On falling-film instabilities and wave breaking

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)]