Bénard-Marangoni convection at large Marangoni numbers: Results of numerical simulations

Bénard-Marangoni convection at large Marangoni and low Prandtl numbers can be efficiently simulated using spectral numerical methods. Previous two-dimensional simulations indicate power-law scaling over a significant range of Marangoni numbers for both laminar and turbulent convection. We summarize these numerical results and describe corresponding phenomenological models. New three-dimensional simulations support the scaling results obtained in the turbulent two-dimensional case.