Mathematical Problems of the Dynamics of Incompressible Fluid on a Rotating Sphere
This book presents selected mathematical problems involving the dynamics of a two-dimensional viscous and ideal incompressible fluid on a rotating sphere. In this case, the fluid motion is completely governed by the barotropic vorticity equation (BVE), an
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Mathematical Problems of the Dynamics of Incompressible Fluid on a Rotating Sphere
Mathematical Problems of the Dynamics of Incompressible Fluid on a Rotating Sphere
Yuri N. Skiba
Mathematical Problems of the Dynamics of Incompressible Fluid on a Rotating Sphere
123
Yuri N. Skiba Center for Atmospheric Sciences National Autonomous University of Mexico Mexico, Distrito Federal, Mexico
ISBN 978-3-319-65411-9 ISBN 978-3-319-65412-6 (eBook) DOI 10.1007/978-3-319-65412-6 Library of Congress Control Number: 2017949885 Mathematics Subject Classification (2010): 76B25, 76B47, 76D03, 76D17, 76E09, 76E20 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To my wife Lina Strelkova
Preface
Some mathematical problems of the dynamics of a two-dimensional viscous and ideal incompressible fluid on a rotating sphere are studied in this book. In this case, the fluid motion is completely governed by the barotropic vorticity equation (BVE). The analysis of vortex dynamics on a sphere is important because this approach is more natural for meteorological applications as compared to, e.g., using a ˇ-plane approximation. Since the mid-twentieth century, this equation has played an important role in the study of hydrodynamic and meteorological processes. For example, in the case of an ideal fluid, a class of exact solutions of this equation represents meteorologically significant Rossby-Haurwitz waves, daily observed on the weather maps. In addition, the laws of conservation of enstrophy, total kinetic energy, and the average spectral number made it possible to study changes in the spectral distribution of the kine
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