Horizontal thermal convection in a shallow cavity: oscillatory regimes and transition to chaos

We develop a numerical analysis of the buoyancy driven natural convection of a fluid in a three dimensional shallow cavity (4.1.1) with a horizontal gradient of temperature along the larger dimension. The fluid is a liquid metal (Prandtl number equal to 0.015) while the Grashof number (Gr) varies in the range 100,000-300,000. The Navier-Stokes equations in vorticity-velocity formulation have been integrated by means of a linearized fully implicit scheme. The evaluation of fractal dimension of the attractors in the phase space has allowed the detection of the chaotic regime. The Ruelle-Takens bifurcation sequence has been observed as mechanism for the transition to chaos: the quasi periodic regime with three incommensurate frequencies is the instability mechanism responsible for the transition to chaos. Physical experiments confirm the existence of this scenario.