The convective flows which arise in shallow cavities filled with
low-Prandtl-number
fluids when subjected to a horizontal temperature gradient are studied
numerically
with a finite element method. Attention is focused on a rigid cavity with
dimensions 4×2×1, for which experimental data
are available. The three-dimensional results indicate
that, after a relative concentration of the initial Hadley circulation,
a transition to
time-dependent flows occurs in the form of a roll oscillation with a purely
dynamical
origin. This transition corresponds to a Hopf bifurcation with a breaking
of symmetry
that gives some specific properties to the time evolution of the flow:
these properties
are shown to be the result of the general behaviour of the dynamical systems.
Calculations performed in the case of mercury compare well with the experiments
with similar power spectra of the temperature, and this validates the analysis
of
the nature of the global flow performed in the limiting case
Pr=0. All these
results are discussed with respect to the linear and nonlinear analyses
and to other
computational experiments. Numerical results obtained in the corresponding
two-dimensional
situation give a different transition to the time-dependent flow: it is
shown that in the three-dimensional cavity this type of two-dimensional
transition is
less probable than the observed transition with breaking of symmetry.
Reservoir computing model of two-dimensional turbulent convection
