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Author : Xiaojing Zhang
Publisher :
ISBN 13 :
Total Pages : 266 pages
Book Rating : 4.:/5 (346 download)
Download or read book On Linear and Nonlinear Stability Theory of Periodic Flows of Incompressible Fluid written by Xiaojing Zhang and published by . This book was released on 1995 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : National Aeronautics and Space Administration (NASA)
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781722455811
Total Pages : 26 pages
Book Rating : 4.4/5 (558 download)
Download or read book On the Nonlinear Stability of the Unsteady, Viscous Flow of an Incompressible Fluid in a Curved Pipe written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-09 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stability of the flow of an incompressible, viscous fluid through a pipe of circular cross-section curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is obtained by identifying the saddle point of the Taylor number in the complex plane of the cross-sectional angle co-ordinate. The equation governing the nonlinear evolution of the leading order vortex amplitude is thus determined. The stability analysis of this flow to periodic disturbances leads to a partial differential system dependent on three variables, and since the differential operators in this system are periodic in time, Floquet theory may be applied to reduce this system to a coupled infinite system of ordinary differential equations, together with homogeneous uncoupled boundary conditions. The eigenvalues of this system are calculated numerically to predict a critical Taylor number consistent with the analysis of Papageorgiou. A discussion of how nonlinear effects alter the linear stability analysis is also given, and the nature of the instability determined. Shortis, Trudi A. and Hall, Philip Unspecified Center NAS1-19480; RTOP 505-90-52-01...
Author : Wiktor Eckhaus
Publisher : Springer
ISBN 13 :
Total Pages : 136 pages
Book Rating : 4.:/5 (44 download)
Download or read book Studies in Non-Linear Stability Theory written by Wiktor Eckhaus and published by Springer. This book was released on 1965 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-linear stability problems formulated in terms of non-linear partial differential equations have only recently begun to attract attention and it will probably take some time before our understanding of those problems reaches some degree of maturity. The passage from the more classical linear analysis to a non-linear analysis increases the mathematical complexity of the stability theory to a point where it may become discouraging, while some of the more usual mathematical methods lose their applicability. Although considerable progress has been made in recent years, notably in the field of fluid mechanics, much still remains to be done before a more permanent outline of the subject can be established. I have not tried to present in this monograph an account of what has been accomplished, since the rapidly changing features of the field make the periodical literature a more appropriate place for such a review. The aim of this book is to present one particular line of research, originally developed in a series of papers published in 'Journal de Mecanique' 1962-1963, in which I attempted to construct a mathematical theory for certain classes of non-linear stability problems, and to gain some understanding of the non-linear phenomena which are involved. The opportunity to collect the material in this volume has permitted a more coherent presentation, while various points of the analysis have been developed in greater detaiL I hope that a more unified form of the theory has thus been achieved.
Author : Trudi A. Shortis
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (317 download)
Download or read book On the Nonlinear Stability of the Unsteady, Viscous Flow of an Incompressible Fluid in a Curved Pipe written by Trudi A. Shortis and published by . This book was released on 1995 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tian Ma
Publisher : American Mathematical Soc.
ISBN 13 : 0821836935
Total Pages : 248 pages
Book Rating : 4.8/5 (218 download)
Download or read book Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics written by Tian Ma and published by American Mathematical Soc.. This book was released on 2005 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a geometric theory for incompressible flow and its applications to fluid dynamics. The main objective is to study the stability and transitions of the structure of incompressible flows and its applications to fluid dynamics and geophysical fluid dynamics. The development of the theory and its applications goes well beyond its original motivation of the study of oceanic dynamics. The authors present a substantial advance in the use of geometric and topological methods to analyze and classify incompressible fluid flows. The approach introduces genuinely innovative ideas to the study of the partial differential equations of fluid dynamics. One particularly useful development is a rigorous theory for boundary layer separation of incompressible fluids. The study of incompressible flows has two major interconnected parts. The first is the development of a global geometric theory of divergence-free fields on general two-dimensional compact manifolds. The second is the study of the structure of velocity fields for two-dimensional incompressible fluid flows governed by the Navier-Stokes equations or the Euler equations. Motivated by the study of problems in geophysical fluid dynamics, the program of research in this book seeks to develop a new mathematical theory, maintaining close links to physics along the way. In return, the theory is applied to physical problems, with more problems yet to be explored. The material is suitable for researchers and advanced graduate students interested in nonlinear PDEs and fluid dynamics.
