Numerical simulation of thermal convection in a two-dimensional finite box

Abstract

The problems of dynamical onset of convection, textural transitions and chaotic dynamics in a two-dimensional, rectangular Rayleigh-Bénard system have been investigated using well-resolved, pseudo-spectral simulations. All boundary conditions are taken to be no-slip. It is shown that the process of creating the temperature gradient in the system, is responsible for roll creation at the side boundaries. These rolls either induce new rolls or move into the interior of the cell, depending on the rate of heating. Complicated flow patterns and textural transitions are observed in both non-chaotic and chaotic flow regimes. Multistability is frequently observed. Intermediate-Prandtl-number fluids (e.g. 0.71) have a quasiperiodic time dependence up to Rayleigh numbers of order 106. When the Prandtl number is raised to 6.8, one observes aperiodic (chaotic) flows of non-integer dimension. In this case roll merging and separation is observed to be an important feature of the dynamics. In some cases corner rolls are observed to migrate into the interior of the cell and to grow into regular rolls; the large rolls may shrink and retreat into corners. The basic flow patterns observed do not change qualitatively when the chaotic regime is entered.