Three-dimensional flow instabilities in a thermocapillary-driven cavity

A linear stability analysis of the buoyant-thermocapillary flow in open rectangular cavities with aspect ratios in the range Gamma=1.2 to 8 is carried out for Prandtl number Pr=10 and conditions of previous experiments. The results are in very good agreement with most available experimental data. The energy transfer between the basic and the perturbation flow reveals that buoyancy is not directly instrumental in the instabilities. For aspect ratios less than about three a stationary three-dimensional cellular flow arises. The instability relies on the lift-up mechanism operating in the shear layer below the free surface and it is aided by weak Marangoni forces. For larger aspect ratios Marangoni effects play a more significant role. While plane hydrothermal waves may appear a certain distance away from the hot wall for sufficiently large aspect ratios, the instability at intermediate aspect ratios is strongly influenced by the local nonparallel basic-flow structure.