Modeling the Spatial Evolution of Roll Waves with Diffusive Saint Venant Equations

Abstract

In this paper, modeling the spatial evolution of roll waves with diffusive Saint Venant equations is examined. A momentum diffusion term is added to the equations to describe turbulent normal stress occurring in extremely nonuniform roll waves. Roll-wave flows with the same hydraulic conditions as in Brock’s experiment are simulated so as to obtain time-averaged wave crest and trough depths. The magnitude of the diffusion effect is found to have significant influence on the spatial growth rate of the wave amplitude. Simulated wave crest and trough depths along the channel agree with experimental data only when the proper turbulent viscosity value is selected. This study indicates that the nondiffusive Saint Venant equations are unable to describe roll-wave flows because the wave amplitude is largely overestimated. The Saint Venant–type model should incorporate comprehensive turbulent stresses and appropriate closure approaches for predicting the spatial evolution of roll waves.