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