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**Fundamentals of two-fluid dynamics. Part I: Mathematical theory and applications.**
*(English)*
Zbl 0784.76002

Interdisciplinary Applied Mathematics. 3. New York: Springer-Verlag. xv, 443 p. (1993).

In their work on the principles and applications of two-fluid systems, Joseph and Renardy present a timely and masterly written treatise on the fundamentals of two-fluid dynamics. The material is organized in two self-contained parts. Part I (with 205 illustrations, 69 in color) is devoted to the mathematical theory and applications and discusses in four chapters: (I) an introduction into the subject, (II) rotating flows of two liquids, (III) the two-layer Bénard problem; and (IV) plane channel flows. Since many of the interesting problems are tied to the loss of stability, which is realized in preferential positioning and shaping of the interface, interfacial stability plays a major role in this study. Linear and nonlinear analyses are dealt with. In particular, the authors exploit Rayleigh’s idea that the most unstable linear wave will appear in the nonlinear dynamics and provide diagnostic tools for determining the cause of instability from the analysis of the energy of the most unstable wave. Besides the book is notable for its emphasis on extensive comparisons of theory and experiments guided by the attitude that experiments are the last resort of physical theories. The physical foundations and governing equations are developed in some detail. Furthermore the analyses and numerical methods are treated in such a way that the text is suitable also for study by graduate students. Part I should be required reading by them. This book is of special interest to technical personnel in industry as well as to engineers, physicists and applied mathematicians. The book is a valuable addition to the literature and should be in the library of researchers in fluid dynamics.

Reviewer: J.Siekmann (Essen)

### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

76T99 | Multiphase and multicomponent flows |

76E05 | Parallel shear flows in hydrodynamic stability |