With the support of Khalifa University of Science and Technology. 

By Didier Clamond, Denys Dutykh and Dimitrios Mitsotakis.

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Published: January 2024

ISBN (electronic):978-90-833476-6-0
ISBN (printed): 978-90-833476-7-7
ISSN: 2959-7978

This Water Monograph shows the benefit of using relaxed variational methods for the water waves problem. It illustrates the advantage of using a variational principle involving as many dependent variables as possible. Its primary purpose here is to provide a generalized framework for deriving model equations for water waves. This methodology is elucidated through a range of examples, a number of which are entirely novel.

Opinions from experts

"This Water Monograph takes the subject of variational principles for water waves to a new level. Lagrangians such as Luke’s are improved via relaxation where a sequence of constraints are added, enforced by Lagrange multipliers, that may be exact or approximate and, in the latter case, a range of new and surprising model equations for water waves emerge, without the need to introduce a small parameter. It is a highly effective strategy and produces Lagrangian, Hamiltonian and multisymplectic structures with equal ease."

Prof. Tom Bridges, University of Surrey, UK

“There are various interesting and new results offered worthy of a great monograph: constrained modelling with rotational aspect leading to advanced Serre-type equations, the seemingly improved shallow-water modelling over uneven bottoms and very good numerical results.”

Prof. Onno Bokhove, University of Leeds, UK

“This monograph provides an excellent introduction into the topic of model equations arising from the relaxed variational principle. This includes many well-known approximate models, such as Serre and Green–Naghdi equations, but also several new model equations. The main idea is that one can choose different approximations for all parameters in the relaxed Lagrangian.”

Dr. Evgeniy Lokharu, Lund University, Sweden

The manuscript is very well-written, accessible, and of appropriate length. The main results are clearly stated. For each new model which is proposed, the physical limits are discussed with scientific honesty and rigour. The authors wish to convince the reader that the variational formulations are more efficient and much simpler to derive approximate models than classical asymptotic expansions. Indeed, the manuscript is rather convincing and nevertheless very interesting to read. Overall, the present monograph is a very valuable contribution to the understanding of the water waves problem, both from the theoretical point of view and the numerical point of view.

Dr. Boris Kolev, ENS Paris-Saclay, France

How to cite

Clamond, Didier, Dutykh, Denys, Mitsotakis, Dimitrios. Variational approach to water waves modelling. IAHR WATER MONOGRAPHS, International Association for Hydro-Environment Engineering and Research (IAHR), Spain. (2024) https://doi.org/10.3850/978-90-833476-6-0_IAHR_Watermonograph_003

https://www.iahr.org/library/infor?pid=29802