Hydrodynamic Stability Theory

Author : A. Georgescu
Publisher : Springer Science & Business Media
Page : 306 pages
File Size : 45,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401718141

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Hydrodynamic stability theory by A. Georgescu Pdf

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.

Author : W. O. Criminale,T. L. Jackson,R. D. Joslin
Publisher : Cambridge University Press
Page : 565 pages
File Size : 46,8 Mb
Release : 2018-12-06
Category : Mathematics
ISBN : 9781108475334

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Theory and Computation in Hydrodynamic Stability by W. O. Criminale,T. L. Jackson,R. D. Joslin Pdf

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

Author : W. O. Criminale,T. L. Jackson,R. D. Joslin
Publisher : Cambridge University Press
Page : 465 pages
File Size : 46,5 Mb
Release : 2003-10-23
Category : Mathematics
ISBN : 9780521632003

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Theory and Computation of Hydrodynamic Stability by W. O. Criminale,T. L. Jackson,R. D. Joslin Pdf

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.

Author : P. G. Drazin
Publisher : Cambridge University Press
Page : 128 pages
File Size : 44,8 Mb
Release : 2002-09-09
Category : Science
ISBN : 9781316582879

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Introduction to Hydrodynamic Stability by P. G. Drazin Pdf

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.

Author : Peter J. Schmid,Dan S. Henningson
Publisher : Springer Science & Business Media
Page : 561 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461301851

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Stability and Transition in Shear Flows by Peter J. Schmid,Dan S. Henningson Pdf

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.

Author : Chia-Chʻiao Lin
Publisher : Unknown
Page : 176 pages
File Size : 47,8 Mb
Release : 1966
Category : Hydrodynamics
ISBN : UCSD:31822012871729

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The Theory of Hydrodynamic Stability by Chia-Chʻiao Lin Pdf

Author : Anatoly Ruban,Jitesh Gajjar,Andrew Walton
Publisher : Oxford University Press
Page : 369 pages
File Size : 41,7 Mb
Release : 2023-07-03
Category : Electronic
ISBN : 9780198869948

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Fluid Dynamics by Anatoly Ruban,Jitesh Gajjar,Andrew Walton Pdf

This is the fourth volume in a four-part series on fluid dynamics: Part 1. Classical Fluid Dynamics Part 2. Asymptotic Problems of Fluid Dynamics Part 3. Boundary Layers Part 4. Hydrodynamic Stability Theory The series is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field. Part 4 is devoted to hydrodynamic stability theory which aims at predicting the conditions under which the laminar state of a flow turns into a turbulent state. The phenomenon of laminar-turbulent transition remains one of the main challenges of modern physics. The resolution of this problem is important not only from a theoretical viewpoint but also for practical applications. For instance, in the flow past a passenger aircraft wing, the laminar-turbulent transition causes a fivefold increase in the viscous drag. The book starts with the classical results of the theory which include the global stability analysis followed by the derivation of the Orr-Sommerfeld equation. The properties of this equation are discussed using, as examples, plane Poiseuille flow and the Blasius boundary layer. In addition, we discuss 'inviscid flow' instability governed by the Rayleigh equation, Kelvin-Helmholtz instability, crossflow instability, and centrifugal instability, taking the form of Taylor-Görtler vortices. However, in this presentation our main attention regards recent developments in the theory. These include linear and nonlinear critical layer theory, the theory of receptivity of the boundary layer to external perturbations, weakly nonlinear stability theory of Landau and Stuart, and vortex-wave interaction theory. The latter allows us to describe self-sustaining nonlinear perturbations within a viscous fluid.

Author : Gordon E Swaters
Publisher : Routledge
Page : 129 pages
File Size : 42,5 Mb
Release : 2019-01-22
Category : Mathematics
ISBN : 9781351436960

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Introduction to Hamiltonian Fluid Dynamics and Stability Theory by Gordon E Swaters Pdf

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.

Author : P. G. Drazin,W. H. Reid
Publisher : Cambridge University Press
Page : 630 pages
File Size : 48,9 Mb
Release : 2004-08-05
Category : Mathematics
ISBN : 0521525411

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Hydrodynamic Stability by P. G. Drazin,W. H. Reid Pdf

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.

Author : Chia Ch'iao Lin
Publisher : Unknown
Page : 128 pages
File Size : 55,7 Mb
Release : 1955
Category : Hydrodynamics
ISBN : LCCN:nun00467452

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The Theory of Hydrodynamic Stability by Chia Ch'iao Lin Pdf

Author : François Charru
Publisher : Cambridge University Press
Page : 411 pages
File Size : 41,8 Mb
Release : 2011-06-30
Category : Science
ISBN : 9781139500548

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Hydrodynamic Instabilities by François Charru Pdf

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.

Author : Akiva M. Yaglom
Publisher : Springer Science & Business Media
Page : 611 pages
File Size : 41,9 Mb
Release : 2012-12-18
Category : Technology & Engineering
ISBN : 9789400742376

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Hydrodynamic Instability and Transition to Turbulence by Akiva M. Yaglom Pdf

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.

Author : C. C Lin
Publisher : Unknown
Page : 155 pages
File Size : 43,6 Mb
Release : 1964
Category : Hydrodynamics
ISBN : OCLC:848330578

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The Theory of Hydrodynamic Stability by C. C Lin Pdf

Author : W. O. Criminale,T. L. Jackson,R. D. Joslin
Publisher : Cambridge University Press
Page : 566 pages
File Size : 40,9 Mb
Release : 2018-12-06
Category : Science
ISBN : 9781108698009

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Theory and Computation in Hydrodynamic Stability by W. O. Criminale,T. L. Jackson,R. D. Joslin Pdf

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 to the most complex, considering linear and nonlinear situations, and analyzing temporal and spatial stability. The authors examine each problem both analytically and numerically. Many 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. The text includes copious illustrations and an extensive bibliography, making it suitable for courses on hydrodynamic stability or as an authoritative reference for researchers. In this second edition the opportunity has been taken to update the text and, most importantly, provide solutions to the numerous extended exercises.

Author : Chia-chiao Lin
Publisher : Unknown
Page : 155 pages
File Size : 42,8 Mb
Release : 1955
Category : Hydrodynamics
ISBN : LCCN:lc56001851

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The Theory of Hydrodynamic Stability by Chia-chiao Lin Pdf