Abstract
This paper considers the roll-wave phenomenon on thin laminar viscous flow down an inclined plane wall on the basis of hydraulic equations which are derived on the assumptions of long wave and parabolic velocity profile. Wave fronts are approximated by discontinuous jumps satisfying physical laws. The solution for the permanent roll-wave train obtained involves one free parameter, and is insufficient to explain observed results. Then, the stability of the said solution to infinitesimal disturbances is investigated. It is found that the roll-wave train is unstable if its wave length is shorter than a certain critical value. Furthermore, wave lengths of the most stable waves are favourably compared with those of waves observed in experiments.
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