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 Contribution to the Theory of Undular Bores

 A journey around the Korteweg-de Vries equation

 With the support of EDFIAHR-WM-Portada_puzzle.jpg 

By Damien Violeau

Published: June 2022     

ISBN (electronic): 978-90-824846-9-4

ISBN (printed): 978-90-832612-0-1

The mission of Contribution to the Theory of Undular Bores. A journey around the Korteweg—de Vries equation is to describe some of the most important and classic theoretical features of undular bores, with the aim of enabling an engineer (or a non-specialist researcher) to journey through this beautiful topic of mathematical physics.Undular bores are water-surface oscillations that propagate between two levels of stationary water. They occur under various circumstances (such as tides, tsunamis, river dams and lock operations) and are a visible part of a larger group of physical phenomena termed dispersive shock waves. Readers will learn in a rigorous way but without difficult mathematical concepts, the theoretical developments that begun at the end of 19th century

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«This is a very interesting book on the computations of undular bores using the Korteweg—de Vries equation. The author is right in stating that the mathematical apparatus for the solution of this approach is not well known in hydraulic engineering, given that it mainly was developed by mathematicians and physicists working on ocean dynamics. From this perspective, I think it is a welcome idea to present this material under the umbrella of IAHR, thereby making it accessible to hydraulic engineers»

Oscar Castro-Orgaz

«The raison d’être of this text is obvious: it is written simply in an accessible and clear language. There are very few texts within the mathematical literature which could compete with the present manuscript in terms of clarity. The exposition is wonderfullly pedagogical, but this is unsurprising if you ever had the opportunity to listen to Prof. Violeau’s lectures»

Denys Dutykh

About the author


Damien Violeau was educated at Ecole des Ponts (literally, the ‘School of Bridges’), one of the most prestigious French scientific educational institutes, where he is now full professor. Also, he is a senior Research engineer at EDF, one of the biggest energy companies in the world. His main fields of interest are free-surface flows, turbulent flows, numerical simulation, coastal protection and river-water works. In 2015, he was awarded Arthur T. Ippen award by IAHR.

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This series presents information on physical processes, measurement techniques, theoretical material, numerical modeling techniques, engineering applications, and historical and cultural matters in an appealing readable and well-illustrated manner.

IAHR publishing tradition | Since 1984 supporting influential books

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  • Directly or in partnership with professional houses, IAHR has published the most renown books in the field of hydraulics, ie Turbulence Models and their Application in Hydraulics” by W Rodi, first published in 1984 by Balkema and I Nezu's book "Turbulence in Open Channel Flows and long-lasting books as Hydraulicians in Europe and Hydraulicians in USA by W. Hager

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  • An important function of any large international organisation is to disseminate the best elements of its discipline through learned works, specialised research publications and state of the art reviews.

  • IAHR is particularly well-served in this regard by its flagship journals and by the extensive and wide body of substantive historical and reflective books that have been published through its auspices over the years. 

  • This series is aimed to disseminate reference research work and state-of-the-art knowledge for researchers and practitioners in the many aspects of hydro-environmental engineering and research. OPEN and easily accessible. 

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