FROM ONSET OF UNSTEADINESS TO CHAOS IN A DIFFERENTIALLY HEATED SQUARECAVITY

We investigate with direct numerical simulations the onset of unsteadi ness, the route to chaos and the dynamics of fully chaotic natural con vection in an upright square air-filled differentially heated cavity w ith adiabatic top and bottom walls. The numerical algorithm integrates the Boussinesq-type Navier-Stokes equations in velocity-pressure form ulation with a Chebyshev spatial approximation and a finite-difference second-order time-marching scheme. Simulations are performed for Rayl eigh numbers up to 10(10), which is more than one order of magnitude h igher than the onset of unsteadiness. The dynamics of the time-depende nt solutions, their time-averaged structure and preliminary results co ncerning their statistics are presented. In particular, the internal g ravity waves are shown to play an important role in the time-dependent dynamics of the solutions, both at the onset of unsteadiness and in t he fully chaotic regime. The influence of unsteadiness on the local an d global heat transfer coefficients is also examined.