Initial phenomenon of roll wave of shallow water on inclined channel
Intermittent surges of debris flows are observed in mountain regions. This type of flow is considered to be characterized by developing roll waves (surges) due to flow instabilities and by a weak sediment concentrations. For a understanding of initial phenomenon and fluctuation of the flow depth, wave equations and understanding characteristics of the solutions are needed. It is presented a wave equation and some solutions of roll waves based on shallow water momentum equation. These results show an improved understanding of the phenomena and wave equation of developing roll wave.
2. WAVE EQUATION AND SOME SOLUTIONS
Considering momentam equation of shallow water on inclined channel and using reductive perturbation method, a wave equation which is a kind of KdV-Burgers equation was obtained. For on long wave velocity, some analitical solutions and numerical solutions ware obtained. Relationships of wave equation, it's solutions and phenomenon are discussed.
A wave of minute disturbance on long wave velocity is governed by Burgers equation. For not fixed boundary condition and initial wave condition of not multiple wave number, an initial wave is deformed to a wave which wave number is one.
The wave is caused a phase and the phenomena is shifted from Burgers equation to KdV-Burgers equation which has the characteristic of the solitary wave.