A High-Resolution Method for Direct Numerical Simulation of Instabilities and Transitions in a Baroclinic Cavity - Modeling Atmospheric and Oceanic Flows - page 303

Azimuthal velocity Axial vorticity

Figure 16.8. Comparison of flow characteristics at midheight between experimental measurements (top) and computed solutions
(bottom) for the structural vacillation regime in the liquid-filled cavity, Pr = 16. For color detail, please see color plate section.

of the flow patterns obtained with the two approaches,
in particular the similarity of large-scale structures, char-
acterized by the same dominant azimuthal wave number
m = 3. The slight discrepancy may result from the dif-
ferent isovalues chosen on contours by each approach.
We note the presence of small-scale fluctuations initially
developing along the inner cold wall, identified as IGWs
and postulated to be the main mechanism responsible for
the spatiotemporal chaotic behavior during the transition
to turbulent flow regimes. Indeed, these small-scale fea-
tures are expected to grow randomly in the whole cavity
for the irregular waves. We refer to Wordsworthetal. [2008]
for a detailed analysis of the experimental investigations.

[2008]). The imposed external conditions represent a tem-
perature difference between the two cylinders of T =2K
with a rotation rate = 3 rad/s for the simulation, corre-
sponding to = 0.016 and Ta = 4.25 10 8 , while for the

experiment = 3.9 rad/s. The mesh used was N

×

× M ×

K = 256 512 in the radial, axial, and azimuthal

directions, respectively, with a dimensionless time step
δt = 0.000125. The preliminary computed solution is com-
pared with experimental measurements in Figure 16.9,
showing the complex flow structure, where any dominant
azimuthal wave number can be extracted as in the SV
regime discussed above (see also the Figure 3 presented
by Wordsworth et al. [2008]). The solution is obviously
still far from its asymptotic state. However, this first result
demonstrates the ability of the present numerical tool to
compute the complex irregular waves in baroclinic cavi-
ties. The computed structures mimic very well the streak
photographs illustrating irregular waves reported by Hide
and Mason [1975] from their experimental studies in a

× 128 ×

16.3.2.4. Irregular Wave Regime. Direct numerical
simulation was carried out to provide a first attempt to
obtain the irregular wave regime in a baroclinic cavity
and to compare the results with experimental data pro-
vided by Wordsworth [2009] (see also Wordsworth et al.