Buoyant-thermocapillary instabilities in extended liquid layers subjected to a horizontal temperature gradient

Abstract

We report experiments on buoyant-thermocapillary instabilities in differentially heated liquid layers. The results are obtained for a fluid of Prandtl number 10 in a rectangular geometry with different aspect ratios. Depending on the height of liquid and on the aspect ratios, the two-dimensional basic flow destabilizes into oblique traveling waves or longitudinal stationary rolls, respectively, for small and large fluid heights. Temperature measurements and space–time recordings reveal the waves to correspond to the hydrothermal waves predicted by the linear stability analysis of Smith and Davis @J. Fluid Mech. 132, 119 ~1983!#. Moreover, the transition between traveling and stationary modes agrees with the work by Mercier and Normand @Phys. Fluids 8, 1433 ~1996!# even if the exact characteristics of longitudinal rolls differ from theoretical predictions. A discussion about the relevant nondimensional parameters is included. In the stability domain of the waves, two types of sources have been evidenced. For larger heights, the source is a line and generally evolves towards one end of the container leaving a single wave whereas for smaller heights, the source looks like a point and emits a circular wave which becomes almost planar farther from the source in both directions.