The Stommel, Arons, and Faller Experiment
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the boundary conditions and mass balance. Hence there is an additional
implicit limit on the magnitude of the forcing by the sources.
There are several interesting cases that Stommel, Arons, and Faller
considered in their experiment.
Suppose first, for example that the full source of fluid is placed at the apex,
i.e., that S1 = 0 and So = S (Fig. 7.2.3a). Then:
(7.2.18)
The boundary layer flows "southward," away from the source with a mass flux
larger than the source strength by an amount S(2gDofD.lr6) which is the
measure of the interior mass flux flowing towards the source due to the interior
stretching of vortex columns. That is, in addition to the flow directly related to
the fluid emerging from the source, a substantial recirculation of the flow is
also taking place, driven in the interior by vortex tube stretching. The
boundary current flowing away from the source must carry the combined flux
of the source and the recirculation of the interior flow which, on entering the
a)
So
b)
f! I\
s1
c)
i
s1
Fig. 7.2.3a-d. Schematic presentation of four experiments with different locations for the sources.
a A single source S0 = Sis placed at the apex. The interior flow is towards the source, and Tw is the
boundary layer transport moving away from the source with a transport greater than the source.
b The source is placed at the outer rim. There is no net source and no interior flow. The flow moves
from the source at the rim to the sink at the apex. d A source is placed on the "eastern" boundary at
one radius, and a sink of equal strength is placed at a larger radius. The flow moves from source to
sink on the indirect path though the western boundary layer as shown