Coarsening Dynamics of Roll Waves

Abstract

Our community will be forever grateful to Steve Davis for exposing us to the myriad of fascinating interfacial dynamics that exist on thin films. One of us (HCC) entered the field after reading Steve’s clear exposition of the Benney equation for falling films. Due precisely to the film’s thinness, which Benney exploited in his longwave lubrication simplification, thin-film or shallow-water waves are typically dissipative and strongly nonlinear. As such, they are distinctly different from deep-water waves and their rich dynamics are beyond the classical inverse scattering and inviscid wave theories. Fortunately, their strongly nonlinear and dissipative nature allows a completely different coherent-structure approach that exploits the prevalence of robust and localized solitary wave structures. Here, we demonstrate this new approach on roll waves that appear on inclined shallow-water channel flow.