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D. J. TRITTON I SECOND EDITION I \7 I - t P O R D SCIENCE PUBLICATIONS

PHYSICAL FLUID DYNAMICS

PHYSICAL FLUID DYNAMICS Second Edition D. J. Tritton Formerly, Department of Physics, University of Newcastle upon Tyne CLARENDON PRESS OXFORD @

OXFORD UNIVERSITY PRESS Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan South Korea Poland Portugal Singapore Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York 0 D. J. Tritton, 1988 The moral rights of the author have been asserted Database right Oxford University Press (maker) First edition published by Van Nostand Reinhold (UK) 1977 Second edition 1988 Reprinted 1989,1990,1991,1992,1993, 1994,1995,1997,1998,1999,2001,2002,2003,2005,2007 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above. You must not circulate this book in any other binding or cover and you must impose this same condition on any acquirer. British Library Cataloguing in Publication Data Tritton, D. J. Physical fluid dynamics-2nd ed. 1. Fluid dynamics I. Title 5329.05 QC151 Tritton, D. J. Library of Congress Cataloging in Publication Data Physical fluid dynamicsID. J. Tritton-2nd Includes index. Bibliography: p. ed. 1. Fluid dynamics. I. Title QC15 1 .T74 1988 5329.05-dc19 87-34162 ISBN 978-0- 19-854493-7 (Pbk) Printed in Great Britain on acid-free paper by Biddles Ltd., King's Lynn, Norfolk

PREFACE TO THE SECOND EDITION I have been gratified by the comment, received from many people, that the first edition was a valuable addition to the range of textbooks on fluid dynamics-mainly its distinctive approach. This second edition endeavours to retain that approach, whilst introducing topics that have assumed greater importance since the first edition was prepared. because of The principal changes and additions are as follows. The discussion of separation is extended-and given a chapter of its own (Chapter 13)-to include a fuller explanation and to cover all cases, not just boundary layer separation. The treatment of instabilities has been substantially reorganized; the phenomenological description and the explanation of linear stability theory are now more intermingled in a single chapter (Chapter 17). BCnard convection is no longer used as an example in the main discussion of instabilities, but is given a brief introduction in Chapter 4 and a full treatment in Chapter 22; the treatment in the first edition was rather fragmented, and there have been substantial advances in our understanding since that material was written. The discussion is extended in Chapter 23 to cover double diffusive convection. Partly as a consequence of these changes, the material on other convection topics in Chapters 4 and 14 is rearranged-but covers much the same ground as before. In the discussion of the structure of turbulent motion (Chapter 21) the parts concerned with large-scale motions (coherent structures) have been completely rewritten. Chapter 24 discusses modern ideas about 'chaos'-not, strictly speaking a fluid dynamical topic, but certainly one that students of fluid dynamics need to know about. Outside the main text, the principal change is the addition of hints and answers for the problems. I have mixed feelings about the value of these. The temptation for a student to look at the hint too soon can be irresistable. However, this addition has been urged on me by a number of readers and on balance I now think that they are right. There are quite a lot of minor changes. I have gone through the whole text, considering whether clarification or updating was needed-and bearing in mind the many helpful comments received from readers. Illustrations have been replaced where more appropriate ones have become available. But much remains unchanged; I hope that the right balance has been struck between the dynamics of a new edition and continuity with the old. So many people have helped in one way or another that to list them all

vi PREFACE TO THE SECOND SDITION is impossible and to list some may be arbitrary. However, I have been particularly helped by expert advice on some of the sections in Chapter 26 from: Professor D. Etling of the University of Hannover (Section 26.2); Dr H. Tsoar of the Ben Gurion University of the Negev (26.4); Dr P. A. Davies of the University of Dundee (26.7); Mr R. G. Gawthorpe of the Railway Technical Centre, Derby (26.10); Dr A. D. W. Jones of B.P. Research Centre, Sunbury (26.11); Dr M. E. J. Holwill of King's College London (26.12); and Dr R. P. Clark of the M.R.C. Clinical Research Centre, Harrow (26.13). I hope that the people who have helped with other parts of the book will accept a blanket, but very sincere, thank you. Many people have provided originals of photographs and diagrams, for which I am most grateful. The originators of all photographs and sets of data are indicated in the captions or by the references. Acknowledgements to bodies who have given permission for the reproduction of copyright material are listed separately. In the preparation of the book I have been much helped by the technical skills of Mrs D. Cooper, who draughted the new diagrams, Mr J. Hunter and Mr G. Robb and the secretarial skills of Mrs L. Whiteford. Finally, my thanks go to the staff of the Oxford University Press for their friendly and efficient collaboration. Newcastle upon Tyne August 1987

