VERIFICATION OF THEORY OF ROLL-WAVE FORMATION

The Vedernikov number V > 1 is the necessary condition for roll-wave f ormation. Using the theory of linear stability, Ponce and Simons in 19 77 confirmed the Vedernikov criterion for turbulent Chezy friction in hydraulically wide channels. In addition, they identified the scale of the disturbances under which roll waves are most likely to develop. B rock, in 1967, experimentally studied roll-wave propagation using a la boratory flume. Using Brock's data, an experimental verification of Po nce and Simons' theory is presented. Results show that dimensionless w ave numbers corresponding to the roll waves documented by Brock's stud y plot near the peak of the theoretical functional relation of logarit hmic decrement delta versus dimensionless wave number sigma. The analy sis confirms that roll waves are most likely to form for large positiv e values of the logarithmic decrement (delta > 0.2), located within a narrow center band of dimensionless wave numbers. In a practical setti ng, this knowledge can be used to promote or inhibit the development o f roll waves.