Studying the topological structure of steady-state travelling solutions for the model of film flow of a viscous fluid entrained by a gas flow

Abstract

The article studies nonlinear waves on a liquid film, flowing under the action of gravity in a known stress field at the interface. In the case of small flow rates for the long-wave modes, the problem is reduced to solving a nonlinear equation for the film thickness deviation from the undisturbed level. The paper presents the results of calculations for this model equation of families of steady-state travelling periodic solutions. For these families, the limiting solutions, solitary waves, have been found. It is also investigated how the topological reorganization of such families occurs with a smooth change in the degree of influence of the gas flow. It is shown that although the eigenform of specific solitons changes smoothly, for certain values of the problem parameter for a particular family an abrupt change in the shape of its limiting soliton occurs.