Chemical reaction systems of practical interest are usually very complex: They consist of a large number of elementary reactions (hundreds or thou sands in a small system), mostly with rate coefficients differing by many orders of magnitude, which leads to serious stiffness, and they are often coupled with surface reaction steps and convective or diffusive processes. Thus, the derivation of a "true" chemical mechanism can be extremely cumbersome. In most cases this is done by setting up "reaction models" which are improved step by step using, for example, perturbation theory, numerical simulation and sensitivity analysis (and - hopefully, in the near future - parameter identification procedures), and by comparison with experimental data on sensitive properties. Because of the complexity of these processes, it was very difficult in the past to convince engineers to apply methods using detailed mecha nisms given in terms of elementary reactions, and even in basic sciences there was scepticism about this ambitious aim. A previous workshop on modelling of chemical reaction systems held in 1980 was an attempt to find a common language of mathematicians, chemists, and engineers working in this interdisciplinary area. Since then considerable progress has been made by the simultaneous development of applied mathematics, an enor mous increase of computer capacity, and the development of experimental techniques in physical chemistry that have made available well-working reaction mechanisms in some fields of reaction kinetics."

This volume arises from an International Symposium on Flow and Transport in the Natural Environment held in Canberra, Australia, in September 1987. The meeting was hosted by the CSIRO Division of Environmental Mechanics (now the Centre for Environmental Mechanics) to mark the opening of the second stage of its headquarters, the F.C. Pye Field Environment Laboratory, twenty-one years after the opening of the first stage. Those twenty-one years have seen much progress in our understanding of the physics of the natural environment and the occasion provided an ideal opportunity to review advances in our knowledge of flow and transport phenomena, particularly with regard to flow and transport in soils, plants and the atmosphere. The contents of this volume are based very closely on the Symposium's program. Undoubtedly, our choices of topics were idiosyncratic, but we believe that those we have selected exhibit progress, innovation, and much scope for practical application. Rather than being encyclopaedic, we have sought to deal with thirteen selected topics in depth.

Non-linear behaviour of water waves has recently drawn much attention of scientists and engineers in the fields of oceanography, applied mathematics, coastal engineering, ocean engineering, naval architecture, and others. The IUTAM Symposium on Non-linear Water Waves was organized with the aim of bringing together researchers who are actively studying non-linear water waves from various viewpoints. The papers contained in this book are related to the generation and deformation of non-linear water waves and the non-linear interaction between waves and bodies. That is, various types of non-linear water waves were analyzed on the basis of various well-known equations, experimental studies on breaking waves were presented, and numerical studies of calculating second-order non-linear wave-body interaction were proposed.

Cellular automata are fully discrete dynamical systems with dynamical variables defined at the nodes of a lattice and taking values in a finite set. Application of a local transition rule at each lattice site generates the dynamics. The interpretation of systems with a large number of degrees of freedom in terms of lattice gases has received considerable attention recently due to the many applications of this approach, e.g. for simulating fluid flows under nearly realistic conditions, for modeling complex microscopic natural phenomena such as diffusion-reaction or catalysis, and for analysis of pattern-forming systems. The discussion in this book covers aspects of cellular automata theory related to general problems of information theory and statistical physics, lattice gas theory, direct applications, problems arising in the modeling of microscopic physical processes, complex macroscopic behavior (mostly in connection with turbulence), and the design of special-purpose computers.

The inaugural Symposium on Turbulent Shear Flows was held at The Pennsylvania State University in 1977. Thereafter the locations for the biennial symposium have alternated between the USA and Europe. However, the ninth Symposium on Turbu lent Shear Flows was awarded to Japan in recognition of the strong support researchers of the Pacific Rim countries have given previous symposia. The University of Kyoto was the host institution and the meeting was held in the Inter national Conference Hall. The Local Arrangements Committee did a superb job scheduling traditional Japanese dinners and arranging visits to the many cultural treasures in the Kyoto region. The meeting attracted more than 260 offers of papers. Thirty-three sessions were scheduled to accommodate the 138 papers accepted for oral presentation. In addition a poster session was scheduled on each of the three days to accommodate a total of 42 poster presentations. From the presentations at the symposium 24 have been selected for inclusion in this volume. The authors of these papers have revised them taking into consideration comments made during their oral presentation and recommendations made by the Editors. Four subject areas are identified, namely closures and fundamentals, free flows, wall flows, and combustion and recirculating flows. Eminent authorities have prepared introductory articles fot each topic to put the individual contributions in context with each other and with related research.