Author : D.L. Dwoyer
Publisher : Springer Science & Business Media
ISBN 13 : 1461247241
Total Pages : 361 pages
Book Rating : 4.4/5 (612 download)
Download or read book Stability of Time Dependent and Spatially Varying Flows written by D.L. Dwoyer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the collection of papers presented at the workshop on 'The Stability of Spatially Varying and Time Dependent Flows" sponsored by the Institute for Computer Applications in Science and Engineering (lCASE) and NASA Langley Research Center (LaRC) during August 19- 23, 1985. The purpose of this workshop was to bring together some of the experts in the field for an exchange of ideas to update the current status of knowledge and to help identify trends for future research. Among the invited speakers were D.M. Bushnell, M. Goldstein, P. Hall, Th. Herbert, R.E. Kelly, L. Mack, A.H. Nayfeh, F.T. Smith, and C. von Kerczek. The contributed papers were by A. Bayliss, R. Bodonyi, S. Cowley, C. Grosch, S. Lekoudis, P. Monkewitz, A. Patera, and C. Streett. In the first article, Bushnell provides a historical background on laminar flow control (LFC) research and summarizes the crucial role played by stability theory in LFC system design. He also identifies problem areas in stability theory requiring further research from the view-point of ap plications to LFC design. It is an excellent article for theoreticians looking for some down-to-earth applications of stability theory.
Author : Claude Bardos
Publisher : Springer Science & Business Media
ISBN 13 : 0387752196
Total Pages : 395 pages
Book Rating : 4.3/5 (877 download)
Download or read book Instability in Models Connected with Fluid Flows II written by Claude Bardos and published by Springer Science & Business Media. This book was released on 2007-12-20 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique collection of papers, all written by leading specialists, that presents the most recent results and advances in stability theory as it relates to fluid flows. The stability property is of great interest for researchers in many fields, including mathematical analysis, theory of partial differential equations, optimal control, numerical analysis, and fluid mechanics. This text will be essential reading for many researchers working in these fields.
Author : Sergey Shklyaev
Publisher : Springer
ISBN 13 : 1493975900
Total Pages : 461 pages
Book Rating : 4.4/5 (939 download)
Download or read book Longwave Instabilities and Patterns in Fluids written by Sergey Shklyaev and published by Springer. This book was released on 2017-12-08 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes the main advances in the field of nonlinear evolution and pattern formation caused by longwave instabilities in fluids. It will allow readers to master the multiscale asymptotic methods and become familiar with applications of these methods in a variety of physical problems. Longwave instabilities are inherent to a variety of systems in fluid dynamics, geophysics, electrodynamics, biophysics, and many others. The techniques of the derivation of longwave amplitude equations, as well as the analysis of numerous nonlinear equations, are discussed throughout. This book will be of value to researchers and graduate students in applied mathematics, physics, and engineering, in particular within the fields of fluid mechanics, heat and mass transfer theory, and nonlinear dynamics.
Author : D. D. Joseph
Publisher : Springer Science & Business Media
ISBN 13 : 364280991X
Total Pages : 295 pages
Book Rating : 4.6/5 (428 download)
Download or read book Stability of Fluid Motions I written by D. D. Joseph and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of stability aims at understanding the abrupt changes which are observed in fluid motions as the external parameters are varied. It is a demanding study, far from full grown"whose most interesting conclusions are recent. I have written a detailed account of those parts of the recent theory which I regard as established. Acknowledgements I started writing this book in 1967 at the invitation of Clifford Truesdell. It was to be a short work on the energy theory of stability and if I had stuck to that I would have finished the writing many years ago. The theory of stability has developed so rapidly since 1967 that the book I might then have written would now have a much too limited scope. I am grateful to Truesdell, not so much for the invitation to spend endless hours of writing and erasing, but for the generous way he has supported my efforts and encouraged me to higher standards of good work. I have tried to follow Truesdell's advice to write this work in a clear and uncomplicated style. This is not easy advice for a former sociologist to follow; if I have failed it is not due to a lack of urging by him or trying by me. My research during the years 1969-1970 was supported in part by a grant from the Guggenheim foundation to study in London.
