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Emergence of dispersion in shallow water hydrodynamics via modulation of uniform flow

Published online by Cambridge University Press:  18 November 2014

Thomas J. Bridges
Thomas J. Bridges*
Affiliation:
Department of Mathematics, University of Surrey, Guildford, Surrey GU2 7XH, UK
*
†Email address for correspondence: [email protected]
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Abstract

A new theory for the emergence of dispersion in shallow water hydrodynamics in two horizontal space dimensions is presented. Starting with the key properties of uniform flow in open-channel hydraulics, it is shown that criticality is the key mechanism for generating dispersion. Modulation of the uniform flow then leads to model equations. The coefficients in the model equations are related precisely to the derivatives of the mass flux, momentum flux and mass density. The theory gives a new perspective – from the viewpoint of hydraulics – on how and why key shallow water models like the Korteweg–de Vries equation and Kadomtsev–Petviashvili equations arise in the theory of water waves.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 761 , 25 December 2014 , R1
Copyright
© 2014 Cambridge University Press 

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