Turbulence modeling both addresses a fundamental problem in physics, 'the last great unsolved problem of classical physics,' and has far-reaching importance in the solution of difficult practical problems from aeronautical engineering to dynamic meteorology. However, the growth of supercom puter facilities has recently caused an apparent shift in the focus of tur bulence research from modeling to direct numerical simulation (DNS) and large eddy simulation (LES). This shift in emphasis comes at a time when claims are being made in the world around us that scientific analysis itself will shortly be transformed or replaced by a more powerful 'paradigm' based on massive computations and sophisticated visualization. Although this viewpoint has not lacked ar ticulate and influential advocates, these claims can at best only be judged premature. After all, as one computational researcher lamented, 'the com puter only does what I tell it to do, and not what I want it to do. ' In turbulence research, the initial speculation that computational meth ods would replace not only model-based computations but even experimen tal measurements, have not come close to fulfillment. It is becoming clear that computational methods and model development are equal partners in turbulence research: DNS and LES remain valuable tools for suggesting and validating models, while turbulence models continue to be the preferred tool for practical computations. We believed that a symposium which would reaffirm the practical and scientific importance of turbulence modeling was both necessary and timely.

obtained are still severely limited to low Reynolds numbers (about only one decade better than direct numerical simulations), and the interpretation of such calculations for complex, curved geometries is still unclear. It is evident that a lot of work (and a very significant increase in available computing power) is required before such methods can be adopted in daily's engineering practice. I hope to l"Cport on all these topics in a near future. The book is divided into six chapters, each· chapter in subchapters, sections and subsections. The first part is introduced by Chapter 1 which summarizes the equations of fluid mechanies, it is developed in C~apters 2 to 4 devoted to the construction of turbulence models. What has been called "engineering methods" is considered in Chapter 2 where the Reynolds averaged equations al"C established and the closure problem studied (§1-3). A first detailed study of homogeneous turbulent flows follows (§4). It includes a review of available experimental data and their modeling. The eddy viscosity concept is analyzed in §5 with the l"Csulting ~alar-transport equation models such as the famous K-e model. Reynolds stl"Css models (Chapter 4) require a preliminary consideration of two-point turbulence concepts which are developed in Chapter 3 devoted to homogeneous turbulence. We review the two-point moments of velocity fields and their spectral transforms (§ 1), their general dynamics (§2) with the particular case of homogeneous, isotropie turbulence (§3) whel"C the so-called Kolmogorov's assumptions are discussed at length.

A selection of invited chapters focusing on developments in the application of Computational Fluid Dynamics (CFD) to compressible or incompressible flows dominated by turbulence effects. These may be applied to complex geometrical configurations or flow-fields in simpler geometries requiring higher-order turbulence modelling, or suitably modified low-order models, to calculate crucial parameters such as instabilities, transition, separation, accurate description of velocity and scalar fields, and local and total forces.

The present book contains papers that have been selected from contributions to the First International Symposium on Turbulent Shear Flows which was held from the 18th to 20th April 1977 at The Pennsylvania State University, University Park, Pennsylvania, USA. Attend ees from close to 20 countries presented over 100 contributions at this meeting in which many aspects of the current activities in turbulence research were covered. Five topics received particular attention at the Symposium: Free Flows Wall Flows Recirculating Flows Developments in Reynolds Stress Closures New Directions in Modeling This is also reflected in the five chapters of this book with contributions from research workers from different countries. Each chapter covers the most valuable contributions of the conference to the particular chapter topic. Of course, there were many additional good con tributions to each subject at the meeting but the limitation imposed on the length of this volume required that a selection be made. The realization of the First International Symposium on Turbulent Shear Flows was p- sible by the general support of: U. S. Army Research Office U. S. Navy Research Office Continuing Education Center of The Pennsylvania State University The conference organization was carried out by the organizing committee consisting of: F. Durst, Universitat Karlsruhe, Karlsruhe, Fed. Rep. of Germany V. W. Goldschmidt, Purdue University, West Lafayette, Ind. , USA B. E. Launder, University of California, Davis, Calif. , USA F. W. Schmidt, Pennsylvania State University, University Park, Penna.

Turbulence modeling both addresses a fundamental problem in physics, 'the last great unsolved problem of classical physics,' and has far-reaching importance in the solution of difficult practical problems from aeronautical engineering to dynamic meteorology. However, the growth of supercom puter facilities has recently caused an apparent shift in the focus of tur bulence research from modeling to direct numerical simulation (DNS) and large eddy simulation (LES). This shift in emphasis comes at a time when claims are being made in the world around us that scientific analysis itself will shortly be transformed or replaced by a more powerful 'paradigm' based on massive computations and sophisticated visualization. Although this viewpoint has not lacked ar ticulate and influential advocates, these claims can at best only be judged premature. After all, as one computational researcher lamented, 'the com puter only does what I tell it to do, and not what I want it to do. ' In turbulence research, the initial speculation that computational meth ods would replace not only model-based computations but even experimen tal measurements, have not come close to fulfillment. It is becoming clear that computational methods and model development are equal partners in turbulence research: DNS and LES remain valuable tools for suggesting and validating models, while turbulence models continue to be the preferred tool for practical computations. We believed that a symposium which would reaffirm the practical and scientific importance of turbulence modeling was both necessary and timely.

Der Band enthält den Abschlußbericht des DFG-Schwerpunktprogramms "Flußsimulation mit Höchstleistungsrechnern". Es führt die Arbeiten fort, die schon als Band 38 in der Reihe "Notes on Numerical Fluid Mechanics" erschienen sind.Work is reported, which was sponsored by the Deutsche Forschungsgemeinschaft from 1993 to 1995. Scientists from numerical mathematics, fluid mechanics, aerodynamics, and turbomachinery present their work on flow simulation with massively parallel systems, on the direct and large-eddy simulation of turbulence, and on mathematical foundations, general solution techniques and applications. Results are reported from benchmark computations of laminar flow around a cylinder, in which seventeen groups participated.