Author : Claude Bardos
Publisher : Springer
ISBN 13 : 9780387752181
Total Pages : 378 pages
Book Rating : 4.7/5 (521 download)
Download or read book Instability in Models Connected with Fluid Flows II written by Claude Bardos and published by Springer. This book was released on 2007-12-10 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique collection of papers, all written by leading specialists, that presents the most recent results and advances in stability theory as it relates to fluid flows. The stability property is of great interest for researchers in many fields, including mathematical analysis, theory of partial differential equations, optimal control, numerical analysis, and fluid mechanics. This text will be essential reading for many researchers working in these fields.
Author : Adelina Georgescu
Publisher : World Scientific
ISBN 13 : 9814289574
Total Pages : 418 pages
Book Rating : 4.8/5 (142 download)
Download or read book Stability Criteria for Fluid Flows written by Adelina Georgescu and published by World Scientific. This book was released on 2010 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Mathematical models governing fluid flows stability. 1.1. General mathematical models of thermodynamics. 1.2. Classical mathematical models in thermodynamics of fluids. 1.3. Classical mathematical models in thermodynamics. 1.4. Classical perturbation models. 1.5. Generalized incompressible Navier-Stokes model -- 2. Incompressible Navier-Stokes fluid. 2.1. Back to integral setting; involvement of dynamics and bifurcation. 2.2. Stability in semidynamical systems. 2.3. Perturbations; asymptotic stability; linear stability. 2.4. Linear stability. 2.5. Prodi's linearization principle. 2.6. Estimates for the spectrum of Ã. 2.7. Universal stability criteria -- 3. Elements of calculus of variations. 3.1. Generalities. 3.2. Direct and inverse problems of calculus of variations. 3.3. Symmetrization of some matricial ordinary differential operators. 3.4. Variational principles for problems (3.3.1)-(3.3.7). 3.5. Fourier series solutions for variational problems -- 4. Variants of the energy method for non-stationary equations. 4.1. Variant based on differentiation of parameters. 4.2. Variant based on simplest symmetric part of operators. 4.3. Variants based on energy splitting -- 5. Applications to linear Bénard convections. 5.1. Magnetic Bénard convection in a partially ionized fluid. 5.2. Magnetic Bénard convection for a fully ionized fluid. 5.3. Convection in a micro-polar fluid bounded by rigid walls. 5.4. Convections governed by ode's with variable coefficients -- 6. Variational methods applied to linear stability. 6.1. Magnetic Bénard problem with Hall effect. 6.2. Lyapunov method applied to the anisotropic Bénard problem. 6.3. Stability criteria for a quasi-geostrophic forced zonal flow. 6.4. Variational principle for problem (5.3.1), (5.3.2). 6.5. Taylor-Dean problem -- 7. Applications of the direct method to linear stability. 7.1. Couette flow between two cylinders subject to a magnetic field. 7.2. Soret-Dufour driven convection. 7.3. Magnetic Soret-Dufour driven convection. 7.4. Convection in a porous medium. 7.5. Convection in the presence of a dielectrophoretic force. 7.6. Convection in an anisotropic M.H.D. thermodiffusive mixture. 7.7. Inhibition of the thermal convection by a magnetic field. 7.8. Microconvection in a binary layer subject to a strong Soret effect. 7.9. Convection in the layer between the sea bed and the permafrost.
Author : Adrian V. Coward
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.:/5 (317 download)
Download or read book Nonlinear Stability of Oscillatory Core-annular Flow: A Generalized Kuramoto-Sivashinsky Equation with Time Periodic Coefficients written by Adrian V. Coward and published by . This book was released on 1994 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Claudio Canuto
Publisher : Springer Science & Business Media
ISBN 13 : 3540307281
Total Pages : 616 pages
Book Rating : 4.5/5 (43 download)
Download or read book Spectral Methods written by Claudio Canuto and published by Springer Science & Business Media. This book was released on 2007-06-30 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following up the seminal Spectral Methods in Fluid Dynamics, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries. These types of spectral methods were only just emerging at the time the earlier book was published. The discussion of spectral algorithms for linear and nonlinear fluid dynamics stability analyses is greatly expanded. The chapter on spectral algorithms for incompressible flow focuses on algorithms that have proven most useful in practice, has much greater coverage of algorithms for two or more non-periodic directions, and shows how to treat outflow boundaries. Material on spectral methods for compressible flow emphasizes boundary conditions for hyperbolic systems, algorithms for simulation of homogeneous turbulence, and improved methods for shock fitting. This book is a companion to Spectral Methods: Fundamentals in Single Domains.
