Geoscience Reference
In-Depth Information
0.15
0.05
0.1
0.025
0.05
0
0
-0.05
-0.025
-0.1
-0.15
-0.05
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
-0.05
-0.025
0
0.025
0.05
(
r
mid
,
z
mid
)
(
r
bl
,
z
bot
)
Figure 16.6.
Phase space diagrams of the temperature field at two fixed
(r
,
z)
locations for
= 0.5125 rad/s in the liquid-filled
cavity, Pr = 16, showing the time series of the sine component versus that of the cosine component of the azimuthal dominant
mode
m
=3.
representation in the phase space based on time series of
cosine and sine components of the dominant azimuthal
wave number from a Fourier analysis of the tempera-
ture at two specific fixed
(r
,
z)
locations. We display these
behaviors in Figure 16.6 at
= 0.5125 rad/s, for which
the intensity of the small-scale features was found high-
est between the computed AV solutions. In agreement
with the experimental findings of
Wordsworth
[2009], the
first plot at midradius and midheight
(r
mid
,
z
mid
)
shows
a “classical” 3AV profile defined by two frequencies: the
wave drift represented by the large circle and the peri-
odic oscillations of the wave amplitude, both related to
the baroclinic instability [
Randriamampianinaetal.
, 2006].
The second map, taken at a radius location
r
bl
inside the
boundary layer along the inner cold cylinder and at a
height near the bottom wall,
z
bot
, clearly exhibits a chaotic
behavior corresponding to a 3MAV regime.
Since such different AV and MAV regimes were
not observed simultaneously under fixed values
of control parameters within the air-filled cavity
[
Randriamampianina et al.
, 2006] but successively
when increasing the values of rotation rate as shown in
Figure 16.1, this localized 3MAV is directly ascribed to
the presence of small-scale features. From their recent
direct numerical simulation in a liquid-filled baroclinic
cavity with Pr= 24.47,
Jacoby et al.
[2011] identified
these small structures, occurring spontaneously and
simultaneously with the large-scale baroclinic waves, as
inertia-gravity waves (IGWs). The characteristics of the
IGWs observed in the present configuration are discussed
by
Randriamampianina
[2013]. The values of the sine and
cosine components reported in Figure 16.6 are related to
IGW activity, more specifically to the balance between
the two phenomena involved, with highest values associ-
ated with baroclinic instability. It reflects the variability
of IGWs and the interaction between these two waves
characterized by very different scales in time and in space.
In particular, it puts forward the ability of the IGWs to
induce locally a chaotic regime of the large-scale flow
motion. Such a behaviour was not mentioned either by
experiments [
Wordsworth
, 2009] or by previous simula-
tions using liquids [
Hignett et al.
, 1985;
Jacoby et al.
,
2011]. From their numerical simulation based on finite
difference approximation,
Hignett et al.
[1985] obtained
also the AV regime, using a liquid defined by Pr = 13.07,
but did not report the presence of these small-scale
features. On the other hand, we did not observe the
appearance of these fluctuations simultaneously with
baroclinic waves when considering air in the present
geometry, but rather we found the same flow structures
reported by
Randriamampianina et al.
[2006] for air
using different geometric dimensions. It clearly reveals
the strong dependence on the Prandtl number of the
baroclinic instability characteristics through the thermal
stratification of the flow. Again we refer the reader to
Chapter 3 in this topic about the detailed analysis of the
amplitude vacillation flow regime, particularly about the
different mechanisms responsible for their occurrence.
16.3.2.3. Structural Vacillation Flow Regime.
In spite
of a well-defined dominant azimuthal wave number, this
flow is characterized by the presence of small-scale fluc-
tuations which progressively destroy the regularity of
