# On kinematic waves I. Flood movement in long rivers

@article{Lighthill1955OnKW, title={On kinematic waves I. Flood movement in long rivers}, author={Michael James Lighthill and Gerald Beresford Whitham}, journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences}, year={1955}, volume={229}, pages={281 - 316} }

In this paper and in part II, we give the theory of a distinctive type of wave motion, which arises in any one-dimensional flow problem when there is an approximate functional relation at each point between the flow q (quantity passing a given point in unit time) and concentration k (quantity per unit distance). The wave property then follows directly from the equation of continuity satisfied by q and k. In view of this, these waves are described as ‘kinematic’, as distinct from the classical…

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