Oscillatory instability and high-frequency wave modes in a Marangoni-Benard layer with deformable free surface

A linear analysis of oscillatory thermocapillary instability associated wit h deformation of the free surface in a finite-depth horizontal liquid layer heated from above is carried out. First, we numerically solve the problem and determine the conditions of marginal stability. Then, assuming that Gal ileo and Marangoni numbers are large enough while the capillary number is s mall enough, which corresponds to the time scales of transverse and longitu dinal oscillations related to the free surface being much smaller than the characteristic viscous and thermal time scales, we construct an asymptotic solution of the problem. Two high-frequency overstable modes - transverse ( capillary-gravity waves) and longitudinal - are identified and analyzed. Mo de-mixing occurring at their possible resonance is also studied.