Simulating nonlinear wavy flow modes developing in a thin horizontal layer of heavy liquid entrained by a gas flow
O.Yu. Tsvelodub^{1,2}
^{1}Kutateladze Institute of Thermophysics SB RAS, Novosibirsk, Russia ^{2}Novosibirsk State University, Novosibirsk, Russia
Keywords: горизонтальный слой вязкой жидкости, газовый поток, модельная система, эволюционное уравнение, устойчивость, horizontal layer of viscous fluid, gas flow, model system, evolution equation, stability
Abstract
The paper considers nonlinear waves generated on a surface of a horizontal liquid layer put into an assigned stress field at the gasliquid interface. The nature of branching for wavy modes from the undisturbed flow was studied. To accomplish this, the solution of a model nonlinear equation written for the deviation of the layer thickness from the undisturbed layer is found. Analytical solutions were constructed for nonlinear steady statetravelling solutions of this equation with the wavenumbers belonging to the vicinity of neutral wavenumbers. Steady statetravelling periodic solutions for the first family were simulated for the case of wavenumbers beyond this vicinity.
