Abstract
By generalising an approach due to Gurtin, the Bernoulli equation is derived which governs the amplitude of an acceleration wave propagating on the surface of water at rest in a vertical walled channel of arbitrarily varying width and depth. Integration of the equation yields an explicit expression for the amplitude of the acceleration wave as a function of position, together with a simple criterion for determining when a wave will break. A special case of a non-breaking elevation wave propagating into deepening water is also found.
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