MODULATIONAL INSTABILITY ANALYSIS OF SURFACE-WAVES IN THE BENARD-MARANGONI PHENOMENON

By using the long-wave approximation, a system of coupled evolution eq uations for the bulk velocity and the surface perturbations of a Benar d-Marangoni system is obtained. It includes nonlinearity, dispersion a nd dissipation, and it is interpreted as a dissipative generalization of the usual Boussinesq system of equations. Then, by considering that the Marangoni number is near the critical value M = -12, we show that the modulation of the Boussinesq waves is described by a perturbed No nlinear Schrodinger Equation, and we study the conditions under which a Benjamin-Feir instability could eventually set in. The results give sufficient conditions for stability, but are inconclusive about the ex istence or not of a Benjamin-Feir instability in the long-wave limit.