Numerical simulation of pattern formation in the Bénard–Marangoni convection

Abstract

The Bénard–Marangoni convection is numerically simulated using the full three-dimensional Navier–Stokes equation. It is shown that hexagonal convection appears when the surface-tension effect dominates over the buoyancy effect. When two effects are comparable to each other, a mixed type of roll and hexagonal convections is stably obtained. It is found that the kinetic energy production by buoyancy does not depend on the convection pattern, whereas that by surface-tension strongly depends on the convection pattern. When the surface-tension effect is dominant, the kinetic energy production by surface-tension in the hexagonal convection is larger than that in the roll convection. Hexagonal convection gives a vertical heat transfer larger than that of roll convection.