### Abstract

The derivation of a generalized, non-linear, diffusion wave equation, which explicitly includes inertial effects, is presented. The generalized equation is an approximation to the Saint-Venant equations of order epsilon, where epsilon is a characteristic ratio of the water surface slope to the bed slope. The derivations are carried out using a general expression for how resistance, representing both friction and form drag. Some simplified forms of the generalized diffusion wave equation, useful for different practical applications, are given, A numerical finite difference model, solving a particular simplified form of the generalized equation, is used to simulate a number of observed floods in a natural river reach, The model is then used to investigate the effects of non-linearity on the characteristics of flood wave propagation. (C) 1997 Elsevier Science B.V.

Original language | English |
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Pages (from-to) | 1-16 |

Journal | Journal of Hydrology |

Volume | 192 |

Issue number | 1-4 |

DOIs | |

Publication status | Published - 1997 |

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## Cite this

Sivapalan, M., Bates, B. C., & Larsen, J. E. (1997). A generalized, non-linear, diffusion wave equation: theoretical development and application.

*Journal of Hydrology*,*192*(1-4), 1-16. https://doi.org/10.1016/S0022-1694(96)03116-2