Geoscience Reference
In-Depth Information
z
/
d
=
0.25
z
/
d
=
0.50
z
/
d
=
0.75
Figure 16.7.
Comparison of flow structures between experimental measurements at midheight
z/d
= 0.50 (top) and computed
solutions at different heights (bottom) for the structural vacillation regime in the liquid-filled cavity, Pr = 16.
the large-scale baroclinic waves and therefore eventually
lead to disordered flow [
Früh and Read
, 1997;
Read
et al.
, 2008]. We have carried out comparisons of flow
structures between our computed results and labora-
tory measurements obtained by
Wordsworth
[2009] (see
also
Wordsworth et al.
[2008]). The rotation rate used
in the experimental study was
= 1.3 rad/s while in the
simulation
= 1.25 rad/s was used, corresponding to
(
,Ta
)
=
(
0.0939,7.37
due to the antisymmetry of the flow with respect to the
midheight [
Randriamampianinaetal.
, 2001]. In particular,
it is clearly visible in Figure 16.7 from the two instanta-
neous computed streaklines at different heights
z/d
= 0.25
and
z/d
= 0.75 located symmetrically with respect to the
midheight, the onset and the growth of additional struc-
tures randomly induce the breakdown of the regularity
of the large-scale baroclinic waves. This phenomenon,
associated with the loss of symmetry of waves, known
to be characteristic of the structural vacillation regime,
ultimately leads to the fully disordered flow. The IGWs
mentioned above at lower rotation rate values,
= 0.35
rad/s and
= 0.5125 rad/s, are found to be the small-scale
fluctuations responsible for the chaotic behavior of this
SV flow, in contrast with the air-filled cavity where the
mechanism of transition resulted from radial buoyancy in
a Rayleigh-Bénard-like rotating flow [
Read et al.
, 2008].
In the latter case the centrifugal acceleration was greater
than the gravity everywhere inside the cavity, giving a local
Froude number Fr
r
≡
10
7
)
, which is located close to
the transition zone in the regime diagram (Figure 16.3),
with a temperature difference
T
= 2 K. In both cases, a
SV regime was obtained. The experiment reported 4SV, as
revealed by instantaneous streaklines in Figure 16.7, but
also 3SV as seen in Figure 16.8 from the azimuthal veloc-
ity and axial vorticity in a horizontal plane. This situation
reflects the intransitivity phenomenon, inherent to rotat-
ing flows in cavities, with the coexistence of different stable
flow structures, e.g., different dominant azimuthal wave
numbers, under the same imposed external conditions (see
also Figure 16.3). The simulation predicts a 3SV regime.
The flow exhibits a chaotic behavior induced by the ran-
dom presence of small-scale fluctuations over an almost
regular arrangement of waves at midheight (
z/d
=0.5),
as can be seen in Figure 16.7. Such a flow structure
was already observed in a rotating cavity under symmet-
rical boundary conditions to ensure mass conservation
×
2
r
∗
/g >
1,
r
∗
∈[
]
a
,
b
, while in the
10
−
2
(see Table 16.1).
We have compared the instantaneous contours of the
azimuthal velocity and of the axial component of the vor-
ticity between the available experimental measurements
[
Wordsworth
, 2009] and the computed solutions at mid-
height in Figure 16.8. We note the overall good agreement
present computations, Fr = 1.67
×
