Modulational instability analysis of surface-waves in the Bénard-Marangoni phenomenon
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Kraenkel, Roberto André [UNESP]
Manna, M. A.
Pereira, J. G. [UNESP]
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By using the long-wave approximation, a system of coupled evolutions equations for the bulk velocity and the surface perturbations of a Bénard-Marangoni system is obtained. It includes nonlinearity, dispersion and 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 Nonlinear Schrödinger 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 existence or not of a Benjamin-Feir instability in the long-wave limit. © 1995.
Physica D: Nonlinear Phenomena, v. 87, n. 1-4, p. 356-360, 1995.