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}
}
  • M. Lighthill, G. Whitham
  • Published 10 May 1955
  • Mathematics
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
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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    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
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On kinematic waves II. A theory of traffic flow on long crowded roads
  • M. Lighthill, G. Whitham
  • Engineering, Computer Science
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1955
TLDR
The theory of kinematic waves is applied to the problem of estimating how a ‘hump’, or region of increased concentration, will move along a crowded main road, and is applicable principally to traffic behaviour over a long stretch of road.
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