The classical hydraulic jump in a model of shear shallow-water flows
Résumé
A conservative hyperbolic two-parameter model of shear shallow-water flows is used to study the classical turbulent hydraulic jump. The parameters of the model, which are the wall enstrophy and the roller dissipation coefficient, are determined from measurements of the roller length and the deviation from the Belanger equation of the sequent depth ratio (experimental data by Hager & Bremen, J. Hydraul. Res., vol. 27, 1989, pp. 565-585; and Hager, Bremen & Kawagoshi, J. Hydraul. Res., vol. 28, 1990, pp. 591-608). Stationary solutions to the model describe with a good accuracy the free-surface profile of the hydraulic jump. The model is also capable of predicting the oscillations of the jump toe. We show that if the upstream Froude number is larger than similar to 1.5, the jump toe oscillates with a particular frequency, while for the Froude number smaller than 1.5 the solution becomes stationary. In particular, we show that for a given flow discharge, the oscillation frequency is a decreasing function of the Froude number.