Section: New Results
Amoss : Comparison with experimental results and unreduced model on flat plane
Participants : B. Nkonga, H. Guillard, S. Gavrilyuck, Y-C. Tai, F. Yang, K.m. Shyue, C-Y Kuo.
The purpose of this work was the numerical study of the roll-waves that develop from a uniform unstable flow down an inclined rectangular channel. In particular, the formation of the roll-waves is studied by two different approaches. In the first approach, the roll-waves were produced in a long channel where a wave maker perturbed the free surface only at the channel inlet. The average discharge was fixed. In the second approach, the roll-waves were produced in a “periodic box” with a uniform flow velocity. The average depth of a perturbed free surface was the same as in the long channel. Formally, the “periodic box” and a long channel correspond to two different physical situations. However, the stationary profile formed for long time in these cases is the same. This allows us to use the “periodic box” as a simpler mathematical tool to study the asymptotic behavior of roll waves. In particular, the “periodic box” does not require a big space domain resolution. Several interesting phenomena were observed. First, it was proven that there exists Lmax such that any single roll wave of length