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Dispersive and dispersive-like bores in channels with sloping banks

Published online by Cambridge University Press:  14 May 2019

R. Chassagne ,
A. G. Filippini ,
M. Ricchiuto Open the ORCID record for M. Ricchiuto [Opens in a new window]  and
P. Bonneton Open the ORCID record for P. Bonneton [Opens in a new window]
R. Chassagne
Affiliation:
University Grenoble Alpes, Irstea, ETNA, 38000 Grenoble, France
A. G. Filippini
Affiliation:
University of Bordeaux, CNRS, UMR 5805 EPOC, Allée Geoffroy Saint-Hilaire, F-33615 Pessac, France
M. Ricchiuto*
Affiliation:
Team CARDAMOM, Inria Bordeaux – Sud-Ouest, 200 Avenue de la Vieille Tour, 33405 Talence CEDEX, France
P. Bonneton
Affiliation:
University of Bordeaux, CNRS, UMR 5805 EPOC, Allée Geoffroy Saint-Hilaire, F-33615 Pessac, France
*
†Email address for correspondence: [email protected]
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Abstract

In this paper a detailed analysis of undular bore dynamics in channels of variable cross-section is presented. Two undular bore regimes, low Froude number (LFN) and high Froude number (HFN), are simulated with a Serre–Green–Naghdi model, and the results are compared with the experiments by Treske (1994). We show that contrary to Favre waves and HFN bores, which are controlled by dispersive non-hydrostatic mechanisms, LFN bores correspond to a hydrostatic phenomenon. The dispersive-like properties of the LFN bores is related to wave refraction on the banks in a way similar to that of edge waves in the near shore. A fully hydrostatic asymptotic model for these dispersive-like bores is derived and compared to the observations, confirming our claim.

JFM classification

Waves/Free-surface Flows: Channel flow Geophysical and Geological Flows: Shallow water flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 870 , 10 July 2019 , pp. 595 - 616
Copyright
© 2019 Cambridge University Press 

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