> C. Ruyer-Quil
Gravity film flow down a smooth plate and corrugated surface
Yuri Trifonov (Institute of Thermophysics, Siberian Branch of Russian Academy of Sciences, Novosibirsk)
The presentation is devoted to a theoretical analysis of a wavy film flow down both a smooth and corrugated vertical plate. We use the Navier-Stokes equations in their full statement and the integral approaches to describe the liquid film hydrodynamics. We consider a wavy interface over a wide variation of parameters. It is well known that the film flow with a smooth free surface down a vertical flat wall is unstable at all values of Reynolds number and we can observe the flat interface only over some distance at the liquid inlet. We found the nonlinear traveling waves and carried out an analysis of their stability and bifurcations using the Floquet theory. In the case of a corrugated vertical wall, there is a region of the parameters (amplitude and period of the corrugations) where all perturbations decay in time at moderate values of Reynolds number. In this case the wall corrugation demonstrates a stabilizing effect. At the same time, there exist corrugation parameters at which the steady-state solution is unstable with respect to perturbations of the same period as the period of corrugation and the solution cannot be observed even at the liquid inlet. The wall corrugation demonstrates a destabilizing effect. We consider also the more complicated regimes of flow down a corrugated wall that are formed as a result of the instability.