FROM T H E PREFACE TO T H E FIRST EDITION? To classify a book as 'experimental' rather than 'theoretical' or as 'pure' rather than 'applied' is liable to imply unreal distinctions. Nevertheless, some classification is necessary to tell potential readers whether the book is for them. In this spirit, this book mapbe said to treat fluid dynamics as a branch of physics, rather than as a branch of applied mathematics or of engineering. I have often heard expressions of the need for such a book, and certainly I have felt it in my own teaching. I have written it primarily for students of physics and of physics-based applied science, although I hope others may find it useful. The book differs from existing 'fundamental' books in placing much greater emphasis on what we know through laboratory experiments and their physical interpretation and less on the mathematical formalism. It differs from existing 'applied' books in that the choice of topics has been made for the insight they give into the behaviour of fluids in motion rather than for their practical importance. There are differences also from many existing books on fluid dynamics in the branches treated, reflecting to some extent shifts of interest in recent years. In particular, geophysical and astrophysical applications have prompted important fundamental developments in topics such as convection, stratified flow, and the dynamics of rotating fluids. These developments have hitherto been reflected in the contents of textbooks only to a limited extent. Much of the book is based on lectures I have given to final year physics students at the University of Newcastle upon Tyne, though I have substantially expanded parts of the material. I have also been influenced by teaching fluid dynamics both at a more elementary level and also to postgraduate students of geophysics and planetary physics. I have tried to learn which approaches to various topics students find most informative, and I hope this experience has led to improvements in what I have written. I have had the final year physics students particularly in mind when deciding what background knowledge to assume of the reader. The mathematical methods used should all be familiar to such students (although substantial parts of the book would be intelligible to a reader at t In this shortened version, the chapter and section numbers refer to the present edition.

... w FROM THE PREFACE TO THE FIRST EDITION an earlier mathematical stage). Also, it is not really paradoxical that a book aimed at physics students should contain less explanation of basic physics (such as related thermodynamics) than some other fluid dynamics texts; knowledge of this can reasonably be assumed. Nevertheless, I hope that the book will be of value to a variety of other types of reader and I have tried to extend its usefulness wherever this has been possible without distorting the primary aim. Workers in widely various types of applied science need an understanding of the phenomena of fluid motion. I have in mind particularly, but not solely, geo- and planetary physicists (meteorologists and oceanographers as well as students of planetary interiors), of whose needs I probably have the most immediate appreciation. Where fluid dynamical topics are taught as part of a geophysics course, I believe that this should be a suitable textbook. I believe also that postgraduate students and other research workers, faced with a project involving fluid dynamics, should find this book of value. It is not uncommon for otherwise interesting geophysical papers to be marred by the employment of fluid dynamical concepts in a way that shows serious misunderstanding of their significance. But these misunderstandings are not surprising in the absence of convenient sources of information. Such readers should not imagine that there are easy short-cuts to an understanding of the phenomena of fluid motion, but I trust that this book may make the long route a little less arduous. The choice of topics in a book of this sort must be controversial. The size of the subject necessitates many arbitrary omissions. The reader wishing to discover just what is included and what is omitted may find it useful to refer not only to the contents list but also to Section 1.2. The major limitation is the restriction to incompressible flow. This will, I know, make the book inadequate for some courses. Compressible flow is, however, such a large topic that it really requires a book of its own; just a chapter would perhaps do it more of an injustice than total omission. Even within the limitation to incompressible flow, I am much aware of omissions that some readers will regret. What I hope I have achieved is a text giving students sufficient knowledge of the basic concepts of fluid dynamics and sufficient insight into the consequences of these concepts that they will be able to use other (probably more advanced) sources to obtain information that is omitted here. The systematic development of the subject occupies Chapters 5 to 24. After the introduction in Chapter I, Chapters 2 to 4 treat three particular topics in a descriptive (thought hopefully not too superficial) way. These topics have been placed ahead of the systematic treatment for two reasons. Primarily they are intended to give the reader some understand- ing of the type of phenomena with which one is concerned; it is a long haul through the basic concepts of Chapters 5 to 8 if one does not know

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