Particle Image Velocimetry (PIV) is a non-intrusive optical measurement technique which allows capturing several thousand velocity vectors within large flow fields instantaneously. Today, the PIV technique has spread widely and differentiated into many distinct applications, from micro flows over combustion to supersonic flows for both industrial needs and research. Over the past decade the measurement technique and the hard- and software have been improved continuously so that PIV has become a reliable and accurate method for "real life" investigations. Nevertheless there is still an ongoing process of improvements and extensions of the PIV technique towards 3D, time resolution, higher accuracy, measurements under harsh conditions and micro- and macroscales. This book gives a synopsis of the main results achieved during the EC-funded network PivNet 2 as well as a survey of the state of the art of scientific research using PIV techniques in different fields of application.

Modelling Fluid Flow presents invited lectures, workshop summaries and a selection of papers from a recent international conference CMFF '03 on fluid technology. The lectures follow the current evolution and the newest challenges of the computational methods and measuring techniques related to fluid flow. The workshop summaries reflect the recent trends, open questions and unsolved problems in the mutually inspiring fields of experimental and computational fluid mechanics. The papers cover a wide range of fluids engineering, including reactive flow, chemical and process engineering, environmental fluid dynamics, turbulence modelling, numerical methods, and fluid machinery.

This volume contains results of a European project on Large Eddy Simulation (LES) of the flow around an airfoil. The main objective of the LESFOIL project was to assess the suitability of LES for airfoil flow. In conclusion, preliminary work was carried out such as development of numerical methods, and subgrid modelling in geometrically simple flows such as fully developed channel flow and periodic flow in a channel with a curved hill-shaped surface. Accurate LES of wall-bounded flow requires fine cells in the near-wall region in all coordinate directions. In an attempt to release this constraint, a large part of the LESFOIL project was aimed at developing and validating different approximate near-wall treatments. In the second half of the book, several LESs of the flow around the Aerospatiale-A airfoil are presented, using different numerical methods, grids, SGS models and near-wall treatments.

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.

Mobile particulate systems involve the mechanics, flow and transport properties of mixtures of fluids and solids. These systems are intrinsic to the rheology of emulsions and suspensions, flocculation and aggregation, sedimentation and fluidization, flow of granular media, nucleation and growth of small particles, segregation, attrition and solidification processes. Its diversity means that the area has been studied by a number of different disciplines (e.g. chemical or civil engineering, mechanics, hydrodynamics, geophysics, condensed matter and statistical physics, etc.). Mobile Particulate Systems features general, orientational lectures and advanced topics, covering state of the art approaches to the study of suspensions, fluidized beds, sedimentation and granular flows.

This book is collection of papers on the main topics of cardiovascular modelling and measurements. Some of the results show how to calculate many non-linear aspects of fluid flow and the turbulence in the arteries and the bifurcation junctions of the cardiovascular system. There are three themes to the papers: first, the fundamental concepts of fluid dynamics and turbulence in the system; the second theme is the flow modelling in arteries and bypass graft; the third section is about haemorheology and haemodynamics and explores the factors that play a role in coronary circulation using data from patients with ischaemic heart disease and acute myocardial infarction.

Flow-induced vibrations and noise continue to cause problems in a wide range of engineering applications ranging from civil engineering and marine structures to power generation and chemical processing. These proceedings bring together more than a hundred papers dealing with a variety of topics relating to flow-induced vibration and noise. The contents of this work constitute a mix of investigations by those working on the mechanisms of vibration and means of their alleviation, and studies by those in industry who draw on the present state of knowledge of these mechanisms to avoid or solve flow-induced vibration and noise problems in industrial applications.

Presenting current knowledge in the field of mudflows, this book includes both rheological mudflow aspects, and information on mudflow characteristics in open channels. It includes sections on:
A- physical properties of suspensions
A- shear rheometry with suspensions
A- rheology of clay-water mixtures
A- rheology of mud suspensions
A- gradually and rapidly varied free surface flows
Part of the IAHR Monograph Series, this informative book also includes fundamental equations for viscoplastic flows and provides the reader with helpful introductions to all the aspects it covers.

