Surface Wave on a Viscous Fluid Film down an Inclined Uneven Wall

The paper is devoted to a theoretical study of nonlinear wave on a free-surface thin film down an inclined uneven plane. The problem is quite different from that of a viscous films flow along a smooth surface. Thus nondimensional variables are introduced in two ways according to the different relationship of the shallow water parameter and the topography parameter. Further, the zero-order and first-order stream function are derivated on the basis of perturbation method. Finally, the equations which govern the surface height of surface wave on a viscous fluid film down an inclined uneven wall are obtained.