The Theory of Laminar Boundary Layers in Compressible Fluids

The Theory of Laminar Boundary Layers in Compressible Fluids. K. Stewartson. Clarendon Press, Oxford. 1964. 191 pp. Illustrated. 3 gns. In this admirable monograph, Professor Stewartson gives a comprehensive account of the theory of laminar boundary layers in compressible fluids. There are chapters on the Navier-Stokes equations, the boundary-layer equations, boundary layers without and with pressure gradients, threedimensional and unsteady boundary layers, interactions with shock waves, and hypersonic boundary layers. The author comments that the two most serious omissions are real-gas effects and the topic of stability, but the absence of a discussion of these questions is understandable, and even without them the monograph is a noteworthy addition to the literature of fluid mechanics. The opening chapter gives a careful discussion of the Navier-Stokes equations and the derivation of them although, curiously, no reference is made to Serrin's article in the Handbuch der Physik or to Truesdell's expositions. The present reviewer finds the second chapter, in which the boundarylayer equations are derived and discussed, not entirely to his taste, especially in a book which is avowedly mathematical. The philosophy adopted by the author is that a certain (Prandtl) limit is taken in which the viscosity, p., tends to zero, but, since fi has dimensions, one naturally asks: with reference to what other quantity (of the same dimensions) does fi become small? In the case of steady boundary layers a Reynolds number provides the answer, and in many unsteady boundary layers a frequency parameter plays a similar role. Such parameters do not appear in the author's derivation, although they could easily have been introduced to derive the Prandtl limit. Doubtless Professor Stewartson has his reasons for his treatment of the Prandtl limit, but to the reviewer it seems, on the one hand, possibly misleading and, on the other hand, inappropriate in a mathematical monograph. This comment is in no way a criticism of the book as a whole, which is generally carefully conceived and written, and is an excellent account of the subject. The more mathematical parts of the study of laminar boundary layers are selected for emphasis, as implied by the title, but reference to experiment is frequent. Trivial mistakes seem few, although the reviewer notes some dimensionally-incorrect formulae (but easily noted and corrected) on pages 140 and 141. In spite of the high price (63s. for a paperback of 190 pages, with two plates) this monograph is strongly recommended to all interested in boundary layers in compressible fluids.—J. T. STUART.