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and rotate. The complex wave interactions and instabilities
that shape their natural systems all have their equivalent
in the annulus experiment.
Our understanding of the annulus flow is by far not
complete and the work discussed in the present chapter
can be seen as a starting point for further studies on the
many facets of the experiment.
In Section 17.3.1 we studied transient features of baro-
clinic waves by using PIV and LDV measurements. The
data sets involved could be expanded by
simultaneous
PIV
and LDV observations. LDV is well suited to resolve fast
local features like gravity waves excited close to the inner
cylinder. At the same time, PIV can capture the state of the
large-scale baroclinic wave that is particularly favorable
for gravity wave excitation.
In Section 17.3.2 we discussed simultaneous surface
temperature and PIV measurements. From these data the
surface eddy heat flux can be derived [
Harlander et al.
,
2012a]. A future systematic study of the surface eddy heat
flux for different flow regimes and annulus geometries
would help to understand better the transient eddies and
their feedback on the mean flow [
Wilson and Williams
,
2006].
In Section 17.3.3 patterns with large growth rates,
so-called singular vectors, have been estimated from data
[
Penland and Sardeshmukh
, 1995]. To our knowledge, no
method is available yet that can do this for systems with
time-dependentsystem matrices. In thatcase, linearization
can no longer be done about a time mean state. Instead,
linearization about a full nonlinear realization of the flow
is necessary. Due to its reproducibility, the annulus experi-
ment is well suited to provide data to test future statistical
methods that can handle problems with time-dependent
system matrices.
Finally, as already mentioned at the end of Section
17.3.4, from simultaneous observed surface temperature
and 2D flow measurements, the 3D flow can be recon-
structed by using radial basis functions [
Harlander et al.
,
2012b]. To further increase the reliability of such a novel
reconstruction, the technique should be tested against
stereo PIV observations that give 3D velocity fields on
2D laser slices. Combining such 3D flow observations
with numerical simulations is a promising strategy to
detect gravity waves and the excitation mechanisms in
the stratified annulus [
Williams et al.
, 2008;
Scolan et al.
,
2013].
Oswald Knoth, and Eric Severac from the MetStröm
rotating annulus group for many helpful discussions and
Yongtai Wang for help regarding measurements and
data handling. In particular the authors thank Emilia
Crespo del Arco and Mani Mathur for helpful comments
that improved the chapter. The work of Wright was
funded in part by the U.S. National Science Foundation
(NSF) under grant DMS-0934581. Wright also wishes
to thank Edward Fuselier of High Point University for
discussing various ideas related to Helmholtz-Hodge
decompositions on bounded domains.
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Acknowledgments.
The work by Harlander, von
Larcher, Alexandrov, and Egbers was partly funded
by the German Science Foundation (DFG) under the
DFG priority program MetStröm (SPP 1276/1-3) (grant
EG 100/13-1-3). They thank Ulrich Achatz, Martin
Baumann, Andreas Dörnbrack, Jochen Fröhlich, Vincent
Heuveline, Stefan Hickel, Illia Horenko, Rupert Klein,