The Boundary Element Method has now become a powerful tool of engineering analysis and is routinely applied for the solution of elastostatics and potential problems. More recently research has concentrated on solving a large variety of non-linear and time dependent applications and in particular the method has been developed for viscous fluid flow problems. This book presents the state of the art on the solution of viscous flow using boundary elements and discusses different current approaches which have been validated by numerical experiments. . Chapter 1 of the book presents a brief review of previous work on viscous flow simulation and in particular gives an up-to-date list of the most important BEM references in the field. Chapter 2 reviews the governing equations for general viscous flow, including compressibility. The authors present a compre hensive treatment of the different cases and their formulation in terms of boundary integral equations. This work has been the result of collaboration between Computational Mechanics Institute of Southampton and Massa chusetts Institute of Technology researchers. Chapter 3 describes the gen eralized formulation for unsteady viscous flow problems developed over many years at Georgia Institute of Technology. This formulation has been extensively applied to solve aer09ynamic problems.

Recently, there have been significant advances in the fields of high-enthalpy hypersonic flows, high-temperature gas physics, and chemistry shock propagation in various media, industrial and medical applications of shock waves, and shock-tube technology. This series contains all the papers and lectures of the 19th International Symposium on Shock Waves held in Marseille in 1993. They are published in four topical volumes, each containing papers on related topics, and preceded by an overview written by a leading international expert. The volumes may be purchased independently.

Recently, there have been significant advances in the fields of high-enthalpy hypersonic flows, high-temperature gas physics, and chemistry shock propagation in various media, industrial and medical applications of shock waves, and shock-tube technology. This series contains all the papers and lectures of the 19th International Symposium on Shock Waves held in Marseille in 1993. They will be published in four topical volumes, each containing papers on related topics, and preceded by an overview written by a leading international expert. The volumes may be purchased independently.

The first four symposia in the series on turbulent shear flows have been held alternately in the United States and Europe with the first and third being held at universities in eastern and western States, respectively. Continuing this pattern, the Fifth Symposium on Turbulent Shear Flows was held at Cornell University, Ithaca, New York, in August 1985. The meeting brought together more than 250 participants from around the world to present the results of new research on turbulent shear flows. It also provided a forum for lively discussions on the implications (practical or academic) of some of the papers. Nearly 100 formal papers and about 20 shorter communications in open forums were presented. In all the areas covered, the meeting helped to underline the vitality of current research into turbulent shear flows whether in experimental, theoretical or numerical studies. The present volume contains 25 of the original symposium presentations. All have been further reviewed and edited and several have been considerably extended since their first presentation. The editors believe that the selection provides papers of archival value that, at the same time, give a representative statement of current research in the four areas covered by this book: - Homogeneous and Simple Flows - Free Flows - Wall Flows - Reacting Flows Each of these sections begins with an introductory article by a distinguished worker in the field.

The present volume entitled "Perspectives in Turbulence Stud ies" is dedicated to Dr. Ing. E. h. Julius C. Rotta in honour of his 75th birthday. J. C. Rotta, born on January 1, 1912, started his outstanding career in an unusual way, namely in a drawing office (1928 - 1931). At the same time he - as a purely self taught perso- took a correspondence course in airplane construction. From 1934 to 1945 he worked in the aircraft industry on different subjects in the fields of flight mechanics, structures, air craft design, and aerodynamics. In 1945 he moved to Gottingen and worked from that time at the Aerodynamische Versuchsanstalt (AVA, now DFVLR) and the Max-Planck-Institut fur Stromungsforschung (1947-1958), interrupted only by a stay in the U. S. at the Glenn L. Martin Company (1954 - 1955) and a visiting professorship at the Laval University in Quebec, Canada (1956). Already during his activities in industry, Dr. Rotta discovered his special liking for aerodynamics. In Gottingen, he was attracted by Ludwig Prandtl's discussions about problems associated with turbulence and in particular his new contribution to fully developed turbulence, published in 1945. At that time, W. Heisenberg and C. F. v. Weizacker pub lished their results on the energy spectra of isotropic turbu lence at large wave numbers. Since that time his main research interest in reasearch has been in turbulence problems."

Shock wave research covers important inderdisciplinary areas which range from basic topics on gasdynamics, combustion and detonation, physico-chemistry of high temperature gases, plasma physics, astro and geophysics, materials science, astronautics and space technology to medical and industrial applications. This book includes 202 papers presented at the 18th the International Symposium on Shock Waves which describe the research frontier of shock wave phenopmena and 14 plenary lectures which show the state of the art of various fields of shock wave research. This proceedings is a unique collection of most important and updated shock wave research.

