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those involving nonlinear interactions of widely differ-
ing scales of motion) that continue to pose serious
challenges to even state-of-the-art numerical models yet
may be readily realizable in the laboratory. This is espe-
cially true of large-scale flow in atmospheres and oceans,
for which relatively close dynamical similarity between
geophysical and laboratory systems is readily achiev-
able. Laboratory experiments in this vein therefore still
have much to offer in the way of quantitative insight
and inspiration to experienced researchers and fresh
students alike.
(a)
(b)
Warm water
Cold water
Working fluid
Figure 1.1.
(a) Schematic diagram of a rotating annulus;
(b) schematic equivalent configuration in a spherical fluid shell
(cf. an atmosphere).
1.2. ROTATING, STRATIFIED EXPERIMENTS AND
GLOBAL CIRCULATION OF ATMOSPHERES AND
OCEANS
The role of laboratory experiments in fluid mechanics
in this scheme would seem at first sight to be as models
firmly in the second category. Compared with a plane-
tary atmosphere or ocean, they are clearly much simpler
in their geometry, boundary conditions, and forcing pro-
cesses (diabatic and mechanical), e.g., see Figure 1.1. Their
behavior is often governed by a system of equations that
can be stated exactly (i.e., with no controversial param-
eterizations being necessary), although even then exact
mathematical solutions (e.g., to the Boussinesq Navier-
Stokes equations) may stillbe impossible toobtain. Unlike
atmospheres and oceans, however, it is possible to carry
out controlled experiments to study dynamical processes
in a real fluid without recourse to dubious approxima-
tions (necessary to both analytical studies and numerical
simulation). Laboratory experiments can therefore com-
plement other studies using complex numerical models,
especially since fluids experiments (a) have effectively infi-
nite resolution compared to their numerical counterparts
(though can only be measured to finite precision and res-
olution), (b) are often significantly less diffusive than the
equivalent fluid, e.g., in eddy-permitting ocean models,
and yet (c) are relatively cheap to run!
In discussing the role of laboratory experiments, how-
ever, it is not correct to conclude that they have no direct
role in the construction of more complex, applications-
oriented models and associated numerical tools (such as
in data assimilation). Because the numerical techniques
used in such models (e.g., finite-difference schemes, eddy
or turbulence parameterizations) are also components of
models used to simulate flows in the laboratory under
similar scaling assumptions, laboratory experiments can
also serve as useful “test beds” for directly evaluating and
verifying the accuracy of such techniques in ways that
are far more rigorous than may be possible by compar-
ing complex model simulations solely with atmospheric
or oceanic observations. Despite many advances in the
formulation and development of sophisticated numeri-
cal models, there remain many phenomena (especially
At its most fundamental level, the general circulation
of the atmosphere is but one example of thermal convec-
tion in response to impressed differential heating by heat
sources and sinks that are displaced in both the vertical
and/or the horizontal
in a rotating fluid of low viscosity
and thermal conductivity. Laboratory experiments inves-
tigating such a problem should therefore include at least
these attributes and be capable of satisfying at least some
of the key scaling requirements for dynamical similarity
to the relevant phenomena in the atmospheric or oceanic
system in question. Such experimental systems may then
be regarded [e.g.,
Hide
, 1970;
Read
, 1988] as schemati-
cally representing key features of the circulation in the
absence of various complexities associated, for example,
with radiative transfer, atmospheric chemistry, boundary
layer turbulence, water vapor, and clouds in a way that is
directly equivalent to many other simplified and approxi-
mated mathematical models of dynamical phenomena in
atmospheres and oceans.
Experiments of this type are by no means a recent phe-
nomenon, with examples published as long ago as the
mid to late nineteenth century [e.g.,
Vettin
, 1857, 1884;
Exner
, 1923]; see
Fultz
[1951] for a comprehensive review
of this early work.
Vettin
[1857, 1884] had the insight
to appreciate that much of the essence of the large-scale
atmospheric circulation could be emulated, at least in
principle, by the flow between a cold body (represent-
ing the cold, polar regions) placed at the center of a
rotating, cylindrical container and a heated region (rep-
resenting the warm tropics) toward the outside of the
container (see Figure 1.2). Vettin's experiments used air
as the convecting fluid, contained within a bell jar on a
rotating platform. As one might expect of a nineteenth
century gentleman, he then used cigar smoke to visual-
ize the flow patterns, demonstrating phenomena such as
convective vortices and larger scale overturning circula-
tions. However, these experiments only really explored the
regime we now know as the axisymmetric or “Hadley”
