E-Book Overview
The work covers asymptotic methods for the derivation of canonical evolution equations, such as the Korteweg-deVries and nonlinear Schrödinger equations, descriptions of the basic solution sets of these evolution equations, and the most relevant and compelling applications. These themes are interlocked, and this will be demonstrated throughout the text. The topics address any fluid flow application, but there is a bias towards geophysical fluid dynamics, reflecting for the most part the areas where many applications been found.
E-Book Content
SpringerWien NewYork CISM COURSES AND LECTURES Series Editors: The Rectors Giulio Maier - Milan Jean Salenfon - Palaiseau Wilhelm Schneider - Wien The Secretary General Bemhard Schrefler - Padua Executive Editor Carlo Tasso - Udine The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences. INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES COURSES AND LECTURES - No. 483 NONLINEAR WAVES IN FLUIDS: RECENT ADVANCES AND MODERN APPLICATIONS EDITED BY ROGER GRIMSHAW LOUGHBOROUGH UNIVERSITY, UK SpringerWien NewYork The publication of this volume was co-sponsored and co-financed by the UNESCO Venice Office - Regional Bureau for Science in Europe (ROSTE) and its content corresponds to a CISM Advanced Course supported by the same UNESCO Regional Bureau. This volume contains 31 illustrations This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 2005 by CISM, Udine Printed in Italy SPIN 11405276 In order to make this volume available as economically and as rapidly as possible the authors' typescripts have been reproduced in their original forms. This method unfortunately has its typographical limitations but it is hoped that they in no way distract the reader. ISBN 3-211-25259-2 SpringerWienNewYork PREFACE Although nonlinear waves occur in nearly all branches of physics and engineering, there is an amazing degree of agreement about the fundamental concepts and the basic paradigms. The underlying unity of the theory for linearized waves is already well-established, with the importance of such universal concepts as group velocity and wave superposition. For nonlinear waves the last few decades have seen the emergence of analogous unifying comcepts. The pervasiveness of the soliton concept is amply demonstrated by the ubiquity of such models as the Korteweg-de Vries equation and the nonlinear Schrodinger equation. Similarly, there is a universality in the study of wave-wave interactions, whether deterministic or statistical, and in the recent developments in the theory of wave-mean flow interactions. The aim of this text is to present the basic paradigms of weakly nonlinear waves in fluids. This book is the outcome of a CISM Summer School held at Udine from September 20-24, 2004.. Like the lectures given there the text covers asymptotic methods for the derivation of canonical evolution equations, such as the Kortewegde Vries and nonlinear Schrodinger equations, descriptions of the basic solution sets of these evolution equations, and the most relevant and compelling applications. These themes are interlocked, and this will be demonstrated throughout the text . The topics address any fluid flow application, but there is a bias towards geophysical fluid d