2007 (IPP)

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Standing and travelling waves in the shallow-water circular hydraulic jump
(2007-08-20) Ray, Arnab K.; Bhattacharjee, Jayanta K.
A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical region of the ﬂow is stabilised by viscosity, and the resulting time scale for the amplitude decay helps in providing a scaling argument for the formation of the hydraulic jump. A standing wave in the super-critical region, on the other hand, displays an unstable character, which, although somewhat mitigated by viscosity, needs nonlinear effects to be saturated. A travelling wave moving upstream from the sub-critical region, destabilises the ﬂow in the vicinity of the jump, for which experimental support has been given