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(a)
(b)
0.382 × Taylor number
10
5
10
6
10
7
10
8
a
Upper
symmetrical
b
c
(c)
(d)
1
Irregular
Regular
waves
d
10
-1
e
f
Lower
symmetrical
10
-2
(e)
(f)
10
-3
10
-2
10
-1
10
0
10
2
10
2
(rad
2
/s
2
)
Ω
Figure 1.3.
Schematic regime diagram for the thermally driven rotating annulus in relation to the thermal Rossby number
(or stability parameter,
T
∝
2
, showing some typical horizontal flow patterns at the top surface,
visualized as streak images at upper levels of the experiment.
−2
) and Taylor number
∝
1.3.1. Principal Flow Regimes
three) most significant dimensionless parameters. These
are typically
(a) a stability parameter or “thermal Rossby number”
Although a number of variations in these boundary
conditions have been investigated experimentally, almost
all such experiments are found to exhibit the same three
or four principal flow regimes, as parameters such as the
rotation rate
or temperature contrast
T
are varied.
These consist of (I) axisymmetric flow (in some respects
analogous to Hadley flow in Earth's tropics and frequently
referred to as the “upper-symmetric regime”; see below)
at very low
for a given
T
(that is not too small); (II)
regular waves at moderate
; and (III) highly irregular,
aperiodic flow at the highest values of
attainable. In
addition, (IV) axisymmetric flows occur at all values of
at a sufficiently low temperature differenceT
T
(a diffu-
sively dominated regime termed “lower symmetric” [
Hide
and Mason
, 1975,
Ghil and Childress
, 1987] to distinguish
it from the physically distinct “upper-symmetric” men-
tioned above). The location of these regimes are usually
plotted on a “regime diagram” with respect to the two (or
gαTd
=
2
,
(1.1)
[
(b
−
a)
]
providing a measure of the strength of buoyancy forces
relative to Coriolis accelerations;
(b) a Taylor number
=
2
(b
a)
5
−
T
,
(1.2)
ν
2
d
measuring the strength of Coriolis accelerations relative
to viscous dissipation; and
(c) the Prandtl number
Pr =
ν
κ
.
(1.3)
Here
g
is the acceleration due to gravity,
α
the thermal
expansion coefficient of the fluid,
ν
the kinematic viscos-
ity,
κ
the thermal diffusivity, and
a
,
b
,and
d
the radii of
