Combined thermocapillary-buoyancy convection has been investigated numerically in an extended cavity with differently heated walls. When the Marangoni number Ma grows, the unicellular flow is replaced by a steady bicellular or multicellular flow and then either by a hydrothermal wave or an oscillatory multicellular flow, depending on the dynamic Bond number ${\mathrm{Bo}}_{\mathrm{dyn}}.$ The appearance of a hydrothermal wave prevents the propagation of the stationary roll structure, which spreads from the hot side, over the whole cavity. The hydrothermal wave itself looks as a succession of the cells moving from the cold side towards the motionless rolls on the hot side. For an intermediate interval of ${\mathrm{Bo}}_{\mathrm{dyn}}$ the parallel flow is unstable with respect to the hydrothermal wave (HTW), but the multicellular periodic structure generated by the side-wall perturbation is stable, so that the HTW decays in space when propagating on the background of the multicellular structure. The nonlinear competition between finite-amplitude, boundary-induced steady patterns and hydrothermal waves is essential. A nonlinear simulation of flow regimes in a wide region of the values of dynamical Bond number and Marangoni number is presented. A number of phenomena that cannot be predicted in the framework of the linear stability theory, specifically those characteristic for the motion in the intermediate interval of ${\mathrm{Bo}}_{\mathrm{dyn}},$ as well as the secondary transition from steady to unsteady flows at large ${\mathrm{Bo}}_{\mathrm{dyn}},$ which takes place when the Marangoni number Ma grows, are described.

• Received 21 October 2002

DOI:https://doi.org/10.1103/PhysRevE.67.066308