A simple analytic description of Favre waves

The so-called 'Favre waves' can occur in a canal upstream of a dam when the gates are closed rapidly. The Favre waves belong to 'Dispersive Shock Waves' (DSW). The theory of DSW was initiated after the pioneering work of Whitham (1965) who showed how non-linear, dispersive waves can be described following a modulation theory. In his seminal paper, Whitham applied his theory to the Korteweg-de Vries equation (KdV), among others. Later on, Gurevich and Pitaevskii (1973, 1987) proposed two analytical models to described DSW from the KdV equation following Whitham's modulation theory. In the present work, we show that Gurevich and Pitaevskii's models (GP) can well predict Favre waves. We propose a quantitative comparison of both GP models with the experimental data by Soares- Frazao and Zech (2002). The 1987 GP model, which includes energy dissipation, is proved to predict better the laboratory data.