This book is one of three volumes entitled "ECARP-European Computational Aerodynamics Research Project", which was supported by the European Union in the Aeronautics Area of the Industrial and Materials Technology Programme. This volume contains optimization techniques for a number of inviscid and viscous problems like drag reduction, inverse, multipoint, wing-pylon-nacelle and riblets (Part A); and methodologies for solving the Navier Stokes equations on parallel architectures for compressible viscous flows in two and three dimensions (Part B). The main objective of this book is to disseminate information about cost effective methodologies for practical design problems and parallel CFD to be used by computer scientists and multidisciplinary engineers.

This volume contains a selection of the papers presented at the Eighth Symposium on Turbulent Shear Flows held at the Technical University of Munich, 9-11 September 1991. The first of these biennial international symposia was held at the Pennsylvania State Uni versity, USA, in 1977; subsequent symposia have been held at Imperial College, London, England; the University of California, Davis, USA; the University of Karlsruhe, Ger many; Cornell University, Ithaca, USA; the Paul Sabatier University, Toulouse, France; and Stanford University, California, USA. The purpose of this series of symposia is to provide a forum for the presentation and discussion of new developments in the field of turbulence, especially as related to shear flows of importance in engineering and geo physics. From the 330 extended abstracts submitted for this symposium, 145 papers were presented orally and 60 as posters. Out of these, we have selected twenty-four papers for inclusion in this volume, each of which has been revised and extended in accordance with the editors' recommendations. The following four theme areas were selected after consideration of the quality of the contributions, the importance of the area, and the selection made in earlier volumes: - wall flows, - separated flows, - compressibility effects, - buoyancy, rotation, and curvature effects. As in the past, each section corresponding to the above areas begins with an introduction by an authority in the field that places the individual contributions in context with one another and with related research.

Computational aeroacoustics is rapidly emerging as an essential element in the study of aerodynamic sound. As with all emerging technologies, it is paramount that we assess the various opportuni ties and establish achievable goals for this new technology. Essential to this process is the identification and prioritization of fundamental aeroacoustics problems which are amenable to direct numerical siIn ulation. Questions, ranging from the role numerical methods play in the classical theoretical approaches to aeroacoustics, to the correct specification of well-posed numerical problems, need to be answered. These issues provided the impetus for the Workshop on Computa tional Aeroacoustics sponsored by ICASE and the Acoustics Division of NASA LaRC on April 6-9, 1992. The participants of the Work shop were leading aeroacousticians, computational fluid dynamicists and applied mathematicians. The Workshop started with the open ing remarks by M. Y. Hussaini and the welcome address by Kristin Hessenius who introduced the keynote speaker, Sir James Lighthill. The keynote address set the stage for the Workshop. It was both an authoritative and up-to-date discussion of the state-of-the-art in aeroacoustics. The presentations at the Workshop were divided into five sessions - i) Classical Theoretical Approaches (William Zorumski, Chairman), ii) Mathematical Aspects of Acoustics (Rodolfo Rosales, Chairman), iii) Validation Methodology (Allan Pierce, Chairman), iv) Direct Numerical Simulation (Michael Myers, Chairman), and v) Unsteady Compressible Flow Computa tional Methods (Douglas Dwoyer, Chairman)."

The Third European Turbulence Conference was held at the Royal Institute of Technology, Sweden, from the 3rd to the 6th of July 1990 under the auspices of the European Mechanics Committee. This series of conferences is primarily devoted to fundamental aspects of turbulence and aimed at bringing together engineers, physicists and mathematicians. The scientific committee - serving also as the European Turbulence Con ference Committee - consisted of the following members: G. Comte-Bellot (Lyon), H.H. Fernholz (Berlin), H. Fiedler (Berlin), U. Frisch (Nice), J.c.R. Hunt (Cambridge), J. Jimenez (Madrid), A.V. Johansson (Stockholm), E. Krause (Aachen), G. Ooms (Amsterdam), and 1. Rhyming (Lausanne). The local organizing committee consisted of A.V. Johansson and P.H. Alfredsson. The conference programme comprised six invited lectures, given by D. Bechert, Y. Gagne, J. Jimenez, M.T. Landahl, C.H. Priddin and G.M. Za slavsky, and 96 contributions given as either oral or poster presentations.There were 172 participants from 17 countries. The members of this scientific com mittee acted as referees for the selection and scrutiny of the papers published in these proceedings. The main topics of this meeting were turbulence structure; transition and dynamical systems; turbulent combustion and mixing; turbulence affected by body forces; turbulence modelling; drag reduction and turbulence control; and novel experimental techniques. During the first evening of the conference the new MTL low-speed, low-turbulence wind-tunnel at KTH was inaugurated. The wind-tunnel outline, also acting as decoration for the "official conference cakes," is shown below."

