Geoscience Reference
In-Depth Information
17
Orthogonal Decomposition Methods to Analyze PIV, LDV,
and Thermography Data of Thermally Driven Rotating
Annulus Laboratory Experiments
Uwe Harlander
1
, Thomas von Larcher
2
, Grady B. Wright
3
, Michael Hoff
4
,
Kiril Alexandrov
1
, and Christoph Egbers
1
17.1. INTRODUCTION
on fundamental features. A large part of this agreement
is owed to the baroclinic instability mechanisms that gov-
ern atmospheric and laboratory flows [
Pierrehumbert and
Swanson
, 1995]. This fact makes the heated rotating annu-
lus an inspiring experiment for the community of geo-
physical fluid dynamics, even in the computer age.
Baroclinic instability has been investigated in the annu-
lus not only in numerous experimental studies but also
theoretically [
Lorenz
, 1962] and numerically [
Miller and
Gall
, 1983;
Lewis and Nagata
, 2004;
Randriamampianina
et al.
, 2006;
von Larcher et al.
, 2013;
von Larcher and
Dörnbrack
, 2014]. The two references mentioned last are
discussed in more detail in chapters 2 and 16 of the
present book.
Due to its relative simple geometry as well as to the
well-definable forcing parameters, the rotating annulus
is still of particular interest not only for research with
respect to atmospheric sciences [
Gyüre et al.
, 2007;
Ravela
et al.
, 2010] but also in the development of computational
fluid dynamics (CFD) models where the annulus data can
be used as reference for the validation of new numeri-
cal concepts. In this context it is worth noting that the
rotating annulus experiment described here is a reference
experiment within the German priority program Multiple
Scales in Fluid Mechanics and Meteorology (MetStröm)
that focuses on the development of model- as well as
grid-adaptive numerical simulation concepts in multidis-
ciplinary projects (see http://metstroem.mi.fu-berlin.de).
The flow regime that develops in the cylindrical gap
of the annulus depends on the radial temperature gradi-
ent between the inner and the outer cylinder,
T
,and
on the rotation rate of the apparatus,
.Thus,a2D
parameter space (called regime diagram) spanned by the
Taylor number (
Already in the 1950s, an elegant laboratory experiment
had been designed to understand how the atmospheric
circulation transports heat from equatorial to polar lati-
tudes (cf. the pioneering studies described by
Hide
[1958,
2010]). It consists of a cooled inner and heated outer cylin-
der mounted on a rotating platform, mimicking the heated
tropical and cooled polar regions of Earth's atmosphere.
Depending on the strength of the heating and the rate of
rotation, different flow regimes had been identified in the
gap: the zonal flow regime, wave regimes that can be clas-
sified by propagating waves of different wave numbers,
and quasi-chaotic regimes where waves and small-scale
vortices coexist.
The baroclinic annulus experiment, often called
the
differentially heated rotating annulus of fluid,
, has been
accepted as a suitable laboratory model for the midlati-
tude large-scale flow in Earth's atmosphere. For example,
Fultz
[1961] and
Lorenz
[1964] used the heated rotating
annulus as an analogy to the complex dynamics of the
large-scale weather when they discussed problems related
to climate variability.
Obviously, large-scale environmental flows and the
flows observed in the rotating annulus show agreement
1
Department
of Aerodynamics
and Fluid Mechan-
ics,
Brandenburg University
of
Technology
(BTU)
Cottbus-Senftenberg, Germany.
2
Institute for Mathematics, Freie Universität Berlin, Berlin,
Germany.
3
Department of Mathematics, Boise State University, Boise,
Idaho, United States of America.
4
Leipzig Institute for Meteorology, University of Leipzig,
Leipzig, Germany.
2
) and by the thermal Rossby number
∝
