The decision of the General Assembly of the International Union of Theoretical and Applied Mechanics to organize a Symposium on Dynamics of Slender Vortices was greeted with great enthusiasm. The acceptance of the proposal, forwarded by the Deutsches Komitee fiir Mechanik (DEKOMECH) signalized, that there was a need for discussing the topic chosen in the frame the IUTAM Symposia offer. Also the location of the symposium was suitably chosen: It was decided to hold the symposium at the RWTH Aachen, where, years ago, Theodore von Karman had worked on problems related to those to be discussed now anew. It was clear from the beginning of the planning, that the symposium could only be held in the von Karman-Auditorium ofthe Rheinisch-Westfalische Technische Hochschule Aachen, a building named after him. The symposium was jointly organized by the editors of this volume, strongly supported by the local organizing committee. The invitations of the scientific committee brought together scientists actively engaged in research on the dynamics of slender vortices. It was the aim of the committee to have the state of the art summarized and also to have the latest results of specific problems investigated communicated to the participants of the symposium. The topics chosen were asymptotic theories, numerical methods, vor tices in shear layers, interaction of vortices, vortex breakdown, vortex sound, and aircraft and helicopter vortices.

Elementary vortices – those tubular swirling vortical structures with concentrated vorticity commonly observed in various kinds of turbulent flows – play key roles in turbulence dynamics (e.g. enhancement of mixing, diffusion and resistance) and characterize turbulence statistics (e.g. intermittency). Because of their dynamical importance, manipulation of elementary vortices is expected to be effective and useful in turbulence control as well as in construction of turbulence modeling. The most advanced research works on elementary vortices and related problems were presented and discussed at the IUTAM Symposium in Kyoto, Japan, 26-28 October 2004. This book contains 40 contributions presented there, the subjects of which cover vortex dynamics, coherent structures, chaotic advection and mixing, statistical properties of turbulence, rotating and stratified turbulence, instability and transition, dynamics of thin vortices, finite-time singularity, and superfluid turbulence. The book should be useful for readers of graduate and advanced levels in the field of fluid turbulence.

Proceedings of the IUTAM Symposium held in Liverpool, UK, 8-11 July 2002

Nonlinearity and stochastic structural dynamics is of common interest to engineers and applied scientists belonging to many disciplines. Recent research in this area has been concentrated on the response and stability of nonlinear mechanical and structural systems subjected to random escitation. Simultaneously the focus of research has also been directed towards understanding intrinsic nonlinear phenomena like bifurcation and chaos in deterministic systems. These problems demand a high degree of sophistication in the analytical and numerical approaches. At the same time they arise from considerations of nonlinear system response to turbulence, earthquacke, wind, wave and guidancy excitations. The topic thus attracts votaries of both analytical rigour and practical applications. This books gives important and latest developments in the field presenting in a coherent fashion the research findings of leading international groups working in the area of nonlinear random vibration and chaos.

The goals ofthe Symposium were to highlight advances in modelling ofatmosphere and ocean dynamics, to provide a forum where atmosphere and ocean scientists could present their latest research results and learn ofprogress and promising ideas in these allied disciplines; to facilitate interaction between theory and applications in atmosphere/ocean dynamics. These goals were seen to be especially important in view ofcurrent efforts to model climate requiring models which include interaction between atmosphere, ocean and land influences. Participants were delighted with the diversity ofthe scientific programme; the opportunity to meet fellow scientists from the other discipline (either atmosphere or ocean) with whom they do not normally interact through their own discipline; the opportunity to meet scientists from many countries other than their own; the opportunity to hear significant presentations (50 minutes) from the keynote speakers on a range ofrelevant topics. Certainly the goal ofcreating a forum for exchange between atmosphere and ocean scientists who need to input to create realistic models for climate prediction was achieved by the Symposium and this goal will hopefully be further advanced by the publication ofthese Proceedings.

New developments in the applications of fracture mechanics to engineering problems have taken place in the last years. Composite materials have extensively been used in engineering problems. Quasi-brittle materials including concrete, cement pastes, rock, soil, etc. all benefit from these developments. Layered materials and especially thin film/substrate systems are becoming important in small volume systems used in micro and nanoelectromechancial systems (MEMS and NEMS). Nanostructured materials are being introduced in our every day life. In all these problems fracture mechanics plays a major role for the prediction of failure and safe design of materials and structures. These new challenges motivated the author to proceed with the second edition of the book. The second edition of the book contains four new chapters in addition to the ten chapters of the first edition. The fourteen chapters of the book cover the basic principles and traditional applications, as well as the latest developments of fracture mechanics as applied to problems of composite materials, thin films, nanoindentation and cementitious materials. Thus the book provides an introductory coverage of the traditional and contemporary applications of fracture mechanics in problems of utmost technological importance. With the addition of the four new chapters the book presents a comprehensive treatment of fracture mechanics. It includes the basic principles and traditional applications as well as the new frontiers of research of fracture mechanics during the last three decades in topics of contemporary importance, like composites, thin films, nanoindentation and cementitious materials. The book contains fifty example problems and more than two hundred unsolved problems. A "Solutions Manual" is available upon request for course instructors from the author.

To Turbulence by ARKADY TSINOBER Department of Fluid Mechanics, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBookISBN: 0-306-48384-X Print ISBN: 1-4020-0110-X ©2004 Kluwer Academic Publishers NewYork, Boston, Dordrecht, London, Moscow Print ©2001 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook maybe reproducedor transmitted inanyform or byanymeans, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://kluweronline. com and Kluwer's eBookstoreat: http://ebooks. kluweronline. com TO My WITS TABLE OF CONTENTS 1 INTRODUCTION 1 Brief history 1 1. 1 1. 2 Nature and major qualitative universal features of turbulent flows 2 1. 2. 1 Representative examples of turbulent flows 2 1. 2. 2 In lieu of definition: major qualitative universal f- tures of turbulent flows 15 1. 3 Why turbulence is so impossibly difficult? The three N's 19 On the Navier-Stokes equations 19 1. 3. 1 1. 3. 2 On the nature of the problem 21 1. 3. 3 Nonlinearity 22 1. 3. 4 Noninegrability 22 Nonlocality 1. 3. 5 23 1. 3. 6 On physics of turbulence 24 1. 3. 7 On statistical theories 24 1. 4 Outline of the following material 25 1. 5 In lieu of summary 26 2 ORIGINS OF TURBULENCE 27 2. 1 Instability 27 2. 2 Transition to turbulence versus routes to chaos 29 2.