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(a)
(b)
x 10
-5
Stream function at level 120 mm
x 10
-5
Velocity potential at level 120 mm
1
1
5
2
0.8
0.8
4
0.6
0.6
1. 5
3
0.4
0.4
1
0.2
0.2
2
0.5
0
0
1
-0.2
-0.2
0
0
-0.4
-0.4
-0.5
-1
-0.6
-0.6
-2
-0.8
-0.8
-1
-1
-
-1
-1
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
1
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
1
(c)
(d)
x 10
-5
x 10
-6
Stream function at level 120 mm
Velocity potential at level 120 mm
1
1
8
2
0.8
0.8
6
0.6
0.6
1. 5
4
0.4
0.4
1
2
0.2
0.2
0
0.5
0
0
-2
-0.2
-0.2
0
-4
-0.4
-0.4
-0.5
-6
-0.6
-0.6
-1
-8
-0.8
-0.8
-10
-1
-1
-1
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
1
-1
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
1
10
7
,
Figure 17.13.
Helmholtz-Hodge decomposition for two sets of parameters
(
,
T
,Ta,Ro,
m)
=
(
5.02rpm, 6.7 K, 1.93
×
10
8
, 1.150, 4
)
for (c) and (d): (a) stream function
m
= 3, (b) velocity potential
m
= 3, (c) stream function
m
= 4, (d) velocity potential
m
=4.
1.189, 3
)
for (a) and (b) and
(
,
T
,Ta, Ro,
m)
=
(
15.00 rpm, 8.0 K, 1.72
×
17.4. CONCLUSION
Here we have applied the techniques solely on data from
the heated rotating annulus that is operated in the lab
of the Brandenburg University of Technology in Cottbus
as part of the Multiple Scales in Fluid Mechanics and
Meteorology initiative.
With the focus on geophysical fluid dynamics, the dif-
ferentially heated and rotating annulus is an ideal test
bed that allows for a rigorous and replicable testing of
theories and computational tools. The atmosphere and
oceans as well as many astrophysical fluids are stratified
This chapter summarized recent experimental work on
the differentially heated rotating annulus. Some experi-
mental techniques used are unique and the work on sin-
gular vectors and the Helmholtz-Hodge decomposition
is novel. All the statistical and mathematical techniques
discussed are versatile and can be applied to any kind
of multivariate data, no matter whether they result from
numerical models or field or laboratory observations.
