This book presents a general classical field theory, incorporating continuum mechanics, electrodynamics, and thermodynamics. The continuum equations of material behavior are derived from the principles of Onsager's non-equilibrium thermodynamics supplemented with dynamic degrees of freedom. The book contains the basic principles and methods of modern continuum mechanics and of rheology. Non-equilibrium thermodynamics is discussed in detail. Applications include elasticity, thermoelasticity, viscoelasticity, plasticity, rheooptics, etc. The models of rheology are developed within a consistent thermodynamic framework. Viscoelastic and plastic response, Ostwald's curve of generalized Newtonian fluids, creep, elasticity preceding plastic flow, the rules of rheooptics, etc., are discussed, and the empirical Cox-Merz rule is proved. The thermodynamic results are compared to the results of microscopic theories. Several kinds of colloids, polymers, and liquid crystals are studied. The technical level of the book is high. It is designed for engineers, physicists, natural scientists and applied mathematicians.

The study of wall-bounded turbulent ows is of considerable interest from both scienti c and practical view points. As such it has attracted a great deal of research over the last 100 years. Much research has concentratedon ows over smooth walls since these are simpler from experimental, numerical and theoretical standpoints. The ow over rough walls has still received considerable attention but progress has necessarilybeenslower.Perhapsthemostessentialproblem(certainlyfromaprac- cal point of view) is to be able to predict the skin-frictiondrag acting on a plate (or a body) given a certain known roughness characteristic of the surface. Unfortunately this has proved to be very dif cult since even the simplest rough surfaces can be characterised by a number of different parameters and we still cannot directly c- nectthese tothe uiddynamicdragin a givensituation.Varioustheoriesandmodels have been proposed in order to make progress but there is still some disagreement in the community as to the correct understanding of these important ows.

The ultrasonic velocity profile (UVP) method, first developed in medical engineering, is now widely used in clinical settings. The fluid mechanical basis of UVP was established in investigations by the author and his colleagues with work demonstrating that UVP is a powerful new tool in experimental fluid mechanics. There are diverse examples, ranging from problems in fundamental fluid dynamics to applied problems in mechanical, chemical, nuclear, and environmental engineering. In all these problems, the methodological principle in fluid mechanics was converted from point measurements to spatio-temporal measurements along a line. This book is the first monograph on UVP that offers comprehensive information about the method, its principles, its practice, and applied examples, and which serves both current and new users. Current users can confirm that their application configurations are correct, which will help them to improve the configurations so as to make them more efficient and effective. New users will become familiar with the method, to design applications on a physically correct basis for performing measurements accurately. Additionally, the appendix provides necessary practical information, such as acoustic properties.

This book was written as a graduate student course--Shock Dynamics. Up to now, the first author has taught this course to the graduate students in the field of Fluid Mechanics, Department of Modern Mechanics, University of Science and Technology of China for seven times. In the spring semester 1989, during his visit to the United States, the first author taught this course to the graduate students of Department of Mathemat ics, University of Colorado at Denver. At the same time, he gave a series of four lectures on Shock Dynamics to the graduate students of Department of Aerospace Engineering Sciences, University of Colorado at Boulder. In 1991, during the first author's visit to Japan, he gave some lectures on Shock Dynamics in Tohoku University, University of Tokyo and Kyushu Uni versity. The dynamic phenomena of shock waves such as propagation, diffraction, reflection, refraction and interaction of shock waves may be studied by using experimental methods, numerical calculations and theoretical analyses. Although the detailed flow patterns of phenomena of shock motion can be obtained by using experimental methods and numerical calculations of solving Euler Equation or Navier-Stokes Equation, for example, the diffractions of shock waves by wedges form various phenomena of reflection--RR, SMR, CMR and DMR, we also need to analyse the process of the formation of shock waves in various phenomena of diffraction, reflection and interaction by using theoretical methods."

Twenty-one years have passed since the first symposium in this series was held in Paris (1976). Since then there have been meetings in Lausanne (1980), Cambridge (1984), Aachen (1987), Beijing (1989), Notre Dame (1991) and Fukuoka (1994). During this period a tremendous development in the field of unsteady aerodynamics and aeroelasticity in turbomachines has taken place. As steady-state flow conditions become better known, and as blades in the turbomachine are constantly pushed towards lower weight, and higher load and efficiency, the importance of unsteady phenomena appear more clearly. th The 8 Symposium was, as the previous ones, of high quality. Furthermore, it presented the audience with the latest developments in experimental, numerical and theoretical research. More papers than ever before were submitted to the conference. As the organising committee wanted to preserve the uniqueness of the symposium by having single sessions, and thus mingle speakers and audience with different backgrounds in this interdisciplinary field, only a limited number of papers could be accepted. 54 papers were accepted and presented at the meeting, all of which are included in the present proceedings.

