Boundary-layer separation from a rigid body surface is one of the fundamental problems of classical and modern fluid dynamics. The major successes achieved since the late 1960s in the development of the theory of separated flows at high Reynolds numbers are in many ways associated with the use of asymptotic methods. The most fruitful of these has proved to be the method of matched asymptotic expansions, which has been widely used in mechanics and mathematical physics. There have been many papers devoted to different problems in the asymptotic theory of separated flows and we can confidently speak of the appearance of a very productive direction in the development of theoretical hydrodynamics. This book will present this theory in a systematic account. The book will serve as a useful introduction to the theory, and will draw attention to the possibilities that application of the asymptotic approach provides.

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.

This is the first book in English devoted to the latest developments in fluid mechanics and aerodynamics. Written by the leading authors in the field, based at the renowned Central Aerohydrodynamic Institute in Moscow, it deals with viscous gas flow problems that arise from supersonic flows. These complex problems are central to the work of researchers and engineers dealing with new aircraft and turbomachinery development (jet engines, compressors and other turbine equipment). The book presents the latest asymptotical models, simplified Navier-Stokes equations and viscous-inviscid interaction theroies and will be of critical interest to researchers, engineers, academics and advanced graduate students in the areas of fluid mechanics, compressible flows, aerodynamics and aircraft design, applied mathematics and computational fluid dynamics. - The first book in English to cover the latest methodology for incopressible flow analysis of high speed aerodynamics, an essential topic for those working on new generation aircraft and turbomachinery - Authors are internationally recognised as the leading figures in the field - Includes a chapter introducing asymptotical methods to enable advanced level students to use the book

Separated flows and jets are closely linked in a variety of applications. They are of great importance in various fields of fluid mechanics including vehicle efficiency, technical branches concerned with gas/liquid flows, atmospheric effects on various constructions, etc. Knowledge of the physics of separated flows and jets and the development of reliable control techniques are prerequisite for future progress in the field. These aspects were in focus during the IUTAM-Symposium which was held in Novosibirsk, 9-13 July, 1990. This volume contains a selection of papers presenting recent results of theoretical and numerical studies as well as experimental work on separated flows and jets. The topics include sub- and supersonic, laminar and turbulent separation as well as organized structures in separated flows and jets. The reader will find here the state of the art and major trends for research in this field of aero-hydrodynamics.

This Volume is the Proceedings of the IUTAM Symposium on Unsteady Separated Flows and Their Control held in Corfu, Greece, 18–22 June 2007. This was the second IUTAM Symposium on this subject, following the symposium in Toulouse, in April 2002. The Symposium consisted of single plenary sessions with invited lectures, - lected oral presentations, discussions on special topics and posters. The complete set of papers was provided to all participants at the meeting. The thematic sessions of this Symposium are presented in the following: Experimental techniques for the unsteady ow separation Theoretical aspects and analytical approaches of ow separation Instability and transition Compressibility effects related to unsteady separation Statistical and hybrid turbulence modelling for unsteady separated ows Direct and Large-Eddy Simulation of unsteady separated ows Theoretical/industrial aspects of unsteady separated ow control This IUTAM Symposium concerned an important domain of Theoretical and Applied Mechanics nowadays. It focused on the problem of ow separation and of its control. It achieved a uni ed approach regrouping the knowledge provided from theoretical, experimental, numerical simulation and modelling aspects for unsteady separated ows (incompressible and compressible regimes) and included ef cient control devices to achieve attenuation or suppression of separation. The subject - eas covered important themes in the domain of fundamental research as well as in the domain of applications.

Mathematics has been behind many of humanity's most significant advances in fields as varied as genome sequencing, medical science, space exploration, and computer technology. But those breakthroughs were yesterday. Where will mathematicians lead us tomorrow and can we help shape that destiny? This book assembles carefully selected articles highlighting and explaining cutting-edge research and scholarship in mathematics with an emphasis on three manifolds.