and
enlightening conversation about the historical development of the StommelArons theory.) However, they considered that the model presented an
important first step to which refinements could be added later. Similarly, the
model treats the abyss as a layer of fluid with a flat bottom. Topography is
395
a geostrophic zonal flow to match the source input. Since n is independent of(),
it follows that when S = 0 the zonal velocity independent of e. Fluid can
proceed across the sector only as shown in Fig. 7 .2.3d. After reaching the
western boundary it can travel along the western boundary to the radius of the
sink, and retracing its path in azimuth, it leaves the sector by flowing eastward
at constant radius to the sink. This is perhaps the most bizarre of all the cases.
The constraints placed on the motion by the potential vorticity dynamics in the
interior and the absence of an eastern boundary layer forces the flow into an
immensely indirect and intricate path to flow from source to sink.
It is even now astonishing to realize that these dynamical ideas achieved
full confirmation in the experiments of Stommel, Arons, and Faller (1958), and
the reader is referred to their original paper both for a complete discussion of
the experimental evidence and for the original sense of wonder at the power of
the constraint imposed by the ambient potential vorticity gradient which yields
such remarkable flow patterns.
With this experimental confirmation in hand Stommel and Arons were
emboldened to apply their ideas to planetary motions in the ocean's abyss.
7.3 Stommel-Arons Theory: Abyssal Flow on the Sphere
Stommel and Arons (1960 a,b) extended the dynamical ideas of the previous
section to describe a theory for the abyssal motion on a spherical earth. They
envisioned the entire ocean as a two-layer model with localized sinking at both
poles from the upper to lower layer and a widespread return flow from the
lower layer, which represents the abyss, into the upper layer, which is meant to
represent the thermocline driven by the wind. The return flow has a vertical
velocity, w0, specified over the area of the ocean basin at the interface between
the two layers, i.e., at the top of the abyssal layer. This distributed sink acting
on the abyss provides the driving mechanism for the interior flow. As in the
analysis of the Stommel, Arons, and Faller experiment, western boundary
currents are added as needed to satisfy mass balance considerations.
In this form the abyss is represented as a single layer, and therefore at each
geographical location the abyss moves in a single direction. As we have noted
above, the evidence from tracer and hydrographic data implies that motion in
the abyss is strongly baroclinic, with interleaving of water masses moving in
quite different directions. The Stommel-Arons model is clearly unable to deal
with this vertical structure and should be considered as a model only for the
vertical average of the abyssal flow. The authors themselves were concerned
about this restriction. (I am indebted to Arnold Arons for a fascinating and
enlightening conversation about the historical development of the StommelArons theory.) However, they considered that the model presented an
important first step to which refinements could be added later. Similarly, the
model treats the abyss as a layer of fluid with a flat bottom. Topography is