A reduced nonlinear model for density stratified viscous film flowing down a slightly inclined wall is derived and explored. Under buoyancy stable stratification the system exhibits various long-wavelength instabilities of noninertial, purely kinetic origin. Unlike many existing models for the film interface evolution in the present study regularization of the pertinent long-scale dynamics is provided directly by the film viscosity rather than surface tension.
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Kliakhandler et al. (1997) studied this question.