Nonlinear waves on a liquid film falling down an inclined corrugated surface

Abstract

In the present study, we performed the direct Navier-Stokes computations on the linear and nonlinear stability of a gravity-driven film flow down an inclined corrugated surface. We focused on the steady-state traveling waves and analyzed their transformations due to the wall corrugations. These solutions have two spatial periods and we have used a double Fourier expansion to compute them. The systematic variations of the Reynolds number and the substrate’s periodicity and amplitude were performed in the nonlinear wave analysis. We found that starting from some “critical” values of the Reynolds number, the wall corrugation has a small influence on the film thickness profile of the traveling waves, and it is close to the waves on the liquid film falling down a smooth plate. This “critical” value strongly depends on the substrate’s periodicity and amplitude. To our knowledge, this is the first theoretical work where the nonlinear waves on the free surface of a liquid film over the topography is computed using the full Navier-Stokes equations.