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Hydrodynamic Stability Theory

Author : A. Georgescu

Publisher : Taylor & Francis

Page : 318 pages

File Size : 21,58 MB

Release : 1985

Category : Mathematics

ISBN : 9789024731206

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Book Description

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.



Introduction to Hydrodynamic Stability

Author : P. G. Drazin

Publisher : Cambridge University Press

Page : 278 pages

File Size : 28,35 MB

Release : 2002-09-09

Category : Science

ISBN : 1316582876

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Book Description

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.



Theory and Computation in Hydrodynamic Stability

Author : W. O. Criminale

Publisher : Cambridge University Press

Page : 565 pages

File Size : 14,92 MB

Release : 2019

Category : Mathematics

ISBN : 1108475337

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Book Description

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



Stability and Transition in Shear Flows

Author : Peter J. Schmid

Publisher : Springer Science & Business Media

Page : 561 pages

File Size : 36,84 MB

Release : 2012-12-06

Category : Science

ISBN : 1461301858

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Book Description

A detailed look at some of the more modern issues of hydrodynamic stability, including transient growth, eigenvalue spectra, secondary instability. It presents analytical results and numerical simulations, linear and selected nonlinear stability methods. By including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course. It is equally of value as a reference for researchers in the field of hydrodynamic stability theory or with an interest in recent developments in fluid dynamics. Stability theory has seen a rapid development over the past decade, this book includes such new developments as direct numerical simulations of transition to turbulence and linear analysis based on the initial-value problem.



Introduction to Hamiltonian Fluid Dynamics and Stability Theory

Author : Gordon E Swaters

Publisher : Routledge

Page : 290 pages

File Size : 22,74 MB

Release : 2019-01-22

Category : Mathematics

ISBN : 1351436961

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Book Description

Hamiltonian fluid dynamics and stability theory work hand-in-hand in a variety of engineering, physics, and physical science fields. Until now, however, no single reference addressed and provided background in both of these closely linked subjects. Introduction to Hamiltonian Fluid Dynamics and Stability Theory does just that-offers a comprehensive introduction to Hamiltonian fluid dynamics and describes aspects of hydrodynamic stability theory within the context of the Hamiltonian formalism. The author uses the example of the nonlinear pendulum-giving a thorough linear and nonlinear stability analysis of its equilibrium solutions-to introduce many of the ideas associated with the mathematical argument required in infinite dimensional Hamiltonian theory needed for fluid mechanics. He examines Andrews' Theorem, derives and develops the Charney-Hasegawa-Mima (CMH) equation, presents an account of the Hamiltonian structure of the Korteweg-de Vries (KdV) equation, and discusses the stability theory associated with the KdV soliton. The book's tutorial approach and plentiful exercises combine with its thorough presentations of both subjects to make Introduction to Hamiltonian Fluid Dynamics and Stability Theory an ideal reference, self-study text, and upper level course book.



Hydrodynamic Instabilities

Author : François Charru

Publisher : Cambridge University Press

Page : 411 pages

File Size : 33,60 MB

Release : 2011-06-30

Category : Science

ISBN : 1139500546

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Book Description

The instability of fluid flows is a key topic in classical fluid mechanics because it has huge repercussions for applied disciplines such as chemical engineering, hydraulics, aeronautics, and geophysics. This modern introduction is written for any student, researcher, or practitioner working in the area, for whom an understanding of hydrodynamic instabilities is essential. Based on a decade's experience of teaching postgraduate students in fluid dynamics, this book brings the subject to life by emphasizing the physical mechanisms involved. The theory of dynamical systems provides the basic structure of the exposition, together with asymptotic methods. Wherever possible, Charru discusses the phenomena in terms of characteristic scales and dimensional analysis. The book includes numerous experimental studies, with references to videos and multimedia material, as well as over 150 exercises which introduce the reader to new problems.



Hydrodynamic Instability and Transition to Turbulence

Author : Akiva M. Yaglom

Publisher : Springer Science & Business Media

Page : 611 pages

File Size : 15,39 MB

Release : 2012-12-18

Category : Technology & Engineering

ISBN : 9400742371

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Book Description

This book is a complete revision of the part of Monin & Yaglom's famous two-volume work "Statistical Fluid Mechanics: Mechanics of Turbulence" that deals with the theory of laminar-flow instability and transition to turbulence. It includes the considerable advances in the subject that have been made in the last 15 years or so. It is intended as a textbook for advanced graduate courses and as a reference for research students and professional research workers. The first two Chapters are an introduction to the mathematics, and the experimental results, for the instability of laminar (or inviscid) flows to infinitesimal (in practice "small") disturbances. The third Chapter develops this linear theory in more detail and describes its application to particular problems. Chapters 4 and 5 deal with instability to finite-amplitude disturbances: much of the material has previously been available only in research papers.



Hydrodynamic stability theory

Author : A. Georgescu

Publisher : Springer Science & Business Media

Page : 306 pages

File Size : 36,56 MB

Release : 2013-04-17

Category : Mathematics

ISBN : 9401718148

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Book Description

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.



The Theory of Hydrodynamic Stability

Author : C C (Chia-Chʻiao) 1916- Lin

Publisher : Hassell Street Press

Page : 176 pages

File Size : 10,64 MB

Release : 2021-09-09

Category :

ISBN : 9781013839368

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Book Description

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.



Non-Linear Mass Transfer and Hydrodynamic Stability

Author : C.B. Boyadjiev

Publisher : Elsevier

Page : 515 pages

File Size : 10,11 MB

Release : 2000-08-16

Category : Science

ISBN : 0080537707

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Book 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.