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Fluid mechanics. 2nd ed. Volume 6 of Course of Theoretical Physics. Transl. from the Russian by J. B. Sykes and W. H. Reid. (English) Zbl 0655.76001
Oxford etc.: Pergamon Press. XIII, 539 p. (1987).
Fluid Mechanics, Volume 6 of a set of ten volumes of the world famous series “Course of Theoretical Physics”, written by Landau and Lifshitz comes out now in the second English edition, almost thirty years after the appearance of the first English edition. The latter one was reviewed in 1963 in Zbl 0146.224, the German translation in Zbl 0146.225. In the new revised edition, written by the late E. M. Lifshitz, “content and treatment... remain in accordance with what was said in the preface to the first edition”... “to develop as fully as possible all matters of physical interest, and to do so in such a way as to give the clearest possible picture of the phenomena and their interrelation. Accordingly, we discuss neither approximate methods of calculation in fluid mechanics, nor empirical theories devoid of physical significance.” The authors have succeeded in their attempt to give a comprehensive account of the subject. As mentioned in the preface of the first edition, the book describes fluid mechanics as a branch of theoretical physics, thus giving the treatise its distinct flavor.
During the past three decades the field has advanced rapidly, in particular with respect to applications. Of course, some topics, although interesting, are beyond the scope of the book. As in the previous edition hydrodynamic stability is presented mainly in terms of results. However, the text has been slightly supplemented and modified, leaving the fundamentals unchanged. About ten new sections were added. Nevertheless the size of the book has remained nearly the same. The discussion of turbulence reflects the progress concerning the understanding of the mechanism whereby turbulence occurs. Some basic ideas are treated in three sections (§§ 30-32) written jointly with M. I. Rabinovich. Within the framework of twenty-six chapters of different size the book covers the whole range of fluid dynamics, beginning with ideal and viscous fluids, turbulence and boundary layers up to combustion, relativistic fluid dynamics and the dynamics of superfluids. In the new edition a chapter on fluctuations in fluid dynamics has been omitted. The problems at the end of sections, complete with solutions deserve special mention. They are not merely pure exercises but provide a deeper understanding of the subject.
The one or other reader would have welcomed the discussion of the one or other topic close to his own interests. It should be kept in mind, however, that the selection of the material is dictated also by the interest of the authors. The references rest heavily on Russian works. A more detailed quotation would have been desirable. These and other omissions are of minor importance in view of the fact that the two distinguished authors have given an almost complete survey of the field. Their lucid and penetrating analysis, combined with a sound physical understanding and a clear presentation of the subject, will certainly influence the writings of future authors. Without doubt researchers and serious students of mathematics, theoretical physics and the engineering sciences will consult this comprehensive and inspiring treatise on fluid mechanics and will profit from the wealth of information. The book will find its place on the shelves of all libraries covering the mechanics of liquids and gases.
Reviewer: J.Siekmann

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