Turbulent and inertial roll waves in inclined film flow

Abstract

Conditions for the onset of high Reynolds number roll waves on inclined interfaces are sought. The model equations of Dressler [Commun. Pure Appl. Math. 2, 149 (1949)] and Needham and Merkin [Proc. R. Soc. London Ser. A 394, 259 (1984)] are analyzed using dynamic singularity theory (normal form techniques) and numerical methods. A new family of roll-wave solutions is discovered. They provide bounds and averages of the velocities of all roll waves at a given Froude number. These are favorably compared to the data of Brock [Proc. Am. Soc. Civ. Eng. 12, 2565 (1970)] and Brauner and Maron [Int. J. Heat Mass Transfer 25, 99 (1982)]. The average wave velocity is demonstrated to be approximately 1.5 times the average fluid velocity.