Three-equation model for a thin layer fluid flowing down an inclined plane

This paper deals with the linear stability of a liquid film flowing down an inclined plane. Using the integral method of moment, the Navier-Stokes equations were reduced into three evolution equations that describe the development of the film depth, the flow rate, and the wall shear stress. Thus, we were able to determine the linear stability threshold and approach well the critical wave number for long waves. Wave properties obtained with the proposed model were found to be in good agreement with experiments. Via the formalism of absolute-convective stability based on the Briggs' collision criteria, we find that the film flow is absolutely stable and convectively unstable for low and moderate Reynolds numbers. Our results are in good agreement with theoretical results found in the literature.