Films over topography: from creeping flow to linear stability, theory and experiments, a review

The present review deals with the effects of topography and inertia on gravity-driven film flows. The article is organized like a rope ladder, with the rungs of topography and inertia being scaled one after another. We begin with an introduction, where we specify the literature reviewed in our article and highlight the physical significance of this type of fluid motion. Next, we address the effects of different types of topographies on creeping film flow and films in lubrication approximation, and on inertial flow. Then, findings on inertial flow with sidewalls as bounding topography are reviewed. In all these cases, the impact of topography and inertia on both the free surface and the flow field structure is shown. Subsequently, we briefly highlight inverse problem theory. The following penultimate section focuses on the stability of film flows. After a short review on the stability of films over flat inclines which we give for convenience, the stability of films over topography is considered. A discussion on the stability of films with sidewalls as bounding topography follows. In each case, the interaction between topography, flow field, and free surface is shown with the theoretical and experimental methods being discussed. Finally, the paper closes with some concluding remarks and an outlook from the authors' perspective-one century after the groundbreaking work of Wilhelm Nusselt.