Propagation of a bore produced by the sudden break of a dam

Abstract

In this paper we study the progress of a bore, produced by the sudden break of a dam, when there is a flow of water ahead of the dam and the bed has a mild slope and offers resistance, employing Whitham's rule. We first derive certain interesting results from the general discussion of the differential equation, expressing the variation of the bore strength with the undisturbed Froude number, M₀, ratio of bedslope to bed resistance, gα/R = a² and the bore strength M(x) Ξ {h(x)/h₀(x)} where h(x) and h₀(x) are the bore height and the undisturbed height of the water immediately ahead of the bore, the horizontal distance x being measured from the dam. The parameters M₀ and a₂ combine to influence the bore strength in a very special way. We also examine the asymptotic cases when the bore strength M and M 1. The intermediate cases are investigated numerically to bring out the effects of the parameters, α, a₂, M₀ and the dam height on the strength of the bore, its velocity and the fluid velocity behind it.