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Modern Fluid Dynamics for Physics and Astrophysics Graduate Texts in Physics Graduate Texts in Physics Oded Regev Orkan M. Umurhan Philip A. Yecko Modern Fluid Dynamics for Physics and Astrophysics Graduate Texts in Physics Series editors Kurt H. Becker, PhD New York, USA Sadri Hassani Urbana, Illinois, USA Jean-Marc Di Meglio Paris, France Bill Munro Kanagawa, Japan Richard Needs Cambridge, UK William T. Rhodes Boca Raton, Florida, USA Professor Susan Scott Canberra, Australia Professor H. Eugene Stanley Boston, Massachusetts, USA Martin Stutzmann Garching, Germany Andreas Wipf Jena, Germany Graduate Texts in Physics publishes core learning/teaching material for graduate and advanced-level undergraduate courses on topics of current and emerging fields within physics, both pure and applied. These textbooks serve students at the MS- or PhD-level and their instructors as comprehensive sources of principles, definitions, derivations, experiments and applications (as relevant) for their mastery and teaching, respectively. International in scope and relevance, the textbooks correspond to course syllabi sufficiently to serve as required reading. Their didactic style, comprehensiveness and coverage of fundamental material also make them suitable as introductions or references for scientists entering, or requiring timely knowledge of, a research field. More information about this series at http://www.springer.com/series/8431 Oded Regev • Orkan M. Umurhan • Philip A. Yecko Modern Fluid Dynamics for Physics and Astrophysics 123 Oded Regev Orkan M. Umurhan Technion, Haifa, Israel NASA Ames Research Center Moffett Field, CA, USA Philip A. Yecko The Cooper Union New York, USA ISSN 1868-4513 ISSN 1868-4521 (electronic) Graduate Texts in Physics ISBN 978-1-4939-3163-7 ISBN 978-1-4939-3164-4 (eBook) DOI 10.1007/978-1-4939-3164-4 Library of Congress Control Number: 2015954646 Springer New York Heidelberg Dordrecht London © Springer Science+Business Media, LLC 2016 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. Printed on acid-free paper Springer Science+Business Media LLC New York is part of Springer Science+Business Media (www. springer.com) We dedicate this book to our teacher, colleague, and friend Edward A. Spiegel Foreword Panta rhei Heraclitus of Ephesus (c. 535–c. 475 BC) In the last hundred years or so, there has been substantial development in fluid dynamics, though it seems to have been “left behind” by physicists, because of a shift in their focus to fundamental quantum mechanics and particle physics. The study of this classical subject was dropped from most curricula of physics departments the world over. This split physicists and astrophysicists to those concentrating on cosmology and high-energy physics, in their quest for the “Holy Grail” of quantum gravity, and those who took on more classical unsolved prob- lems. Alongside other topics like plasma physics, kinetic theory, and dynamical systems theory, fluid dynamics (FD) and magnetohydrodynamics (MHD) are today disciplines formulated as branches of physics. Therefore, their study is essential not only for the physics graduate student, who chooses to do his or her research in a field related to fluid dynamics, but also for graduate students in a number of additional physical disciplines, as well as for their supervisors and scientists, many of whom have had to learn the subject on their own because FD was not part of their formal studies when they themselves were graduate students. There is little doubt, at least in our opinion, that FD and MHD are indispensable for, e.g., a mathematical or condensed matter physicist, astrophysicist, geophysicist, and biophysicist and should be taught as a compulsory graduate course. In this book, we concentrate on FD with one chapter on MHD. In our view, it would be impossible to cover all the topics of FD and MHD in sufficient depth. Thus we had to make a subjective choice as to what can be omitted without missing our main goal: endowing the relevant PhD student with solid knowledge vii viii Foreword of FD and a basic one of MHD. Moreover, both FD and MHD, as disciplines by themselves, are advancing rapidly in their evermore sophisticated experimental and observational aspects, as well as in both the utilization of powerful digital computers for the solution of problems and the expansion of analytical tools applied toward developing a better understanding of the underlying nonlinear phenomena and mechanisms. For example, there are new ideas on transition to turbulence via transiently growing stable linear modes and perhaps linear, or nonlinear, secondary instabilities, new approaches to turbulence itself, which still remain an enigma of fluid dynamics despite intensive research efforts and advances and expanded use of asymptotic approximation methods, which give analytical or semi-analytical results to complement numerical treatments. Advancing the understanding of the nonlinear aspects of FD is important to relevant physical and astrophysical study, and this is generally achieved with the aid of numerical solutions of governing nonlinear equations. Consequently, it has become an ever-increasing modern practice to simulate flows on computers, and as such, we briefly discuss (in Appendix B) some important considerations that should be taken into account when developing numerical codes. It is in this sense that the word “modern” in the title of this work should be understood: the subject obviously remains classical with those forays into nonlinearity and digital computing considered as a “modern” flavor. Because of the diversity of various university programs around the world offering graduate study in physics and astrophysics (e.g., departments of physics, astrophysics, and sometimes even mathematics and geophysics), we do not presume to suggest at what point in the training of the graduate student a thorough course in FD, like the one based on this book, should be included, leaving such delib- erations to curriculum committees. Before courses in FD were routinely adopted by astronomy and astrophysics departments and even physics departments, books on the topic were typically self-contained and drew examples from a variety of fields. For example, Landau and Lifshitz included Fluid Mechanics in their course of theoretical physics, and that volume, the second edition of which was actually written by Lifshitz and Pitaevskii, quickly acquired the status of a classic and has been used by physics and astrophysics students for (often enigmatic) self-study. Close to the turn of the millennium, the Department of Physics of the Technion- Israel Institute of Technology yielded (rather reluctantly) to the pressure of a growing number of faculty members, whose research (and of their students) was in astrophysics, soft condensed matter, and biophysics, to offer a course in FD. One of us (O.R.) was tasked in preparing the course entitled The physics of Fluids (a nineteenth-century subject, according to some who consider anything not “quantum” as not belonging to modern physics) to be taught to senior undergraduate and graduate students in the department. The course turned out to be an exceptional success among senior undergraduate and graduate students. Students of astrophysics and also of several fields of condensed matter, biophysics, and mathematical physics, plus a substantial group of engineering students, as well as some established researchers in several fields, attended. This book is largely based on that course. Owing to its success, this course began to be offered regularly, approximately every 2 years, by the Technion Department of Physics. Foreword ix To the best of our knowledge, most astronomy, astrophysics, and geophysics departments (which prefer books using their own approach and nomenclature) include nowadays in their curricula a serious course on fluid dynamics, and this is also the case in most physics departments. As mentioned above, this book is on a senior undergraduate or graduate level, depending, of course, on the different institutions’ programs and syllabi. It contains too much material for a one-semester course, and the various departments will have to decide what will be the scope of specific senior undergraduate and graduate courses. It is assumed that the students are mathematically equipped with a working knowledge of analysis, including intermediate-level ordinary and partial differential equations, as well as a good command of vector calculus and linear algebra. In physics, the student will benefit by having already taken some courses more advanced than introductory undergraduate
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