On falling-film instabilities and wave breaking

Abstract

Long‐wave instabilities of thin viscous films flowing down inclined planes are studied. Numerical solutions of the full long‐wave evolution equation show that wave profiles grow superexponentially and evolve toward breaking when the surface tension takes on realistically small values. This contrasts with the solutions of the Kuramoto–Sivashinsky equation, which do not tend toward breaking. The use of the full equation thus dispenses with the need to introduce the formally small curvature terms into the Kuramoto–Sivashinsky equation, as suggessted by Rosenau and Oron [Phys. Fluids A 1, 1763 (1989)].