Nonstationary periodic spatial waves on the surface of a viscous liquid film falling down a vertical cylinder

The flows of viscous liquid film over the outer surface of a vertical cylinder are examined. Investigation of wave regimes in the case of low flow rates and large cylinder radii is reduced to the analysis of solutions to a nonlinear evolution equation for the film thickness. There are countable numbers of steady-state traveling solution families in the considered model. In turn, most of them are unstable to 2D and 3D perturbations. Thus, evolution of initial perturbations in different ranges of parameter values differs significantly. Some typical scenarios of perturbation development are presented in this work. Initial perturbations with some symmetries, kept in the process of evolution, are of a particular interest. In these cases, solutions are drawn up to the steady-state traveling solutions with similar symmetry.