Routes to Absolute Instability in Porous Media

This book addresses the concepts of unstable flow solutions, convective instability and absolute instability, with reference to simple (or toy) mathematical models, which are mathematically simple despite their purely abstract character. Within this parad

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Routes to Absolute Instability in Porous Media

Routes to Absolute Instability in Porous Media

Antonio Barletta

Routes to Absolute Instability in Porous Media


Antonio Barletta Department of Industrial Engineering Alma Mater Studiorum Università di Bologna Bologna, Italy

ISBN 978-3-030-06193-7 ISBN 978-3-030-06194-4


Library of Congress Control Number: 2018964933 © Springer Nature Switzerland AG 2019 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. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

What we cannot speak about we must pass over in silence. Ludwig Wittgenstein


Stability theory has an old and venerable history in the context of fluid mechanics: much is known and much remains to be discovered. In our desire to model accurately our highly nonlinear world, it is quite natural to begin slowly by determining first the flow field for small values of a parameter such as the Reynolds, Rayleigh, Taylor or Görtler numbers. In such cases, the flow is slow and nonlinear effects are barely felt. Perhaps it is unsurprising then that such flows are stable, not that we have yet defined this word. One potential definition of stability might be that the flow is unique, but this idea is unsatisfactory because it mentions neither the presence of nor the rôle played by disturbances of any kind. Consideration of these matters is central to stability theory and is essential before pressing on to fully numerical simulations and the transition to turbulence. We all have an intuitive idea of what the words stable and unstable mean because they may be related to many aspects of human life and experience: nitroglycerine is unstable; a cyclist in motion is stable; a poorly constructed building

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