We investigate with direct numerical simulations the onset of unsteadiness,
the route
to chaos and the dynamics of fully chaotic natural convection in an upright
square air-filled
differentially heated cavity with adiabatic top and bottom walls. The numerical
algorithm integrates the Boussinesq-type Navier–Stokes equations
in
velocity–pressure formulation with a Chebyshev spatial approximation
and a
finite-difference second-order
time-marching scheme. Simulations are performed for Rayleigh numbers up
to
1010, which is more than one order of magnitude higher
than the onset of unsteadiness.
The dynamics of the time-dependent solutions, their time-averaged structure
and
preliminary results concerning their statistics are presented. In particular,
the internal
gravity waves are shown to play an important role in the time-dependent
dynamics
of the solutions, both at the onset of unsteadiness and in the fully chaotic
regime.
The influence of unsteadiness on the local and global heat transfer coefficients
is also
examined.