Stability and Transition in Shear Flows

Peter J. Schmid, Dan S. Henningson

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English

Springer Verlag
01 June 2001

Mathematics & Sciences; Maths for scientists; Fluid mechanics; Maths for engineers; Flow, turbulence, rheology

Series: Applied Mathematical Sciences

This book is a detailed look at some of the more modern issues of hydrodynamic stability, including transient growth, eigenvalue spectra, secondary instability. Analytical results and numerical simulations, linear and (selected) nonlinear stability methods will be presented. 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 will also be of value as a reference for researchers in the field of hydrodynamic stability theory or with an interest in recent developments in fluid dynamics. Since the appearance of ""Drazin & Reid"", no book on hydrodynamic stability theory has been published. However, stability theory has seen a rapid development over the past decade. Direct numerical simulations of transition to turbulence and linear analysis based on the initial-value problem are two of many such developments that will be included in the book.

By: Peter J. Schmid, Dan S. Henningson
Imprint: Springer Verlag
Country of Publication: United States
Volume: v. 142
Dimensions: Height: 235mm, Width: 155mm, Spine: 31mm
Weight: 2.160kg
ISBN: 9780387989853
ISBN 10: 0387989854
Series: Applied Mathematical Sciences
Pages: 569
Publication Date: 01 June 2001
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

1 Introduction and General Results.- 1.1 Introduction.- 1.2 Nonlinear Disturbance Equations.- 1.3 Definition of Stability and Critical Reynolds Numbers.- 1.4 The Reynolds-Orr Equation.- I Temporal Stability of Parallel Shear Flows.- 2 Linear Inviscid Analysis.- 3 Eigensolutions to the Viscous Problem.- 4 The Viscous Initial Value Problem.- 5 Nonlinear Stability.- II Stability of Complex Flows and Transition.- 6 Temporal Stability of Complex Flows.- 7 Growth of Disturbances in Space.- 8 Secondary Instability.- 9 Transition to Turbulence.- III Appendix.- A Numerical Issues and Computer Programs.- A.1 Global versus Local Methods.- A.2 Runge-Kutta Methods.- A.3 Chebyshev Expansions.- A.4 Infinite Domain and Continuous Spectrum.- A.5 Chebyshev Discretization of the Orr-Sommerfeld Equation.- A.6 MATLAB Codes for Hydrodynamic Stability Calculations.- A.7 Eigenvalues of Parallel Shear Flows.- B Resonances and Degeneracies.- B.1 Resonances and Degeneracies.- B.2 Orr-Sommerfeld-Squire Resonance.- C Adjoint of the Linearized Boundary Layer Equation.- C.1 Adjoint of the Linearized Boundary Layer Equation.- D Selected Problems on Part I.

Reviews for Stability and Transition in Shear Flows

From the reviews: SIAM REVIEW This book presents a modern treatment of stability in shear flows. Stability theory has seen a number of classic treatments over the years...Schmid and Henningson's book builds on these and offers much new material relevant to stability in shear flows...The MATLAB codes included in the appendix and a discussion of the effects of rounding error and resolution on the computations of eigenvalues of linear stability operators will be particularly helpful for students and researchers as they get started with stability computations...As the basis for a course, the first part of the book would permit students to build a solid foundation in classical and modern stability theory, while a selection of advanced topics from the second half of the book could be treated later in the course or through projects and independent study by students. ZENTRALBLATT MATH The book addresses to graduate students as well as to a broad community of researchers with a basic knowledge of fundamental fluid dynamics...The topics are treated with mathematical rigor while the physical motivation and usefulness of mathematical concepts is kept close at hand. The work is elegantly structured, and the graphical material is very suggestive.