INERTIAL BENARD-MARANGONI CONVECTION

Two-dimensional surface-tension-driven Benard convection in a layer wi th a free-slip bottom is investigated in the limit of small Prandtl nu mber using accurate numerical simulations with a pseudospectral method complemented by linear stability analysis and a perturbation method. It is found that the system attains a steady state consisting of count er-rotating convection rolls. Upon increasing the Marangoni number Ma the system experiences a transition between two typical convective reg imes. The first one is the regime of weak convection characterized by only slight deviations of the isotherms from the linear conductive tem perature profile. In contrast, the second regime, called inertial conv ection, shows significantly deformed isotherms. The transition between the two regimes becomes increasingly sharp as the Prandtl number is r educed. For sufficiently small Prandtl number the transition from weak to inertial convection proceeds via a subcritical bifurcation involvi ng weak hysteresis. In the viscous zero-Prandtl-number limit the trans ition manifests itself in an unbounded growth of the flow amplitude fo r Marangoni numbers beyond a critical value Ma(i). For Ma < Ma(i) the zero-Prandtl-number equations provide a reasonable approximation for w eak convection at small but finite Prandtl number. The possibility of experimental verification of inertial Benard-Marangoni convection is b riefly discussed.