Author : Akiva M. Yaglom
Publisher : Springer Science & Business Media
ISBN 13 : 9400742371
Total Pages : 611 pages
Book Rating : 4.4/5 (7 download)
Download or read book Hydrodynamic Instability and Transition to Turbulence written by Akiva M. Yaglom and published by Springer Science & Business Media. This book was released on 2012-12-18 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : W. O. Criminale
Publisher : Cambridge University Press
ISBN 13 : 110869800X
Total Pages : 566 pages
Book Rating : 4.1/5 (86 download)
Download or read book Theory and Computation in Hydrodynamic Stability written by W. O. Criminale and published by Cambridge University Press. This book was released on 2018-12-06 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : P. A. Davidson
Publisher : Oxford University Press
ISBN 13 : 0192640046
Total Pages : 528 pages
Book Rating : 4.1/5 (926 download)
Download or read book Incompressible Fluid Dynamics written by P. A. Davidson and published by Oxford University Press. This book was released on 2021-10-21 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Incompressible Fluid Dynamics is a textbook for graduate and advanced undergraduate students of engineering, applied mathematics, and geophysics. The text comprises topics that establish the broad conceptual framework of the subject, expose key phenomena, and play an important role in the myriad of applications that exist in both nature and technology. The first half of the book covers topics that include the inviscid equations of Euler and Bernoulli, the Navier-Stokes equation and some of its simpler exact solutions, laminar boundary layers and jets, potential flow theory with its various applications to aerodynamics, the theory of surface gravity waves, and flows with negligible inertia, such as suspensions, lubrication layers, and swimming micro-organisms. The second half is more specialised. Vortex dynamics, which is so essential to many natural phenomena in fluid mechanics, is developed in detail. This is followed by chapters on stratified fluids and flows subject to a strong background rotation, both topics being central to our understanding of atmospheric and oceanic flows. Fluid instabilities and the transition to turbulence are also covered, followed by two chapters on fully developed turbulence. The text is largely self-contained, and aims to combine mathematical precision with a breadth of engineering and geophysical applications. Throughout, physical insight is given priority over mathematical detail.
Author : Anatoly I. Ruban
Publisher : OUP Oxford
ISBN 13 : 0191503967
Total Pages : 336 pages
Book Rating : 4.1/5 (915 download)
Download or read book Fluid Dynamics written by Anatoly I. Ruban and published by OUP Oxford. This book was released on 2014-05-08 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book in a four-part series 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. The present Part 1 consists of four chapters. Chapter 1 begins with a discussion of Continuum Hypothesis, which is followed by an introduction to macroscopic functions, the velocity vector, pressure, density, and enthalpy. We then analyse the forces acting inside a fluid, and deduce the Navier-Stokes equations for incompressible and compressible fluids in Cartesian and curvilinear coordinates. In Chapter 2 we study the properties of a number of flows that are presented by the so-called exact solutions of the Navier-Stokes equations, including the Couette flow between two parallel plates, Hagen-Poiseuille flow through a pipe, and Karman flow above an infinite rotating disk. Chapter 3 is devoted to the inviscid incompressible flow theory, with particular focus on two-dimensional potential flows. These can be described in terms of the "complex potential", allowing the full power of the theory of functions of complex variables to be used. We discuss in detail the method of conformal mapping, which is then used to study various flows of interest, including the flows past Joukovskii aerofoils. The final Chapter 4 is concerned with compressible flows of perfect gas, including supersonic flows. Particular attention is given to the theory of characteristics, which is used, for example, to analyse the Prandtl-Meyer flow over a body surface bend and a corner. Significant attention is also devoted to the shock waves. The chapter concludes with analysis of unsteady flows, including the theory of blast waves.
