Vorticity, Statistical Mechanics, and Monte Carlo Simulation
This book is drawn from across many active fields of mathematics and physics, and has connections to atmospheric dynamics, spherical codes, graph theory, constrained optimization problems, Markov Chains, and Monte Carlo methods. It addresses how to access
- PDF / 5,038,361 Bytes
- 295 Pages / 441 x 666 pts Page_size
- 80 Downloads / 221 Views
Chjan Lim
Joseph Nebus
Vorticity, Statistical Mechanics, and Monte Carlo Simulation
Chjan Lim Department of Mathematical Sciences Rensselaer Polytechnic Institute Troy, NY 12180-3590 USA [email protected]
Joseph Nebus Department of Mathematics National University of Singapore Singapore [email protected]
Mathematics Subject Classification (2000): 76-01, 76B47, 82-01, 82B26, 82B80 Library of Congress Control Number: 2006930876 ISBN-10: 0-387-35075-6 ISBN-13: 978-0387-35075-2 Printed on acid-free paper. © 2007 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, 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 in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 springer.com
To Siew Leng and Sean – CCL To Joseph Francis and Dr Mary Casey – JN
Preface
This book is meant for an audience of advanced undergraduates and graduate students taking courses on the statistical mechanics approach to turbulent flows and on stochastic simulations. It is also suitable for the self-study of professionals involved in the research and modelling of large scale stochastic fluid flows with a substantial vortical component. Several related ideas motivate the approach in this book, namely, the application of equilibrium statistical mechanics to two-dimensional and 2.5dimensional fluid flows in the spirit of Onsager [337], and Kraichnan [227], is taken to be a valid starting point, and the primary importance of non-linear convection effects combined with the gravitational and rotational properties of large scale stratified flows over the secondary effects of viscosity is assumed. The latter point is corroborated by the many successful studies of fluid viscosity which limit its effects to specific and narrow regions such as boundary layers, and to the initial and transient phases of the experiment such as in the Ekman layer and spin-up [154] [344]. The main point of applying equilibrium statistical methods to the problems in this book is underscored by the values of the Knudsen number K = λ/l (where λ is the mean free path of the molecules of the fluid and l is the smallest relevant macroscopic length scale in the flow) in the body of twodimensional and 2.5-dimensional large scale fluid flows treated here, namely K < 10−6 . We further elucidate this point by stressing the fact that in this book, the methods of statistical mechanics are applied not to the fluid as an ensemble of molecules but rather to the flow as an ensemble of vorticity p
Data Loading...
