Influence of Relative Roughness and Reynolds Number on the Roll-Waves Spatial Evolution

The paper analyzes the influence of resistance coefficient dependence on flow variables, viscosity and wall roughness onto the spatial development of roll-waves in the initial phase. To this aim, two models, based on time-asymptotic solutions of linearized St. Venant equations, subjected to either impulsive or oscillating perturbation, have been modified by including the dependence of the resistance coefficient on flow conditions. Independently on the perturbation type, the results show that the hypothesis of constant resistance coefficient may lead to a non-negligible underestimation of the instability spatial growth rate. Theoretical achievements are compared with results of a fully non-linear model for several combinations of Froude and Reynolds numbers and relative roughness values. The comparison shows that the spatial linear analysis with a suitable oscillating perturbation allows to accurately reproduce both spatial growth rate and celerity of the roll-waves. Such findings have to be properly accounted for in defining criteria for roll-waves occurrence in natural and manmade channels.