Hydrodynamic Stability

Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.

Offers modern and numerical techniques for the stability of fluid flow with illustrations, an extensive bibliography, and exercises with solutions.

The great number of varied approaches to hydrodynamic stability theory appear as a bulk of results whose classification and discussion are well-known in the literature. Several books deal with one aspect of this theory alone (e.g. the linear case, the influence of temperature and magnetic field, large classes of globally stable fluid motions etc.). The aim of this book is to provide a complete mathe matical treatment of hydrodynamic stability theory by combining the early results of engineers and applied mathematicians with the recent achievements of pure mathematicians. In order to ensure a more operational frame to this theory I have briefly outlined the main results concerning the stability of the simplest types of flow. I have attempted several definitions of the stability of fluid flows with due consideration of the connections between them. On the other hand, as the large number of initial and boundary value problems in hydrodynamic stability theory requires appropriate treat ments, most of this book is devoted to the main concepts and methods used in hydrodynamic stability theory. Open problems are expressed in both mathematical and physical terms.

Hydrodynamic stability is of fundamental importance in fluid mechanics and is concerned with the problem of transition from laminar to turbulent flow. Drazin and Reid emphasise throughout the ideas involved, the physical mechanisms, the methods used, and the results obtained, and, wherever possible, relate the theory to both experimental and numerical results. A distinctive feature of the book is the large number of problems it contains. These problems not only provide exercises for students but also provide many additional results in a concise form. This new edition of this celebrated introduction differs principally by the inclusion of detailed solutions for those exercises, and by the addition of a Foreword by Professor J. W. Miles.

Publisher Description

Surveyed in this book are the kinetics of non-linear mass transfer and its effects on hydrodynamic stability in systems with intensive interphase mass transfer, in electrochemical systems with high current density and in chemically reacting systems. In Part 1 the non-linear mass transfer as a result of an intensive interphase mass transfer in the gas (liquid)-solid surface, gas-liquid and liquid-liquid systems is considered in the duffusion boundary layer approximation as well as in flat channel taking the longitudinal diffusion into account. The influence of the direction of the intensive interphase mass transfer on heat transfer and multi-component mass transfer is illustrated. Part 2 discusses non-linear mass transfer in electrochemical systems with high current density using the examples of the anode dissolving of metals in the electrolyte flow and the electro-separation of metals out of concentrated solutions. The theory of the measured electrochemical treatment of metals and alloys, which is a method of wide practical use, has been elaborated on this basis. In Part 3 the non-linear mass transfer in chemically reacting systems is considered in the cases of: non-linearity of the equations of the chemical reaction's kinetics and intensive interphase mass transfer or thermo-capillary effect due to chemical reactions. On this basis, the mechanisms and the macro-kinetics of the chemical transformations in the gas-liquid systems are discussed. Part 4 is dedicated to the chemical reaction kinetics in stationary two phase systems at an arbitrary contact time between phases. In Part 5 the effects of concentration gradients are considered in the approximations of the linear theory of the hydrodynamic stability of almost parallel flows. In systems with intensive interphase mass transfer, the Marangoni effect could also be observed, beside the effect of non-linear mass transfer. A comparative analysis of both effects is made in this book.

The study of hydrodynamic stability is fundamental to many subjects, ranging from geophysics and meteorology through to engineering design. This treatise covers both classical and modern aspects of the subject, systematically developing it from the simplest physical problems, then progressing chapter by chapter to the most complex, considering linear and nonlinear situations, and analysing temporal and spatial stability. The authors examine each problem both analytically and numerically: many chapters end with an appendix outlining relevant numerical techniques. All relevant fluid flows are treated, including those where the fluid may be compressible, or those from geophysics, or those that require salient geometries for description. Details of initial-value problems are explored equally with those of stability. As a result, the early transient period as well as the asymptotic fate for perturbations for a flow can be assessed. The text is enriched with many exercises, copious illustrations and an extensive bibliography and the result is a book that can be used with courses on hydrodynamic stability or as an authoritative reference for researchers.

Hydrodynamic stability is of fundamental importance in the mechanics of fluids and is mainly concerned with the problem of the transition to turbulence. This book is devoted to publication of original research papers, research-expository and survey articles with an emphasis on unsolved problems and open questions in the mathematical modeling and computational aspects of hydrodynamic stability. Review chapters on the mathematical modeling and numerical simulation aspects of hydrodynamic stability, the physical background, and the limitations of the modeling and simulation procedures, due to particular mathematical or computational methods used, are included. This book will be appropriate for use in research and in research-related courses on the subject. It includes chapters on bifurcations in fluid systems, flow patterns, channel flows, non-parallel shear flows, thin-film flows, strong viscous shear flows, Gortler vortices, bifurcations in convection, wavy film flows and boundary layers. Contents:The Linear Stability of Görtler Vortices Revisited (A Bottaro & P Luchini)The Sequence-of-Bifurcations Approach Towards an Understanding of Complex Flows (F H Busse & R M Clever)Derivation and Simulations of Evolution Equations of Wary Film Flows (A L Frenkel & K Indireshkumar)Instabilities Due to Soret Diffusion Coupled to the Morphology of a Solid-Liquid Interface (L Hadji)The Instability of Finite Amplitude Waves in Strong Viscid and Inviscid Shear (W R C Phillips)Nonlinear Stability Analysis and Modeling for Convective Flows (D N Riahi)Modeling and Simulation for Primary Instabilities in Shear Flows (D N Riahi)Görtler Vortices with System Rotation (A Zebib et al.) Readership: Scientists, engineers and students in mechanics, physics and mathematics. keywords:Stability;Hydrodynamic Stability;Flow Stability;Flow Instability;Stability Modeling;Stability Simulation;Nonlinear Hydrodynamics;Modeling in Stability;Simulation in Stability