Verification of Theory of Roll‐Wave Formation

The Vedernikov number $V>1$ is the necessary condition for roll‐wave formation. Using the theory of linear stability, Ponce and Simons in 1977 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. Brock, in 1967, experimentally studied roll‐wave propagation using a laboratory flume. Using Brock's data, an experimental verification of Ponce and Simons' theory is presented. Results show that dimensionless wave numbers corresponding to the roll waves documented by Brock's study plot near the peak of the theoretical functional relation of logarithmic decrement $\Delta$ versus dimensionless wave number $\sigma$. The analysis confirms that roll waves are most likely to form for large positive values of the logarithmic decrement $\left(\delta >0.2\right)$, located within a narrow center band of dimensionless wave numbers. In a practical setting, this knowledge can be used to promote or inhibit the development of roll waves.