A generalized, non-linear, diffusion wave equation: Theoretical development and application

Murugesu Sivapalan, Bryson C. Bates, Jens E. Larsen

Research output: Contribution to journalArticlepeer-review


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 ε where ε is a characteristic ratio of the water surface slope to the bed slope. The derivations are carried out using a general expression for flow 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.

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalJournal of Hydrology
Issue number1-4
StatePublished - May 1997
Externally publishedYes

ASJC Scopus subject areas

  • Water Science and Technology


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