An accurate modeling of thin film flows down an incline for inertia dominated regimes

An accurate modeling of a wavy film flow down an inclined plane is developed using the weighted residual technique which was first proposed by Ruyer-Quil and Manneville [Eur. Phys. J. B 15 (2000) 357]. The model includes third order terms in order to better capture the effects of small Weber and high Reynolds numbers. This is made possible by an appropriate refinement of the velocity profile. To this end, a free parameter α acting on the flexibility of the velocity profile is introduced. It is shown, from linear stability analysis that the model follows quite closely, for a suitable choice of α, the Orr-Sommerfeld equation for all Weber and Kapitza numbers. The improvement is of course more substantial in the inertia dominated regimes. Some prominent qualitative and quantitative characteristics of traveling wave solutions are then derived from a simplified version of the model that is before hand converted into a three dimensional dynamical system.