Why are propeller blades of speedboats strongly eroded? Why does a syringe have to be filled slowly in order to avoid the formation of a vapour cavity near the piston? Why does a pump for watering the garden not work efficiently if it is placed too high above the ground water level? These questions, and many others taken from day to day experience, refer to situations which apparently have no connection between them, except for the fact that the motion of a liquid in part of the system plays an essential role.

Cavitation science is that part of liquid physics which addresses the motion of liquids near -or beyond- the limit of vaporization. Generally, vaporization occurs if liquid velocities are large, causing pressure to decrease below a critical value at which the liquid continuum is broken at one or several points. Vapor cavities appear there and various unexpected effects follow for the system such as noise, lower performance, vibrations, wall erosion For a long time, it was believed that cavitation phenomena should be avoided entirely because of the generally negative character of their consequences. However, over the years it appeared that such a constraint could be costly, though not necessarily justified on scientific grounds. A limited development of cavitation - if carefully defined and controlled - can be allowed. This promotes the development of high speed hydrodynamics and hydraulics.

The present book is aimed at providing a comprehensive presentation of cavitation phenomena in liquid flows. It is further backed up by the experience, both experimental and theoretical, of the authors whose expertise has been internationally recognized. A special effort is made toplace the various methods of investigation in strong relation with the fundamental physics of cavitation, enabling the reader to treat specific problems independently. Furthermore, it is hoped that a better knowledge of the cavitation phenomenon will allow engineers to create systems using it positively. Examples in the literature show the feasibility of this approach.

Part textbook, part exploratory work, this book aims to raise the awareness of students, physicists, and engineers in turbulence on the modeling of gravitationally induced turbulent mixing flows as produced, for instance, by Rayleigh-Taylor instabilities. The discussion is centered on the differences between single-fluid and two-fluid approaches, and it is illustrated with a 0D analysis of two specific elementary models in common use. Important deviations are shown to appear on many features, among others the prominence of directed energy, the simultaneous restitution of test cases, the responses to variable acceleration and shocks, and the behavior of various length scales.

The fifth ERCOFfAC workshop 'Direct and Large-Eddy Simulation-5' (DLES-5) was held at the Munich University of Technology, August 27-29, 2003. It is part of a series of workshops that originated at the University of Surrey in 1994 with the intention to provide a forum for presentation and dis cussion of recent developments in the field of direct and large-eddy simula tion. Over the years the DLES-series has grown into a major international venue focussed on all aspects of DNS and LES, but also on hybrid methods like RANSILES coupling and detached-eddy simulation designed to provide reliable answers to technical flow problems at reasonable computational cost. DLES-5 was attended by 111 delegates from 15 countries. Its three-day pro gramme covered ten invited lectures and 63 original contributions partially pre sented in parallel sessions. The workshop was financially supported by the fol lowing companies, institutions and organizations: ANSYS Germany GmbH, AUDI AG, BMW Group, ERCOFfAC, FORTVER (Bavarian Research Asso ciation on Combustion), JM BURGERS CENTRE for Fluid Dynamics. Their help is gratefully acknowledged. The present Proceedings contain the written versions of nine invited lectures and fifty-nine selected and reviewed contributions which are organized in four parts: 1 Issues in LES modelling and numerics 2 Laminar-turbulent transition 3 Turbulent flows involving complex physical phenomena 4 Turbulent flows in complex geometries and in technical applications.

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.

In the last 25 years, one of the most striking advances in Fluid Mecha nics was certainly the discovery of coherent structures in turbulence: lab oratory experiments and numerical simulations have shown that most turbulent flows exhibit both spatially-organized large-scale structures and disorganized motions, generally at smaller scales. The develop ment of new measurement and visualization techniques have allowed a more precise characterization and investigation of these structures in the laboratory. Thanks to the unprecedented increase of computer power and to the development of efficient interactive three-dimensional colour graphics, computational fluid dynamicists can explore the still myste rious world of turbulence. However, many problems remain unsolved concerning the origin of these structures, their dynamics, and their in teraction with the disorganized motions. In this book will be found the latest results of experimentalists, theoreticians and numerical modellers interested in these topics. These coherent structures may appear on airplane wings or slender bodies, mixing layers, jets, wakes or boundary-layers. In free-shear flows and in boundary layers, the results presented here highlight the intense three-dimensional character of the vortices. The two-dimensional large scale eddies are very sensitive to three-dimensional perturbations, whose amplification leads to the formation of three-dimensional coherent vorti cal structures, such as streamwise, hairpin or horseshoe vortex filaments. This book focuses on modern aspects of turbulence study. Relations between turbulence theory and optimal control theory in mathematics are discussed. This may have important applications with regard to, e. g. , numerical weather forecasting.

