, Volume 2, Issue 4, pp 347-366
Date: 12 Oct 2012

A dispersive model for undular bores

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Abstract

In this article, consideration is given to weak bores in free-surface flows. The energy loss in the shallow-water theory for an undular bore is thought to be due to upstream oscillations that carry away the energy lost at the front of the bore. Using a higher-order dispersive model equation, this expectation is confirmed through a quantitative study which shows that there is no energy loss if dispersion is accounted for.

This article is dedicated to the memory of our friend and colleague Vladimir Varlamov.