Lectures on the Theory of Water Waves

A range of experts contribute introductory-level lectures on active topics in the theory of water waves.

Thomas J. Bridges (Edited by), Mark D. Groves (Edited by), David P. Nicholls (Edited by)

9781107565562, Cambridge University Press

Paperback / softback, published 4 February 2016

298 pages, 50 b/w illus.
22.8 x 15.2 x 1.7 cm, 0.43 kg

'In 2014, there was a special four-week programme on water waves at the Isaac Newton Institute for mathematical Sciences in Cambridge. A large group of experts gathered together to look at the state of the art and to develop a strategy for future directions of research … This is not an introductory text, in that it really requires some serious background from e.g. an undergraduate degree programme … However, it should provide an excellent overview for those keen to move into the field and would therefore be a good introduction for Ph.D. students, as well as being good for specialists wishing to widen their expertise … This would have been a stimulating and rewarding programme to have attended, and these papers give a very useful resource summarising the current state of this research area - one which is likely to prove interesting, demanding and probably elusive for a long time to come!' Frank Berkshire, Contemporary Physics

In the summer of 2014 leading experts in the theory of water waves gathered at the Newton Institute for Mathematical Sciences in Cambridge for four weeks of research interaction. A cross-section of those experts was invited to give introductory-level talks on active topics. This book is a compilation of those talks and illustrates the diversity, intensity, and progress of current research in this area. The key themes that emerge are numerical methods for analysis, stability and simulation of water waves, transform methods, rigorous analysis of model equations, three-dimensionality of water waves, variational principles, shallow water hydrodynamics, the role of deterministic and random bottom topography, and modulation equations. This book is an ideal introduction for PhD students and researchers looking for a research project. It may also be used as a supplementary text for advanced courses in mathematics or fluid dynamics.

Preface Thomas J. Bridges, Mark D. Groves and David P. Nicholls
1. High-Order Perturbation of Surfaces (HOPS) Short Course – boundary value problems David P. Nicholls
2. HOPS Short Course – traveling water waves Benjamin F. Akers
3. High-Order Perturbation of Surfaces (HOPS) Short Course – analyticity theory David P. Nicholls
4. HOPS Short Course – stability of travelling water waves Benjamin F. Akers
5. A novel non-local formulation of water waves Athanassios S. Fokas and Konstantinos Kalimeris
6. The dimension-breaking route to three-dimensional solitary gravity-capillary water waves Mark D. Groves
7. Validity and non-validity of the nonlinear Schrödinger equation as a model for water waves Guido Schneider
8. Vortex sheet formulations and initial value problems: analysis and computing David M. Ambrose
9. Wellposedness and singularities of the water wave equations Sijue Wu
10. Conformal mapping and complex topographies André Nachbin
11. Variational water wave modelling: from continuum to experiment Onno Bokhove and Anna Kalogirou
12. Symmetry, modulation and nonlinear waves Thomas J. Bridges.

Subject Areas: Mathematical physics [PHU], Fluid mechanics [PHDF], Mathematical modelling [PBWH], Numerical analysis [PBKS], Differential calculus & equations [PBKJ]