Geoscience Reference
In-Depth Information
16
A High-Resolution Method for Direct Numerical Simulation
of Instabilities and Transitions in a Baroclinic Cavity
Anthony Randriamampianina
1
and Emilia Crespo del Arco
2
16.1. INTRODUCTION
The system is well known to exhibit a rich variety
of different flow regimes, depending upon the imposed
conditions (primarily the temperature contrast
T
and
rotation rate
), ranging from steady, axisymmetric cir-
culations through highly symmetric, regular wave flows to
fully developed geostrophic turbulence [
Hide
, 1958;
Fowlis
and Hide
, 1965].
With the exponential increase in computing power these
last decades, direct numerical simulation has become
an indispensable tool for investigating the complex spa-
tiotemporal behaviors of baroclinic instability in the lab-
oratory, complementarily with experiments. Even though
it does not yet allow for a complete study of the fully
developed turbulent regimes, it provides new insight into
the mechanisms responsible for these disordered flows.
Moreover, direct numerical simulation, free of uncertain-
ties related to turbulence modelings and of imperfections
of experimental setups, can supply more extensive data
than measurements and thus facilitate the detailed anal-
ysis of the wave dynamics. In particular, it is useful to
explore the different nonlinear flow regimes in the param-
eter space in order to accurately delineate a bifurcation
diagram. Moreover, direct numerical simulation provides
relevant information about the small-scale fluctuations
that progressively destroy the regularity of the flow dur-
ing the transition toward geostrophic turbulence. Thereby
it can efficiently serve as a guide to experiments and also
supplement measurements.
Baroclinic instability is recognized to be one of the
dominant energetic processes in the large-scale atmo-
spheres of terrestrial planets, such as Earth and Mars,
e.g.,
Pierrehumbert and Swanson
[1995], and in the oceans.
Its fully developed form as sloping convection is strongly
nonlinear and has a major role in the transport of heat and
momentum in the atmospheric and oceanic motions. Its
time-dependent behavior also exerts a dominant influence
on the intrinsic predictability of the atmosphere and the
degree of chaotic variability in its large-scale meteorology
[e.g,
Pierrehumbert and Swanson
, 1995;
Read et al.
, 1998;
Read
, 2001]. On the other hand, the close analogy between
the dynamics of the ocean and atmosphere has been
reported by
OrlanskiandCox
[1973]: “Similar phenomena
take place from the high frequency range characterized
by internal gravity waves to the low range of frequen-
cies dominated by quasi-geostrophic motion. Detailed
temperature measurements indicate that the ocean has
relatively large-scale density discontinuities that are very
much like atmospheric fronts. The oceanic fronts have a
characteristic slope which is determined by the density
difference, rotation and vertical shear of the currents par-
allel to the front. Since atmospheric fronts are known to
be baroclinically unstable, it appears to be appropriate to
suspect the same mechanism may be present in the ocean.”
Since the pioneering works of
Hide
[1958] in the 1950s,
the differentially heated, rotating cylindrical annulus has
been an archetypal means of studying the properties of
fully developed baroclinic instability in the laboratory.
16.2. NUMERICAL MODEL
16.2.1. Background
1
Laboratoire Mécanique, Modélisation & Procédés Propres,
UMR 7340 CNRS, Aix Marseille Université, Marseille, France.
2
Departamento de Física Fundamental, Universidad
Nacional de Educación a Distancia (UNED), Madrid, Spain.
The first numerical investigations devoted to baro-
clinic waves in the differentially heated rotating cylindri-
cal annulus were reported by
Williams
[1969] based on
