Ra. Kraenkel et al., DISSIPATIVE BOUSSINESQ SYSTEM OF EQUATIONS IN THE BENARD-MARANGONI PHENOMENON, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 49(2), 1994, pp. 1759-1762
By using the long-wavelength approximation, a system of coupled evolut
ion equations for the bulk velocity and the surface perturbations of a
Benard-Marangoni system is obtained. It includes nonlinearity, disper
sion, and dissipation, and it can be interpreted as a dissipative gene
ralization of the usual Boussinesq system of equations. As a particula
r case, a strictly dissipative version of the Boussinesq system is obt
ained.