Simulating the nonlinear wave mode evolution in the problem of the falling thin layer of a viscous liquid

All-Russian Conference with the School for Young Scientists “Thermophysics and Physical Hydrodynamics –2016”

Vozhakov, I.S.^1,2 ; Arkhipov, D.G.^1 ; Tsvelodub, O. Yu^1

Kutateladze Institute of Termophysics, SB, RAS, Lavrentev Ave. 1, Novosibirsk

630090, Russia^1

Novosibirsk State University, Pirogov Str. 2, Novosibirsk

630090, Russia^2

关键词: Calculation results;    Flowing liquid;    Model equations;    Nonlinear periodic waves;    Nonlinear waves;    Reduced basis;    Traveling solutions;    Viscous liquids;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/754/3/032022/pdf
DOI  :  10.1088/1742-6596/754/3/032022

来源: IOP

【 摘 要 】

The work is devoted to numerical simulation of the dynamics of nonlinear periodic waves on the surface of freely flowing liquid film realized with the use of the previously discovered symmetry of model equations. The calculation results have been presented for the dynamics of amplitudes of significant harmonics and for the wave surface evolution. They prove to be in good agreement with previously calculated steady-state traveling solutions obtained on the full and the reduced bases. In addition, the work has identified intervals of wavenumbers in which the evolution of perturbations with small initial amplitude leads to a wave signal periodically changing in time rather than to the steady-state traveling solution.