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(a)
(b)
(c)
(d)
(e)
(f)
Figure 4.14 The development of turbulence through the formation of billows. Top panel shows
billows developing in an accelerating stratified flow in a tilted tank. The lower panels (a-f)
show stages in the transition to turbulence in a stratified fluid in a tilting tank experiment.
From (Thorpe, 1971 ), with permission from Cambridge University Press.
lower panels, Fig. 4.14a -f. The tank has been returned to the horizontal after the flow
has been accelerated. The flow is still laminar but unstable as Ri
0.06. Fig. 4.14a -c
show the evolving instability and the emergence of billows with initiation of turbu-
lence in the centre of the billows. Fig. 4.14d -f show the amalgamation of turbulent
patches to form a turbulent layer. Turbulence will continue only for a limited period
as, with the tank horizontal, no further energy is supplied to mean flow. Such
experiments have confirmed the validity of the Ri criterion for the onset of turbulence
and have also shown how the scale of the billows depends on the initial thickness of
the interface. Billows are frequently observed in cloud formations in the atmosphere
and have been directly observed in the thermocline of the Mediterranean Sea
(Woods, 1968 ). It has been postulated, although not yet confirmed, that billow
turbulence is the source of the majority of turbulence observed in the ocean.
We now have two very different conditions for the occurrence of turbulence
encapsulated in the Reynolds and Richardson numbers. For the ocean, if we take
the water depth as the relevant lengthscale, the Reynolds number is generally very
large (
10 6 ) so we might conclude that turbulence will be ubiquitous except in thin
regions very close to the boundaries where the length is restricted. In a homogeneous
(i.e. completely unstratified) ocean this would be the case and the intensity of the
turbulence would be limited only by the energy supply which is required to supply the
dissipation of energy to heat by viscosity. In the real ocean, however, stratification
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