Benard-Marangoni convection at low Prandtl number

Surface-tension-driven Benard convection in low-Prandtl-number fluids is st udied by means of direct numerical simulation. The flow is computed in a th ree-dimensional rectangular domain with periodic boundary conditions in bot h horizontal directions and either a free-slip or no-slip bottom wall using a pseudospectral Fourier-Chebyshev discretization. Deformations of the fre e surface are neglected. The smallest possible domain compatible with the h exagonal flow structure at the linear stability threshold is selected. As t he Marangoni number is increased from the critical value for instability of the quiescent state to approximately twice this value, the initially stati onary hexagonal convection pattern becomes quickly time-dependent and event ually reaches a state of spatio-temporal chaos. No qualitative difference i s observed between the zero-Prandtl-number limit and a finite Prandtl numbe r corresponding to liquid sodium. This indicates that the zero-Prandtl-numb er limit provides a reasonable approximation for the prediction of low-Pran dtl-number convection. For a free-slip bottom wall, the flow always remains three-dimensional. For the no-slip wall, two-dimensional solutions are obs erved in some interval of Marangoni numbers. Beyond the Marangoni number fo r onset of inertial convection in two-dimensional simulations, the convecti ve flow becomes strongly intermittent because of the interplay of the flywh eel effect and three-dimensional instabilities of the two-dimensional rolls . The velocity field in this intermittent regime is characterized by the oc currence of very small vortices at the free surface which form as a result of vortex stretching processes. Similar structures were found with the free -slip bottom at slightly smaller Marangoni number. These observations demon strate that a high numerical resolution is necessary even at moderate Maran goni numbers in order to properly capture the small-scale dynamics of Maran goni convection at low Prandtl numbers.