Modulation equations for wave flows of a fluid film along a vertical wall

Abstract

We considered the flow of a thin layer of a viscous Newtonian fluid along a vertical wall. In the long wave approximation, the set of equations describing the influence of the combined effects of nonlinearity and viscosity on the development of the wave mode of flow is of the hyperbolic type. For the two parametrical family of periodic wave flows (roll waves), we investi gated modulation equations and formulated the crite rion of nonlinear stability of wave packets. The self similar solutions of the modulation equations are used for explaining the features of the evolution of nonlin ear wave packets at the forced mode of development of perturbations in the fluid film