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.

The present work is not exactly a "course," but rather is presented as a monograph in which the author has set forth what are, for the most part, his own results; this is particularly true of Chaps. 7-13. Many of the problems dealt with herein have, since the school year 1975-76, been the subject of a series of graduate lectures at the "Universire des Sciences et Techniques de Lille I" for students preparing for the "Diplome d'Etudes Ap profondies de Mecanique (option fluides)." The writing of this book was thus strongly influenced by the author's own conception of meteorology as a fluid mechanics discipline which is in a privi leged area for the application of singular perturbation techniques. It goes without saying that the modeling of atmospheric flows is a vast and complex problem which is presently the focal point of many research projects. The enonnity of the topic explains why many important questions have not been taken up in this work, even among those which are closely related to the subject treated herein. Nonetheless, the author thought it worthwhile for the development of future research on the modeling of atmospheric flows (from the viewpoint of theoretical fluid mechanics) to bring forth a book specifying the problems which have already been resolved in this field and those which are, as yet, unsolved."

Since 1964 the main function of the European Mechanics Committee has been to arrange Euromech Colloquia. These are three- or four-day meetings for the discussion of current research on a specified and relatively narrow topic in mechanics, by about 50 specialists chosen for their active involvement in research in that topic. The organization of each Euromech Colloquium is entrusted by the Committee to one or two selected scientists of repute in the field, and these organizers are enjoined to achieve a friendly and informal forum for discussion, with a minimum of paper work and expenditure. Over 220 Euromech Colloquia have been held since 1964 (about 40 each in France, West Germany and Britain and the remainder in 18 countries in both western and eastern Europe) on a wide range of topics drawn from the mechanics of solid materials, hydrodynamics, gas dynamics and mechanical systems. The Committee believes that collectively, Euromech Colloquia have made a significant contribution to the exchange of ideas on topics in mechanics within Europe and have thereby helped to overcome the barriers to easy scientific communication in that sorely divided continent. A few years ago the European Mechanics Committee turned its atten tion to the possible need for European conferences on a larger scale than Euromech Colloquia."

Macroscopic physics provides us with a great variety of pattern-forming systems displaying propagation phenomena, from reactive fronts in combustion, to wavy structures in convection and to shear flow instabilities in hydrodynamics. These proceedings record progress in this rapidly expanding field. The contributions have the following major themes: - The problems of velocity selection and front morphology of propagating interfaces in multiphase media, with emphasis on recent theoretical and experimental results on dendritic crystal growth, Saffman-Taylor fingering, directional solidification and chemical waves. - The "unfolding" of large-scale, low-frequency behavior in weakly confined homogeneous systems driven far from equilibrium, and more specifically, the envelope approach to the mathematical description of textures in different cases: steady cells, propagating waves, structural defects, and phase instabilities. - The implications of the presence of global downstream transport in open flows for the nature, convective or absolute, of shear flow instabilities, with applications to real boundary layer flows or shear layers, as reported in contributions covering experimental situations of fundamental and/or engineering interest.

The present volume entitled "Recent Contributions to Fluid Mechanics" is dedicated to Professor Dr.-Ing. Alfred Walz in honour of his 75th birthday. Alfred Walz, born on 11 May 1907, began his outstanding career as an electrical engineer. A few years after obtaining his university degree he became extremely engaged in fluid dynamics. Walking in the footsteps of Prandtl he was able to direct the development of theoretical activities in an inimitable way. He had the great opportunity to work both as an engaged fluid dynamicist -always trying to get to the bottom of things -and as a popular and patient teacher. To all of these things - in his own words - he gave his heart. Consequently, it is a great pleasure to publish the following 34 contributions summarizing the efforts of 56 authors. These artic les in total cover the wide range of experimental as well as theore tical fluid dynamics and reflect the present state of the art. Moreover, all colleagues and friends of Alfred Walz wish that he may be able to continue his work and his influence on the work of all of us via his enlightening ideas. Friedrichshafen, August 1982 Werner Haase Chairman of the Scientific Committee Table of Contents SURVEY PAPER Shear Layer Studies - Past, Present, Future P. Bradshaw .......................................... ."

Recently, there have been significant advances in the fields of high-enthalpy hypersonic flows, high-temperature gas physics, and chemistry shock propagation in various media, industrial and medical applications of shock waves, and shock-tube technology. This series contains all the papers and lectures of the 19th International Symposium on Shock Waves held in Marseille in 1993. They are published in four topical volumes, each containing papers on related topics, and preceded by an overview written by a leading international expert. The volumes may be purchased independently.

