On simulation of complex regimes of the Rayleigh–Benard convection

The 2D and 3D turbulent convectional flows of viscous and incompressible fluids in a rectangular parallelepiped are numerically simulated when heating from below. The horizontal boundaries are stress-free for the 3D case, and stress-free or rigid for the 2D simulation. It is shown that in spite of the quantitative discrepancy between the results of the 3D simulation and the experiment, the 3D simulation shows the correct power laws for temperature and vertical velocity pulsations versus supercriticality. In the 2D simulation, a similar correspondence is observed at a relatively low supercriticality (approximately up to 250). At a high superriticality, in the 2D convection, the existence of a large-scale structure is dominating, as it determines the property of a flow.