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Asymptotic Theory of Separated Flows . V.V. Sychev et al. Cambridge University Press, The Edinburgh Building, Cambridge CB2 2RU, UK. 1998. 334pp. Illustrated. £30. ISBN 0-521-45530-8.

This book is almost completely devoted to the study of laminar separation by asymptotic and triple deck methods. The recognition that there was a singularity in the boundary layer equations was first noted by Howarth and Hartree in 1938/9 and the first serious treatment of the singularity was made by Coldstein in 1948, since then many attacks on the problem have been made by numerous workers throughout the world and this work has lead to a better appreciation of the mechanism of separation on smooth surfaces. This book is a translation of a Russian edition written and published in 1987 by four of the main Russian workers in this field . A number of new sections have been added to the English edition to bring the work up to date and the edition is edited by the two principal American workers in the field A.F. Messiter and Milton Van Dyke. Thus overall it represents an authoritative review of the subject. Mathematical minded readers will find this book of greatest interest and one needs a solid grounding in basic boundary layer theory to make progress through the text. However, the effort is worthwhile, although the rewards would be greater to those interested in aircraft, if the results had been presented in a more accessible manner. This is particularly true in the chapter on separation at the leading edge of a thin aerofoil since this chapter is concerned with the conditions for the first occurrence and subsequent bursting of the short bubble leading-edge separation. After a lot of complex algebraic and numerical analysis one arrives at the intriguing statement "Using the results of the above analysis we can, for any profile, reduce the problem of determining the angle of attack at which a short bubble is generated, and the angle of attack at which this bubble is destroyed, to integration of the classical equation of Prandtl for the boundary layer on the profile surface." Although simple formulae to do this are given no attempt is made to compare any result obtained with the behaviour on a real aerofoil. This is disappointing since the last few paragraphs of this chapter sketch the extension of the analysis to unsteady flows and hints that this may help in the understanding of the dynamic separation effects seen on oscillating aerofoils. Overall this book has reinforced my feeling that in the forest of work on the use of matched asymptotic expansions in both laminar and turbulent flow it difficult to see the forest for the mathematical trees. There is a great need to use the analytic formulae to produce numerical results for direct comparison with experiment. This is true for both the laminar separation discussed in this book and for the corresponding work on turbulent separation, particularly in shock interactions. Such comparison could have considerable implications for the validation of CFD codes and I hope that the appearance of the present volume will inspire work on these lines.