Hysteresis induced by interaction of oblique hydraulic jumps on shallow water
A.N. Kudryavtsev1, U.V. Mikhailova1,2
1Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, Novosibirsk, Russia
2Novosibirsk State Technical University, Novosibirsk, Russia
Keywords: shallow water equations, regular reflection, Mach reflection, numerical simulation, hydraulic jumps, transition criteria, hysteresis
Abstract
Reflections of hydraulic jumps on shallow water are studied. Theoretical criteria of the transition between the regular and Mach reflections are derived, and it is shown that there is a domain of wave incidence angles where both types of reflection are possible. Numerical simulations reveal a hysteresis of this transition, which is consistent with theoretical predictions. It is shown that the hysteresis can be obtained by smoothly varying both the angle of the wedge generating the hydraulic jump and the free-stream Froude number.
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