A wave equation for a time-dependent perturbation about the steadyshallow-water solution emulates the metric an acoustic white hole, even uponthe incorporation of nonlinearity in the lowest order. A standing wave in thesub-critical region of the flow is stabilised by viscosity, and the resultingtime scale for the amplitude decay helps in providing a scaling argument forthe formation of the hydraulic jump. A standing wave in the super-criticalregion, on the other hand, displays an unstable character, which, althoughsomewhat mitigated by viscosity, needs nonlinear effects to be saturated. Atravelling wave moving upstream from the sub-critical region, destabilises theflow in the vicinity of the jump, for which experimental support has beengiven.
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