Both of the authors of this book are disciples and collaborators of the Brussels school of thermodynamics. Their particular domain of competence is the application of numerical methods to the many highly nonlinear problems which have arisen in the context of recent developments in the thermodynamics of irreversi ble processes: stability of states far from equilibrium, search for marginal critical states, bifwrcation phenomena, multiple stationnary states, dissipative structures, etc. These problems cannot in general be handled using only the clas sical and mathematically rigorous methods of the theory of differential, partial differential, and int grodifferential equations. The present authors demonstrate how approximate methods, re lyi ng usually on powerful computers, lead to significant progress in these areas, if one is prepa red to accept a certain lack of rigor, such as, for example, the lack of proof for the convergence of the series used in the context of problems which are not self adjoint, nor even linear. The results thus obtained must consequently be submit ted to an exacting confrontation with experimental observations. - Even though, the '1 imited information obtained concerning the, often unsuspec ted, mechanisms underlying the observed phenomena is both precious and frequently sufficient. This information results from the properties of the trial functions best suited to the constraints of the problem such as the initial, boundary, and "feedback" conditions, and the analysis of their behavior in the course of the evolution of the system."

The General Assembly of the International Union of Theoreti cal and Applied Mechanics decided in Cambridge, United King dom, in 1982 to arrange the Symposium on Optical Methods in the Dynamics of Fluids and Solids. This decision was stimu lated by the fact that optical diagnostic methods are a more and more important tool in experimental mechanics. In contrast to the foregoing Symposium in Poitiers. 1976, which was devoted exclusively to optical methods in the me chanics of solids, it was a fruitful idea to bring together during the present Symposium scientists engaged in optical methods in the dynamics of all phases. It was proposed by the International Scientific Committee of the Symposium that contributions in experimental fluid dynamics should deal with transition from laminar to turbu lent flow, compressible fluid flow including high temperatu re flow, non-equilibrium phenomena in fluid dynamics and the interaction of fluid flow with solid boundaries and bodies. As regard. the mechanics of solids, the contributions should deal with the application of optical methods in the wave propagation in shock loaded bodies, in phenomena connected with the fracture mechanism, in nonstationary Vibrations of elements and parts of systems and in nonstationary strains in structures. The International Scientific Committee preferred to avoid invited lectures and in cooperation with the National Com mittees of IUTAM called for contribution from individual countries.

Substantial progress has been made in the field of fluid mechanics under compensated gravity effects (microgravity). The main task of this disciplinehas evolved tremendously. Starting out with the aim of providing assistance in describing flow problems in other microgravity sciences, microgravityfluid mechanics has itself now become acknowledge as a powerful means of research. The IUTAM Symposium on Microgravity Fluid Mechanics has pro- vided the long-awaited forum for scientists from 15 coun- tries to discuss and concretize the "state-of-the-art" in this discipline. The main themes treated are: Interface Phe- nomena, Convective Processes; Marangoni effects, Solidifica- tion, Combustion, Physico-Chemical Processes, Multiphase Phenomena, Residual Acceleration effects, Fluid Handling and Non-Newtonian Flows.

would like to thank all those people in the life of Walter Noll I who helped me to write this book: Chancellor ofIndiana Univer- sity Professor Herman B. Wells, Dr. Klaus Andre, Professor Bemard D. Coleman, Stella DeVito, Dr. Peter Frankel, Professor Morton E. Gurtin, Studiendirektor i.R. Rudolf Hohensee, Faye Mark, Profes- sor Victor J. Mizel, Professor Dietrich Morgenstern, Professor Ralph Raimi, Professor Juan J. Schaffer, Professor Clifford A. Truesdell III, Professor Epifanio G. Virga, Dr. Paul Winkler and many oth- ers. I will be always indebted to Inge Lind, my teacher and friend, for a careful reading ofthe manuscript and her invaluable comments. This book would never have been written without the compas- sion and assistance of many people in Bochum and Marburg. I am especially grateful to Ursula Arras, Dieter and Karola Behm, Achim Buhl, Birgit Berger, Professor Klaus Bohmer, Ute Hagen, Irene Jo- raszik, Professor Hans-Heinrich Korle, Elke and Manfred Kuhne, Jutta Kuster, Johannes Lind, Inka Lins, Annemarie Matt, Astrid Milenz, Matthias Naher, Eckart Rosch, Manfred Schonsee, Profes- sor Werner von Seelen, Christa Seip, Heike Willig, Anita Wolf and many others.