Modulation Equations for Roll Waves on Vertically Falling Films of a Power-Law Fluid

Abdelaziz Boudlal, Valery Liapidevskii

Laboratoire de Mecanique de Lille, UMR CNRS 8107, Villeneuve d’Ascq, France.
Lavrentyev Institute of Hydrodynamics, Novosibirsk State University, Novosibirsk, Russia.

DOI: 10.4236/wjm.2012.21001                

Abstract

Waves of finite amplitude on a thin layer of non-Newtonian fluid modelled as a power-law fluid are considered. In the long wave approximation, the system of equations taking into account the viscous and nonlinear effects has the hyper- bolic type. For the two-parameter family of periodic waves in the film flow on a vertical wall the modulation equations for nonlinear wave trains are derived and investigated. The stability criterium for roll waves based on the hyperbolicity of the modulation equations is suggested. It is shown that the evolution of stable roll waves can be described by self-similar solutions of the modulation equations.

Keywords

Power-Law Fluid; Thin Film Flow; Vertical Wall; Modulation Equations; Nonlinear Stability; Roll Wave

Conflicts of Interest

The authors declare no conflicts of interest.

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