Stability of roll waves in open channel flows. (English) Zbl 1177.76127

Boudlal, Abdelaziz; Liapidevskii, Valery Yu.

C. R., Méc., Acad. Sci. Paris 330, No. 4, 291-295 (2002).

Summary: We study the stability of finite amplitude roll waves that may develop at a liquid free surface in inclined open channels of arbitrary cross-section. In the framework of shallow water theory with turbulent friction, the modulation equations for wave series are derived and a nonlinear stability criterion is obtained.

MSC:

76E17	Interfacial stability and instability in hydrodynamic stability
76E30	Nonlinear effects in hydrodynamic stability
76B15	Water waves, gravity waves; dispersion and scattering, nonlinear interaction

Keywords:

shallow water theory; modulation equations; nonlinear stability criterion