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Standing and travelling waves in the shallow-water circular hydraulic jump

Arnab K. Ray·J. K. Bhattacharjee
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Abstract

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.

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Arnab K. Ray, J. K. Bhattacharjee. 2007-11-07. Standing and travelling waves in the shallow-water circular hydraulic jump. https://doi.org/10.1016/j.physleta.2007.07.073

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