This book contains papers presented at a workshop, jointly organized by the EUROPIV 2 project, the PivNet 2 Thematic Network, and the ERCOFTAC Spe cial Interest Group on PIV (SIG 32). EUROPIV 2 was a research program, funded by the European Community which started in April 2000 and ended in June 2003. The aim of this project was to develop and demonstrate the Particle Image Velocimetry technique (PIV), which allows to measure the velocity of large flow fields instantaneously, in order to make it available as an operational tool for the European aeronautical industry. A total of 17 teams from 5 different countries cooperated during these 3 years to im prove the method, both hardware and software, and to demonstrate its capabilities in large industrial wind tunnels. PivNet 2 is a European thematic network devoted to the transfer of the PIV technique to IndUStry. It has started in April 2002 for four years. It is coordinated by Dr J. Kompenhans from DLR Gottingen. Details on PivNnet 2 can be found at http: //pivnet.sm.go.dlr.de. ERCOFTAC (European Research Community on Flow, Turbulence and Com bustion) is an international association with the aim to promote research and coop eration in Europe on fluid flows, turbulence and combustion. Details can be found at http: //www.ercoftac.org and http: //www.univ-lillellpivnet."

Mechanical engineering, an engineering discipline born of the needs of the industrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound issues of productivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series is a series featuring graduate texts and research monographs intended to address the need for information in contemporary areas of mechanical engineering. The series is conceived as a comprehensive one that covers a broad range of concentrations important to mechanical engineering graduate education and research. We are fortunate to have a distinguished roster of consulting editors, each an expert in one of the areas of concentration. The names of the consulting editors are listed on the following page of this volume. The areas of concentration are applied mechanics, biomechanics, computational mechanics, dynamic systems and control, energetics, mechanics of materials, processing, thermal science, and tribology. Professor Winer, the consulting editor for tribology, and I are pleased to present this volume of the series: Laminar Viscous Flow, by Professor Constantinescu. The selection of this volume underscores again the interest of the Mechanical Engineering Series to provide our readers with topical monographs as well as graduate texts.

The subject of wave phenomena is well-known for its inter-disciplinary nature. Progress in this field has been made both through the desire to solve very practical problems, arising in acoustics, optics, radiophysics, electronics, oceanography, me teorology and so on, and through the development of mathematical physics which emphasized that completely different physical phenomena are governed by the same (or similar) equations. In the immense literature on physics of waves there is no lack of good presentations of particular branches or general textbooks on mathematical physics. But if one restricts the attention to pulse propagation phenomena, one no tices that many useful facts are scattered among the various books and journals, and their connections are not immediately apparent. For example, the problems involv ing acoustic pulse propagation in bubbly liquids and those related to electromagnetic pulses in resonant media are usually treated without much cross reference in spite of their obvious connections. The authors of this book have attempted to write a coherent account of a few pulse propagation problems selected from different branches of applied physics. Although the basic material on linear pulse propagation is included, some topics have their own unique twists, and a comprehensive treatment of this body of material can hardly be found in other sources. First of all, the problem of pulse propagation in non equilibrium media (unstable or admitting attenuation) is far more delicate than it is apparent at a first glance."

Designed for engineers, this work considers flow-induced vibrations. It covers topics such as body oscillators; fluid loading and response of body oscillators; fluid oscillators; vibrations due to extraneously-induced excitation; and vibrations due to instability-induced excitation.

A review of open channel turbulence, focusing especially on certain features stemming from the presence of the free surface and the bed of a river. Part one presents the statistical theory of turbulence; Part two addresses the coherent structures in open-channel flows and boundary layers.

This book provides an introduction to the subject of turbulence modelling in a form easy to understand for anybody with a basic background in fluid mechanics, and it summarizes the present state of the art. Individual models are described and examined for the merits and demerits which range from the simple Prandtl mixing length theory to complex second order closure schemes.

