Surface-temperature-induced Marangoni effects on developing buoyancy-driven flow

Abstract

To investigate the initial development of the Rayleigh–Bénard–Marangoni (RBM) instability in a relatively deep domain, direct numerical simulations for a large range of Marangoni and Rayleigh numbers were performed. In the simulations, the surface was assumed to be flat and surface cooling was modelled by a constant heat flux. The small-scale dynamics of the flow and temperature fields near the surface was fully resolved by using a non-uniform vertical grid distribution. A detailed investigation of the differences in physical mechanisms that drive the Rayleigh- and Marangoni-dominated instabilities is presented. To this end, various properties such as the maturation rate of convection cells, the fluctuating kinetic energy and the surface characteristic length scale were studied. It was confirmed that buoyancy forces and surface-temperature-gradient-driven Marangoni forces enhance one another in promoting the development of the RBM instability. When using a relevant measure of the effective thermal boundary layer thickness as length scale, both the critical Marangoni and Rayleigh numbers, obtained for the purely Marangoni- and purely Rayleigh-driven instabilities, were found to be in good agreement with the literature.