An accurate low dimension model for the waves on thin layer fluid flowing down an inclined plane

This technical brief deals with the surface instability mode of a liquid film flowing down an inclined plane. A four-equation model that describes the development of the film depth, the flow rate, the free-surface velocity, and the wall shear stress is proposed. The obtained results were found to be in very good agreement with experimental and theoretical results of Liu et al. (1993, "Measurements of the Primary Instability of Film Flow,"J. Fluid Mech., 250, pp. 69-101) and Brevdo et al. (1999, "Linear Pulse Structure and Signalling in Film Flow on an Inclined Plane,"J. Fluid Mech., 396, pp. 37-71).