Power-law scaling in Benard-Marangoni convection at large Prandtl numbers - art. no. 027303

Benard-Marangoni convection at large Prandtl numbers is found to exhibit st eady (nonturbulent) behavior in numerical experiments over a very wide rang e of Marangoni numbers Ma far away from the primary instability threshold. A phenomenological theory, taking into account the different character of t hermal boundary layers at the bottom and at the free surface, is developed. It predicts a power-law scaling for the nondimensional velocity (Peclet nu mber) and heat flux (Nusselt number) of the form Pe similar to Ma(2/3), Nu similar to Ma(2/9). This prediction is in good agreement with two-dimension al direct numerical simulations up to Ma=3.2X10(5).