Geoscience Reference
In-Depth Information
these modes from the data alone without using a linear
model operator. Finally, in Section 17.3.4 we decompose
the annulus flow in a purely rotational and a purely diver-
gent part. This decomposition is based on radial basis
functions (RBFs) and it might prove useful in discriminat-
ing different wave types in the flow. We close the chapter
with Section 17.4, where we summarize our results and
provide an outlook on future work.
of the annulus. The radial temperature difference between
the outer and inner walls is realized by heating the fluid in
the outer annulus-shaped chamber by a heating coil and
by cooling the fluid in the inner cylinder by using a ther-
mostat. Deionized water is used as working fluid in all
experiments.
All experiments were conducted in the classical
f
-plane
configuration though a sloping bottom could easily be
inserted and then
β
-plane experiments could also be per-
formed. Furthermore, the surface is free rather than a
rigid lid. We refer the reader to
Fein
[1973] for a com-
parison of experiments with a free surface and a rigid lid
and to
Mason
[1975] for details of the influence of a slop-
ing bottom on the flow regimes. In cases of experiments
on baroclinic channel flows with narrows, a barrier was
inserted in the gap, as described in Section 17.3.2.
By keeping the temperature gradient fixed but varying
the rotation rate of the apparatus, sequences of regime
transitions can be observed. Once the radial temperature
gradient is settled, the spin-up time is found to be less
than 30 min for steady waves and up to 40 min for com-
plex flows. Observations were usually done up to several
hours per parameter point, extended partly in complex
flow regimes.
17.2. EXPERIMENTAL SETUP, PARAMETERS,
AND FLOW REGIMES
17.2.1. Setup
Our setup (Figure 17.1), described in more detail by
von Larcher and Egbers
[2005b], consists of a tank with
three concentric cylinders mounted on a turntable that
rotates around its vertical axis of symmetry. The inner
cylinder is made of anodized aluminum; the middle and
outer ones are made of borosilicate glass. The temperature
of the inner and outer cylinders and the rotation rate of
the apparatus are controlled by the experiment software
which is programmed in LabVIEW
. Temperature sen-
sors are part of the inner and outer side walls: at the inner
wall at one azimuthal position in two different heights, at
the outer wall at four equidistant positions in midheight
17.2.2. Parameters
The shape of the annulus is defined by the radius ratio
η
and the aspect ratio
with
Ω
Inner side wall of
outer cylinder
Inner cylinder
η
=
a
d
b
,
=
a
,
(17.2)
b
−
where the inner radius
a
= 45 mm, the outer radius
b
= 120 mm, and the fluid depth
d
= 135 mm (implying
η
= 0.38 and
= 1.8 for our apparatus).
Beyond these geometric parameters, the fluid motion
is governed by the two dynamic control parameters, the
rotation rate of the annulus,
, and the radial tempera-
ture difference in the cylindrical gap,
T
. These parame-
ters determine the nondimensional Taylor number Ta and
thermal Rossby number Ro, as already mentioned above.
The two numbers read
Warm
Cold
d
Drift
b
a
Ta =
4
2
(b
a)
5
−
o=
gdαT
2
(
b
g
,
a
)
2
,
(17.3)
ν
2
d
−
where
ν
is the kinematic viscosity,
g
the acceleration due
to gravity, and
α
the volumetric expansion coefficient. The
Taylor number measures the rotation rate with respect
to the viscous effect, and the thermal Rossby number
corresponds to the ratio of buoyancy and Coriolis terms
and therefore indicates a thermal stratification of the flow.
Figure 17.1.
Sketch of the rotating annulus with illustration of
a typical large-scale jet stream of wave number
m
= 4 that has
a drift relative to the rotating reference system.