TUrbulence modeling encounters mixed evaluation concerning its impor tance. In engineering flow, the Reynolds number is often very high, and the direct numerical simulation (DNS) based on the resolution of all spatial scales in a flow is beyond the capability of a computer available at present and in the foreseeable near future. The spatial scale of energetic parts of a turbulent flow is much larger than the energy dissipative counterpart, and they have large influence on the transport processes of momentum, heat, matters, etc. The primary subject of turbulence modeling is the proper es timate of these transport processes on the basis of a bold approximation to the energy-dissipation one. In the engineering community, the turbulence modeling is highly evaluated as a mathematical tool indispensable for the analysis of real-world turbulent flow. In the physics community, attention is paid to the study of small-scale components of turbulent flow linked with the energy-dissipation process, and much less interest is shown in the foregoing transport processes in real-world flow. This research tendency is closely related to the general belief that universal properties of turbulence can be found in small-scale phenomena. Such a study has really contributed much to the construction of statistical theoretical approaches to turbulence. The estrangement between the physics community and the turbulence modeling is further enhanced by the fact that the latter is founded on a weak theoretical basis, compared with the study of small-scale turbulence."

The purpose of this text is to benefit users, manufacturers and engineers by drawing together an overall view of the technology. It attempts to give the reader an appreciation of the extent to which slurry transport is presently employed, the theoretical basis for pipeline design and the practicalities of design and new developments.

This book gives the basic analytical framework for the description of turbulent flows and discusses various types encountered by civil engineers involved in hydraulic analysis and design, as well as environmental engineers. It also presents a detailed exposition of the various dimensions of turbulent flow. The book is extremely useful for practising engineers, particularly in the field of hydraulic analysis and design, building dynamics and environmental engineering.

This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.

For centuries, physical models have been used to investigate complex hydraulic problems. Leonardo da Vinci (1452-1519) stated, "I will treat of such a subject. But first of all, 1 shall make a few experiments and then demonstrate why bodies are forced to act in this matter. " Even with the current advancements of mathematical numerical models, certain complex three-dimensional flow phenomena must still rely on physical model studies. Mathematical models cannot provide adequate solutions if physical processes involved are not completely known. Physical models are particularly attractive to investigate phenomena-involved sediment movements because many three-dimensional sediment processes are still unclear at this stage. Theoretically, there are numerous factors governing movable bed processes and it is nearly impossible to design model studies to obey all the model criteria. Sometimes, appropriate lightweight materials are difficult or too costly to obtain. Often, distorted models are used due to the limitation of available space and the requirement for greater vertical flow depth to investigate vertical differences of various parameters. The turbulence level in the model may also be maintained at a sufficient level to reproduce a similar flow pattern in the prototype. Frequently, engineers are forced to employ distorted models that cannot be designed to satisfy all governing criteria correctly. Thus each hydraulic laboratory has developed its own rules for model testing and a great deal of experience is needed to interpret model results.

The idea of organising a colloquium on turbulence emerged during the sabbatical leave of Prof. Arkady Tsinober in Zurich. New experimental observations and the insight gained through direct numerical simulations have been stimulating research in turbulence and are leading to the developments of new concepts. The organisers felt the necessity to bring together researchers who have contributed significantly to the advances in this field in a colloquium in which the current achievements and the future development in the theoretical, numerical and experimental approaches would be discussed. The main emphasis of the colloquium was put on discussions. These discussions led to an interesting and exciting exchange of ideas, but also involved its very laborious transcription onto paper. It was due to the personal efforts of Mrs. A. Vyskocil, Dr. N. Malik and Dr. X. Studerus that this work could be completed. The colloquium was held in the relaxed atmosphere of the Centro Stefano Franscini in Monte Verita near Ascona, a locality of exceptional natural beauty, which was put at our disposal by the Swiss Federal Institute of Technology. We would like to express our gratitude for this generous financial and logistic support, which contributed considerably to the success of the colloquium. Zurich, April 1993 Th. Dracos, A. Tsinober Participants Adrian, R. J. Kambe, T. Antonia, R. A. Kit,E. Aref, H. Landahl, M. T. Betchov, R. Lesieur, M. Bewersdorff, H. -W. Malik, N. Castaing, B. Moffatt, H. K. Chen, J. Moin,P. Dracos, T. Mullin, T. Frisch, U. Novikov, E. A.

