The N-Vortex Problem Analytical Techniques
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Paul K. Newton
The N- Vortex Problem Analytical Techniques
With 79 Figures
Springer
Paul K. Newton Department of Aerospace and Mechanical Engineering and Department of Mathematics University of Southern California Los Angeles, CA 90089-1191 USA [email protected]
Editors Jerrold E. Marsden Control and Dynamical Systems, 107-81 California Institute of Technology Pasadena, CA 91125 USA
Lawrence Sirovich Division of Applied Mathematics Brown University Providence, RI 02912 USA
Mathematics Subject Classification (2000): 37199, 37NIO, 76B47 Library of Congress Cataloging-in-Publication Data Newton, Paul K. The N-Vortex problem: analytical techniques / Paul K. Newton p. cm. - (Applied mathematical sciences; 145) Includes bibliographical references and index. 1. Vortex-motion. I. Title. New York, Inc.) ; v. 145. QAl .A647 no. 145 [QA925) 510 s-dc21 [532'.0595)
II. Applied mathematical sciences (Springer-Verlag
00-053198
Printed on acid-free paper. © 2001 Springer-Verlag New York, Inc.
Softcover reprint of the hardcover 1st edition 2001 All rights reserved. This work may not be translated or copied in whole or in part without the written pennission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 1001 0, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production managed by Michael Koy; manufacturing supervised by 1acqui Ashri. Photocomposed copy prepared from the author's LATEX2e files.
987654321 ISBN 978-1-4419-2916-7 ISBN 978-1-4684-9290-3 (eBook) DOl 10.1007/978-1-4684-9290-3 Springer-Verlag New York Berlin Heidelberg A member of Berte/smannSpringer Science+Business Media GmbH
This book is dedicated with all my love
to Lynn and Daniel.
Preface
This book is an introduction to current research on the N-vortex problem of fluid mechanics in the spirit of several works on N-body problems from celestial mechanics, as for example Pollard (1966), Szebehely (1967), or Meyer and Hall (1992). Despite the fact that the field has progressed rapidly in the last 20 years, no book covers this topic, particularly its more recent developments, in a thorough way. While Saffman's Vortex Dynamics (1992) covers the general theory from a classical point of view, and Marchioro and Pulvirenti's Mathematical Theory of Incompressible Nonviscous Fluids (1994), Doering and Gibbon's Applied Analysis of the Navier-Stokes Equations (1995), and Majda and Bertozzi's Vorticity and Incompressible Flui
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