Abstract
A solution for the weak bore is found in which the mean profile is dominated by viscosity, so that the velocity variation is given essentially by a quasi-uniform Poiseuille flow. It is found that such a transition between flows of different depths is possible provided the Froude number is less than 1·58. The possibility of superposing an inviscid perturbation on such a flow is then investigated. Under favourable circumstances the effect of this perturbation is to add to the profile of the free surface a term which decays exponentially in front of the bore, but is oscillatory behind it.
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