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A Simple Analytic Description of Favre Waves

Author(s): Damien Violeau

Linked Author(s): Damien Violeau

Keywords: Dams; Undular bores; Favre waves; Dispersive waves

Abstract: The so-called ‘Favre waves’ can occur in a canal upstream of a dam when the gates are closed rapidly. They appear when the Froude number is smaller than a certain threshold; otherwise a hydraulic jump takes place. The Favre waves consist of a series of oscillations of the free surface propagating upstream, the first of which being about twice higher than the hydraulic jump that would occur otherwise. Predicting these waves are useful for hydraulic safety, i.e. in order to predict possible local flooding. The Favre waves belong to what is known since the 70s as ‘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 also 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. A first qualitative attempt has been done by Prüser and Zielke (1994) from the 1973 GP model; here we propose a quantitative comparison of both GP models with the experimental data by Soares-Frazão and Zech (2002). The 1987 GP model, which includes energy dissipation, is proved to predict better the laboratory data. References Gurevich, A.V., Pitaevskii, L.P. (1973), Nonstationary structure of a collision less shock wave, Sov. Phys. JETP 38(2):291. Gurevich, A.V., Pitaevskii, L.P. (1987), Averaged description of waves in the Korteweg–de Vries–Burgers equation, Sov. Phys. JETP 66(3):90. Prüser, H.-H., Zielke, W. (1994), Undular bores (Favre Waves) in open channels. Theory and Numerical Simulation, J. Hydr. Res. 32(3):337. Soares-Frazão, S., Zech, Y. (2002), Undular bores and secondary waves. Experiments and hybrid finite volume modeling, J. Hydr. Res. 40(1):33. Whitham, G.B. (1965), Non-linear dispersive waves, Proc. Roy. Soc. A 283:238.


Year: 2022

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