V. Ya. Shkadov and G. M. Sisoev

Moscow State University

Abstract

The parameters of regular nonlinear waves observed in experiments at the finite liquid rates are reproduced by numerical solution of film's equations. The film shapes, velocities, rates and amplitudes of waves are calculated as solutions of the bifurcation problem. The most complete analysis describing bifurcations of the periodical wave families including that known up to now and new ones is presented. To select regular waves realizable in experiments with small initial perturbations of waveless flows the attractors of nonstationary problem have been investigated. In the cases of nonuniqueness of periodical solutions at fixed wavelength the so--called dominating wave that defined as regular periodical wave with maximal values of amplitude and phase velocity is formed. Attractive properties of regular waves and their stability by the numerical solution at large time interval with help of stable computation methods are defined. It is shown that evolution in time of initial value problem for model equations leads to dominating regime which is not depend on small initial perturbations. The evolution of dominating waves have been carried out at different liquid rates (Reynolds numbers). It is assumed that regular waves observed in experiments at result of spatial development from small perturbations are the same as dominating waves with equal length. With help of tables containing parameters of dominating waves the basic experimental results on regular waves in different liquids known to the present are reproduced.