Improved two-equation model for thin layer fluid flowing down an inclined plane problem

We are presenting a substantial improvement to the two-equation model proposed by Usha and Uma [Phys. Fluids 16, 7 (2004)] for the thin film of fluid flowing down an inclined plane. Incorporating the shear stress in the parabolic velocity profile, we satisfy exactly a tangential dynamical condition at the free surface. This correction has significant implications on the occurrence conditions for both heteroclinic and Hopf bifurcations of long stationary waves.