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

Abstract

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.

Citation

Bucchignani, E. and Mansutti, D. (2000), "Horizontal thermal convection in a shallow cavity: oscillatory regimes and transition to chaos", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 10 No. 2, pp. 179-195. https://doi.org/10.1108/09615530010312338