Synopses & Reviews
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.
Review
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."
Synopsis
"Stability theory has seen rapid development over the past decade. This textbook gives a modern introduction to the hydrodynamic stability theory of shear flows. It treats both classical theories such as modal analysis, weakly nonlinear theory and resonances, and more recent developments such as non-modal analysis, receptivity and secondary instability theory. The last chapter addresses transition in shear flows and applies numerous techniques developed in the book to analyze and quantify transition scenarios for a variety of shear flows. Simple model problems to motivate mathematical concepts are used throughout the book, as are experimental results and computed illustrations to complement theoretical findings. This text will be useful to graduate students, as well as be a valuable reference for researchers in the field of hydrodynamic stability theory or with an interest in recent developments in fluid dynamics. Additionally those who are involved in general and applied fluid mechanics may also find this book of interest."
Synopsis
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.
Table of Contents
Introduction.- General results.- Linear inviscid analysis.- Eigensolutions to the viscous problem.- Linear transient growth.- Non-linear results.- The spatial problem.- Appendix A. Notes on numerical methods for accurate results.- Appendix B. Model problem.