This book provides concise, up-to-date and easy-to-follow information on certain aspects of an ever important research area: multiphase flow in porous media. This flow type is of great significance in many petroleum and environmental engineering problems, such as in secondary and tertiary oil recovery, subsurface remediation and CO2 sequestration. This book contains a collection of selected papers (all refereed) from a number of well-known experts on multiphase flow. The papers describe both recent and state-of-the-art modeling and experimental techniques for study of multiphase flow phenomena in porous media. Specifically, the book analyses three advanced topics: upscaling, pore-scale modeling, and dynamic effects in multiphase flow in porous media. This will be an invaluable reference for the development of new theories and computer-based modeling techniques for solving realistic multiphase flow problems. Part of this book has already been published in a journal. Audience This book will be of interest to academics, researchers and consultants working in the area of flow in porous media.

In the last decades, a lot of effort has been directed towards manipulation of turbulent boundary layers by passive devices such as external manipulators (thin flat plates or aerofoil section devices embedded in the outer layer) and/or internal manipulators (small streamwise grooves acting directly on the inner region) for the purpose of reducing viscous drag. The former are commonly referred to as LEI3U s or BLADEs and the laHer riblets or grooves. Though the details of the mechanisms are not firmly understood, world-wide experimenta.! data are available and consistent enough in order to assert the potential of such devices for turbulent drag reduction. It should be noted that following on from recent and successful flight tests, the concept of using grooved surfaces is rather close to finding industrial applications. During the last few years, in Europe, there has been considerable interest in lookillg at the behaviour of such passi,'e turbulence manipulators. A lot of intense research, concerning both experimental and theoretical studies. has been carried out in some European research centres. For the last fi\'e years. informal gatherings. called ,.\ \'orking Pi\l'ty i\Ieetings" , have been set up, once a year; the aim of these meetings is not only to bring together European researchers acti,'e in the field of turbulent drag reduction by passi"e means and to hear about recent de\'c!opments but also to o u t1 ine sui tit ble directions for future research or collaborative programmes.

The purpose of this book is to present a broad panorama of model problems encountered in nonviscous Newtonian fluid flows. This is achieved by investigating the significant features of the solutions of the corresponding equations using the method of asymptotic analysis. The book thereby fills a long-standing gap in the literature by providing researchers working on applied topics in hydro-aerodynamics, acoustics and geophysical fluid flows with exact results, without having to invoke the complex mathematical apparatus necessary to obtain those insights. The benefit of this approach is two-fold: outlining the idea of the mathematical proofs involved suggests methodologies and algorithms for numerical computation, and also often gives useful information regarding the qualitative behaviour of the solutions. This book is aimed at researchers and students alike as it also provides all the necessary basic knowledge about fluid dynamics.

This book offers to students, engineers, CFD modelers, and scientists a detailed synthetic presentation of turbulence physics and modeling with the possibility to find a quick route through the jungle of publications and models. Chapters 1 to 4 show that turbulence models may be derived and analyzed in a physically sound manner with their potential merits and drawbacks. Chapters 5 and 6 review the physics of (inhomogenous) turbulent flows starting from the most simple flow cases and adding more and more complexity. The status and uncertainties of available experimental data and the practical performance of currently available turbulent models are discussed.

This volume contains the proceedings of the CEAS/DragNet European Drag Reduction Conference 2000. The conference addressed the recent advances in all areas of drag reduction research, development, validation and demonstration including laminar flow technology, adaptive wing concepts, turbulent and induced drag reduction, separation control and supersonic flow aspects. This volume is of particular interest to engineers, scientists and students working in the aeronautics industry, research establishments or academia.