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"Although there are many texts and monographs on fluid dynamics, I do not know of any which is as comprehensive as the present book. It surveys nearly the entire field of classical fluid dynamics in an advanced, compact, and clear manner, and discusses the various conceptual and analytical models of fluid flow." - Foundations of Physics on the first editionTheoretical Fluid Dynamics functions equally well as a graduate-level text and a professional reference. Steering a middle course between the empiricism of engineering and the abstractions of pure mathematics, the author focuses on those ideas and formulations that will be of greatest interest to students and researchers in applied mathematics and theoretical physics. Dr. Shivamoggi covers the main branches of fluid dynamics, with particular emphasis on flows of incompressible fluids. Readers well versed in the physical and mathematical prerequisites will find enlightening discussions of many lesser-known areas of study in fluid dynamics.This thoroughly revised, updated, and expanded Second Edition features coverage of recent developments in stability and turbulence, additional chapter-end exercises, relevant experimental information, and an abundance of new material on a wide range of topics, including:* Hamiltonian formulation* Nonlinear water waves and sound waves* Stability of a fluid layer heated from below* Equilibrium statistical mechanics of turbulence* Two-dimensional turbulence
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THEORETICAL FLUID DYNAMICS This page intentionally left blank Theoretical Fluid Dynamics Second Edition B h i m s e n K. S h i v a m o g g i University of Central Florida Orlando, Florida A Wiley Interscience Publication J O H N WILEY & SONS, INC. New York · Chichester · Weinheim · Brisbane · Singapore · Toronto This book is printed on acid-free paper. Copyright ©1998 by John Wiley & Sons, Inc. All rights reserved Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (508) 750-8400, fax (508) 750-4744. Requests to the Publisher for permission should be addressed to the permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008, E-Mail: PERMREQ @ WILEY.COM. Library of Congress Cataloging in Publication Data: Shivamoggi, Bhimsen K. Theoretical fluid dynamics / Bhimsen K. Shivamoggi. — 2 n d ed. p. cm. Includes bibliographical references and index. ISBN 0-471-05659-6 (cloth : alk. paper) 1. Fluid dynamics. I. Title. QA911.S463 1997 532.05—dc21 97-10383 10 9 8 7 6 5 4 3 2 1 Seek therefore to find of what and how the world is made, so that you may learn a better way of life. —Pythagoras TO MY MOTHER WITH LOVE AND RESPECT This page intentionally left blank CONTENTS Preface xvii Acknowledgments xix Chapter 1. Review of Basic Concepts and Equations of Fluid Dynamics 1 1.1 Introduction to Fluid Dynamics 1 Fluid Model of Systems 1 The Objective of Fluid Dynamics 1 The Fluid State 2 Description of the Flow Field 3 Volume Forces and Surface Forces 4 Relative Motion Near a Point 7 Stress-Strain Relations 10 Equations of Fluid Flows 11 The Transport Theorem