Two experiments were performed, aimed at improving the understanding of the flow structure and scaling of separated flows. The backward-facing step geometry was chosen as a representative separated flow. The experiments were.

This volume contains 37 contributions in which the research work is summarized which has been carried out between 1984 and 1990 in the Priority Research Program "Physik abgeloster Stromungen" of the Deutsche Forschungsgemeinschaft (DFG, German Research Society). The aim of the Priority Research Program was the inten sive research of the whole range of phenomena associated with separated flows. Physi cal models as well as prediction methods had to be developed based on detailed experi mental investigations. It was in accordance with the main concept of the research program that scientists working on problems of separated flows in different technical areas of application participated in this program. The following fields have been represented in the program: aerodynamics of wings and bodies, aerodynamics of auto mobiles, turbomachinery, ship hydrodynamics, hydraulics, internal flows, heat exchan gers, bio-fluid-dynamics, aerodynamics of buildings and structures. In order to concentrate on problems common in all those areas the emphasis of the program was on basic research dealing with generic geometric configurations showing the fundamental physical phenomena of separated flows. The engagement and enthusiasm of all participating scientists are highly appreciated. The program was organized such that all researchers met once a year to report on the progress of their work. Special thanks ought to go to Prof. E. A. Muller (Gottingen), Prof. H. Oertel jun. (Braunschweig), Dr. W. Schmidt (Dornier), Dr. H. -W. Stock (Dornier) and Dr. B. Wagner (Dornier), who had the functions of referees on those annual meetings.

The structure of a turbulent reattaching flow behind a backward-facing step was studied experimentally in a low-velocity water channel, in order to observe the physical structure of the flow and to better understand the relation.

The knowledge of quantitative turbulence mechanics relies heavily upon the definition of the concept of a vortex in mathematical terms. This reference work introduces the reader to Liutex, which is an accepted, accurate and mathematical definition of a vortex. The core of this book is a compilation of several papers on the subject. presented in the 13th World Congress of Computational Mechanics (WCCM2018), Symposium 704, Mathematics and Computations for Multiscale Structures of Turbulent and Other Complex Flows, New York, United States on July 27, 2018. This compilation also includes other research papers which explain the work done on the vortex definition, vortex identification and turbulence structure from different insight angles including mathematics, computational physics and experiments. The thirteen chapters in this volume will be informative to scientists and engineers who are interested in advanced theories about fluid dynamics, vortex science and turbulence research.