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 third supplement to the "Encyclopedia of Fluid Mechanics" series covers recent advances in basic fluid dynamics studies and transport mechanisms, with emphasis on heat transfer research. It extends to a number of fluid flow topics covered in greater depth in the main series volumes. Areas of research relying more heavily on numerical approaches and solutions are treated extensively. Several chapters also deal with analytical solutions to complex flow situations. This book has been compiled by a panel of 30 authors conducting research in hydrodynamics and heat transfer. It also contains the comprehensive index for series volumes 1-10 and supplements 1 and 2. This feature should enhance the usefulness and convenience of the entire series.

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 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.

Comprehensive, unique coverage of turbulent flow including modern prediction and measurement

Turbulent Flow presents the essential physical and analytical background that enables readers to make informed decisions when choosing the best method for the study and prediction of turbulent flows. Critical focus is given to experimental and numerical methods as well as what these methods have revealed about turbulent motion.

Coverage includes an introduction to turbulence theory, the fundamental equations of turbulent flow and their meaning, the techniques used in physical experiments and computer simulations, a review of the progress made in understanding the properties of turbulence, turbulence closures and their applications, and large eddy simulation methods.

Cutting-edge material includes:

• State-of-the-art turbulence closure and simulation techniques
• Up-to-date presentations of major theoretical and experimental advances
• Vortex analysis of turbulence structure, transport, and modeling

Turbulent Flow is an essential book for students and an invaluable reference for mechanical and aerospace engineers, physicists and mathematicians in related disciplines, and engineers and scientists in such fields as chemical, biological, and ocean engineering.

Turbulent ?ows are ubiquitous in most application ?elds, ranging from - gineering to earth sciences and even life sciences. Therefore, simulation of turbulent ?ows has become a key tool in both fundamental and applied - search. The complexity of Navier-Stokes turbulence, which is illustrated by the fact that the number of degrees of freedom of turbulence grows faster 11/4 thanO(Re ), where Re denotes the Reynolds number, renders the Direct Numerical Simulation (DNS) of turbulence inapplicable to most ?ows of - terest. To alleviate this problem, truncated solutions in both frequency and wavenumbermaybesought, whosecomputationalcostismuchlowerandmay ideally be arbitrarily adjusted. The most suitable approach to obtain such a low-cost three-dimensional unsteady simulation of a turbulent ?ow is Large- EddySimulation(LES), whichwaspioneeredtocomputemeteorological?ows in the late 1950s and the early 1960s. One of the main issues raised by LES is a closure problem: because of the non-linearity of the Navier-Stokes equations, the e?ect of unresolved scales must be taken into account to recover a reliable description of resolved scales of motion (Chap. 2). This need to close the governing equations of LES has certainly been the main area of investigation since the 1960s, and numerous closures, alsoreferredtoassubgridmodels, havebeenproposed. Mostexisting subgrid models have been built using simpli?ed viewsof turbulence dynamics, the main physical phenomenon taken into account being the direct kinetic - ergycascade from largeto small scales that is observed in isotropic turbulence and high-Reynolds fully developed turbulent ?ows. The most popular pa- digm for interscale energy transfer modeling is subgrid viscosity (C

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."

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 monograph focusing on gas flows addresses mostly theoretical issues and develops semi-analytical models as well as numerical methods for stimulating micro flows. It is appropriate for researchers in fluid mechanics interested in this new flow field as well as for electrical or mechanical engineers or physicists who need to incorporate flow modeling into their work. From the reviews: "For those who want to compute flows at the micro scale, this monograph is a must. It describes the state of the art and helps by providing coefficients, such as [are] needed in situations of slip. Those who wonder what new fluid dynamics there is in the microworld are served by the overview of theory and treasures of numerical methods." ?EUROPEAN JOURNAL OF MECHANICS B / FLUIDS

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.

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.

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."

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.