This IUTAM Symposium was the first international conference on asymptotic methods for turbulent shear flows. It was the aim of this Symposium to bring together the experts and research workers to discuss recent work in this field. There was general consensus among the participants of the Symposium, that the asymptotic methods provide powerful tool for turbulence modelling, which ought to be used more intensively in practice in addition to the numerical meth ods. This was the Scientific Committee: K. Gersten (Germany, Chairman) A. Kluwick (Austria) J. - P. Guiraud (France) F. T. Smith (United Kingdom) V. V. Sychev (Russia) S. Kida (Japan) H. K. Moffat (United Kingdom) J. D. A. Walker (USA) We are very thankful that the Symposium was sponsored by the following organizations: International Union of Theoretical and Applied Mechanics Deutsche Forschungsgemeinschaft, Bonn Gesellschaft der Freunde der Ruhr-Universitiit, Bochum Institut fur Energie-, System-, Material- und Umwelttechnik e. V. , Bochum Ruhrgas AG, Essen Dresdner Bank, Bochum Kluwer Academic Publishers, Dordrecht Vieweg-Verlag, Wiesbaden We thank in particular the Rektor of the Ruhr University, Professor M. Bormann, who was host of the Symposium and made possible that the Symposium could take place on the campus. The following persons, who helped in organizing the Symposium and made sure that everything was working smoothly and efficiently during the Symposium, de serve our special thanks: Bernard Rocklage, Gerta Marliani, Petra Berkner and Th.

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Session 1.- Different approaches to asymptotic expansions in turbulent boundary layers (Invited lecture).- Turbulent Poiseuille channel flow interpreted by composite expansions.- A high Reynolds number analysis of turbulent heat transfer in the entrance region of a pipe or channel.- Asymptotic analysis of turbulent flow for a rotating cylinder.- Session 2.- Asymptotics for turbulent shear flows: A survey of some French contributions (Invited lecture).- Application of the defect formulation to the incompressible turbulent boundary layer.- Axisymmetric turbulent sink flows.- Wake layer in a turbulent boundary layer with pressure gradient: a new approach (Invited lecture).- Session 3.- Recent advances in wall-bounded shear flows. Survey of contributions from the USA (Invited lecture).- Asymptotic and computational results for a turbulent jet impinging on a nearby wall.- Asymptotic analysis of fully turbulent flows in slender convergent and divergent channels.- Heat and momentum transfer in turbulent boundary layers in the presence of strong adverse pressure gradients.- Similarity of turbulent shear flows: The natural convection boundary layer next to heated vertical surfaces.- Section 4.- Asympotic methods in turbulent combustion (Invited lecture).- Asymptotic study of turbulent swirling jets.- Longitudinal vortex embedded in turbulent Couette flow.- Section 5.- Progress in computation of rapid distortion of turbulent flows (Invited lecture).- Structure of a confined turbulent wake under shear and irrotational strain.- A theoretical model for nonlinear spots.- Intermittency of turbulence and the scaling hypothesis.- Analytical and numerical multiscale calculations for eddy viscosity.- Section 6.- Asymptotic stability of turbulent swirling jets fanning out along a plate.- Lagrangian direct-interaction approximation for homogeneous isotropic turbulence.- Generalised multiple expansion for the jet problem.- Back of the envelope analysis of turbulence models.