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Hydrodynamic stability. Foreword by John Miles. 2nd ed. (English) Zbl 1055.76001
Cambridge Mathematical Library. Cambridge: Cambridge University Press (ISBN 0-521-52541-1/pbk). xx, 605 p. (2004).
During the last twenty years the book has become a classic in hydrodynamic stability. Even today, the book is a masterly introduction to the subject. It makes the reader familiar with the most important topics of the field ranging from the classical problem of thermal instability in an infinite liquid layer over centrifugal instabilities to inviscid and viscous stability theory for parallel shear flows. A variety of examples for flow instabilities are analyzed, as well as the stability of time-varying flows. The final chapter is an introduction to the nonlinear stability i.e., the mathematical description of the flow beyond the threshold. One strength of the book is a clear presentation of the physics of the flow and of the mathematical structure of solution/approximation procedures.
It is in the nature of a reprint after nearly 25 years that some subjects have been significantly advanced since the first printing in 1981 (Zbl 0449.76027). This applies in particular to the theory of transient growth, its role for the transition is shear flows, and nonlinear models of transition process. Likewise, the generalized linear stability theory with concepts of absolute and convective instability, even though introduced in two sections, would probably be given more space today, because of the many new results obtained in the meantime. Despite these natural deficits, the book continues to be an essential reading in hydrodynamic stability, in particular for the novice. The major modification of this second edition concerns the inclusion of detailed solutions to many problems given at the end of each section. They are elaborated on nearly 80 pages towards the end of the book.

MSC:
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76Exx Hydrodynamic stability
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