Stability of return thermocapillary flows under gravity modulation

The effect of gravity modulation on the stability of a time-harmonic parall el flow in a slot geometry is studied. A constant temperature gradient appl ied along the length of a slot with a flat free interface at the top drives a steady thermocapillary return flow. A vertical time-harmonic gravity mod ulation drives a time-periodic buoyant return flow. The relative strength o f the two components is characterized by the Marangoni number Ma and the Ra yleigh number Ra, respectively. There is potential for Rayleigh-Benard, she ar, and hydrothermal wave instabilities. The linear stability for two-dimen sional rolls is studied and the stability boundaries are obtained by Floque t theory. Stability diagrams in the Ra-Ma plane are obtained for fixed modu lation frequency and various Prandtl numbers and a disturbance kinetic-ener gy analysis is used to determine the instability mechanism. Buoyant and hyd rothermal instabilities are found at small Ma and small Ra, respectively, w hereas shear instabilities are found not to be important in the parameter r egime studied. The two active mechanisms are found to either reinforce or o ppose each other in different parameter regimes. This leads to regions of s tability in the Ra-Ma plane where flows are stable due to the combined effe ct of buoyancy and thermocapillarity whereas a purely buoyant or a purely t hermocapillary flow at the same Ra or Ma would be unstable. These results a re contrasted with those obtained by Nield [J. Fluid Mech. 19, 341 (1964)] in the case of steady gravity, for which thermocapillarity and buoyancy rei nforce each other. (C) 2001 American Institute of Physics.