Power-law scaling in Bénard-Marangoni convection at large Prandtl numbers.
Bénard-Marangoni convection at large Prandtl numbers is found to exhibit steady (nonturbulent) behavior in numerical experiments over a very wide range of Marangoni numbers Ma far away from the primary instability threshold. A phenomenological theory, taking into account the different character of thermal boundary layers at the bottom and at the free surface, is developed. It predicts a power-law scaling for the nondimensional velocity (Peclet number) and heat flux (Nusselt number) of the form Pe approximately Ma(2/3), Nu approximately Ma(2/9). This prediction is in good agreement with two-dimensional direct numerical simulations up to Ma=3.2 x 10(5).
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Max-Planck-Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
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