Stability and Transition in Shear Flows

Stability and Transition in Shear Flows PDF

Author: Peter J. Schmid

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 561

ISBN-13: 1461301858

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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.

Stability and Transition in Shear Flows

Stability and Transition in Shear Flows PDF

Author: Peter J. Schmid

Publisher: Springer Science & Business Media

Published: 2000-12-28

Total Pages: 578

ISBN-13: 9780387989853

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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.

Stability and Transition in Shear Flows

Stability and Transition in Shear Flows PDF

Author: Peter J. Schmid

Publisher: Springer

Published: 2012-09-16

Total Pages: 0

ISBN-13: 9781461265641

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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.

Physics of Transitional Shear Flows

Physics of Transitional Shear Flows PDF

Author: Andrey V. Boiko

Publisher: Springer Science & Business Media

Published: 2011-09-15

Total Pages: 286

ISBN-13: 9400724985

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Starting from fundamentals of classical stability theory, an overview is given of the transition phenomena in subsonic, wall-bounded shear flows. At first, the consideration focuses on elementary small-amplitude velocity perturbations of laminar shear layers, i.e. instability waves, in the simplest canonical configurations of a plane channel flow and a flat-plate boundary layer. Then the linear stability problem is expanded to include the effects of pressure gradients, flow curvature, boundary-layer separation, wall compliance, etc. related to applications. Beyond the amplification of instability waves is the non-modal growth of local stationary and non-stationary shear flow perturbations which are discussed as well. The volume continues with the key aspect of the transition process, that is, receptivity of convectively unstable shear layers to external perturbations, summarizing main paths of the excitation of laminar flow disturbances. The remainder of the book addresses the instability phenomena found at late stages of transition. These include secondary instabilities and nonlinear features of boundary-layer perturbations that lead to the final breakdown to turbulence. Thus, the reader is provided with a step-by-step approach that covers the milestones and recent advances in the laminar-turbulent transition. Special aspects of instability and transition are discussed through the book and are intended for research scientists, while the main target of the book is the student in the fundamentals of fluid mechanics. Computational guides, recommended exercises, and PowerPoint multimedia notes based on results of real scientific experiments supplement the monograph. These are especially helpful for the neophyte to obtain a solid foundation in hydrodynamic stability. To access the supplementary material go to extras.springer.com and type in the ISBN for this volume.

Introduction to Hydrodynamic Stability

Introduction to Hydrodynamic Stability PDF

Author: P. G. Drazin

Publisher: Cambridge University Press

Published: 2002-09-09

Total Pages: 278

ISBN-13: 1316582876

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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.

Hydrodynamic Instability and Transition to Turbulence

Hydrodynamic Instability and Transition to Turbulence PDF

Author: Akiva M. Yaglom

Publisher: Springer Science & Business Media

Published: 2012-12-18

Total Pages: 611

ISBN-13: 9400742371

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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

Hydrodynamic Stability PDF

Author: P. G. Drazin

Publisher: Cambridge University Press

Published: 2004-08-05

Total Pages: 630

ISBN-13: 9780521525411

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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.

Stability Study on Shear Flow and Vortices in Late Boundary Layer Transistion

Stability Study on Shear Flow and Vortices in Late Boundary Layer Transistion PDF

Author: Jie Tang

Publisher:

Published: 2017

Total Pages: 90

ISBN-13:

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Turbulence is still an unsolved scientific problem, it has been regarded as “the most important unsolved problem of classical physics”. Dr. Liu proposed a new mechanism about turbulence generation and sustenance after decades of research on turbulence and transition. His new idea challenged the classical theorem in many aspects. One of them is the flow stability of transition. Dr. Liu believes that inside the flow field, shear (dominant in laminar) is very unstable while rotation (dominant in turbulence) is relative stable. This inherent property of flow creates the trend that non-vertical vorticity must transfer to vertical vorticity, and causes the occurrence of transition. To verify this new idea, this dissertation analyses the linear stability on twodimensional shear flow and quasi-rotation flow. 1) Chebyshev collocation spectral method is discussed to solve Orr-Sommerfeld equation, the famous eigenvalue function describing the linear modes of disturbance. Several typical parallel shear flows are tested as the basicstate flows in the equation. The instability of shear flow is demonstrated by the existence of positive eigenvalues associated with disturbance modes (eigenfunctions), i.e. the growth of these linear modes. 2) Quasi-rotation flow is considered under Cylindrical coordinate. An eigenvalue perturbation equation is derived to study the stability problem with symmetric flows. Shifted Chebyshev polynomial with Gauss collocation points is used to solve the equation. To investigate the stability of vortices generation in real-world case, I tracked a ring-like vortex and a leg-like vortex over time from our Direct Numerical Simulation (DNS) data. The result shows that, with the generation over time, both ring-like vortex and leg-like vortex become more stable in the fact of decreasing positive eigenvalues.

Instability, Transition, and Turbulence

Instability, Transition, and Turbulence PDF

Author: M.Y. Hussaini

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 626

ISBN-13: 1461229561

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This volume contains the proceedings of the Workshop on In stability, Transition and Turbulence, sponsored by the Institute for Computer Applications in Science and Engineering (ICASE) and the NASA Langley Research Center (LaRC), during July 8 to August 2, 1991. This is the second workshop in the series on the subject. The first was held in 1989, and its proceedings were published by Springer-Verlag under the title "Instability and Transition" edited by M. Y. Hussaini and R. G. Voigt. The objectives of these work shops are to i) expose the academic community to current technologically im portant issues of transition and turbulence in shear flows over the entire speed range, ii) acquaint the academic community with the unique combination of theoretical, computational and experimental capabilities at LaRC and foster interaction with these capabilities, and iii) accelerate progress in elucidating the fundamental phenomena of transition and turbulence, leading to improved transition and turbulence modeling in design methodologies. The research areas covered in these proceedings include receptiv ity and roughness, nonlinear theories of transition, numerical simu lation of spatially evolving flows, modelling of transitional and fully turbulent flows as well as some experiments on instability and tran sition. In addition a one-day mini-symposium was held to discuss 1 recent and planned experiments on turbulent flow over a backward facing step.

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