TheCarg'eseSummerSchool"Sound-?owinteractions"washeldinthe- stitutd'EtudesScienti?quesdeCarg'eseinCorsica,Francefrom19thJune to1stJuly,2000. Theunderstandingofsoundand?owinteractionshasmadesomerema- ableprogresssincethepioneeringworksoftheRussianandBritishschools, inthe1950s. Inaddition,thegrowingavailabilityduringthepast10years ofsophisticatedcomputer/electronics/materialstechniquesallowsforthe- velopmentofagrowingnumberofapplicationsaswellasthepossibilityof addressingnewfundamentalproblems. Thecouplingbetweenacousticwaves and?owmotionisbasicallynonlinear,sothatthesoundpropagationand generationismodi?edbythe?owandthe?owcanalsobemodi?edbythe sound. Asaresult,thisproblemisinvestigatedinmanydi?erentscienti?c communities,suchasappliedmathematics,acousticsand?uidmechanics, amongothers. Inouropinion,thetimehadcometotrytogatherthe- searchersinthedi?erentcommunitiestogetherinatutorialenvironemnt. So, thisschoolbroughttogetherworldwidespecialistsinordertopresentvarious aspectsofsound-?owinteractions,andshareexpertiseandmethodologiesso astopromotecross-fertilisation. ThebasicknowledgeintheareaisintroducedbyA. HirschbergandC. Schram. Hepresentstheaeroacousticsofinternal?owinaverylivelyway withalotofillustrationdevices. Heintroducesaeroacousticanalogiesand applicationslikemusicalinstruments,theRijketube,speechproductionetc. M. S. Howeintroducesthetheoryofvortexsoundinaverydidacticway. From Lighthill'sacousticanalogy,heshowshowvorticityandentropy?uctuations canbeseenassourcesofsound. Then,usingthecompactGreen'sfunctions, heshowshowtocomputethevortexsound. Asanexampleofthemethod presented,heappliesthistheorytopressuretransientsgeneratedbyhi- speedtrains. F. Lundgivesthebasicequationsofsound-?owinteractions. Thenheintroducesveryclearlythescatteringofsoundbecauseofvorticity andgivesthemostrecentresultsonultrasoundpropagationthroughadis- dered?ow. V. Ostashevpresentsgeometricalacousticsinmovingmediaand theimportantpracticalproblemofsoundpropagationinturbulence(at- sphere,ocean). A. Fabrikantexaminestheplasma-hydrodynamicsanalogies includingtheresonantwave-?owinteractioninshear?ows,wavesofnegative VI Preface energyandover-re?ectionandacousticoscillatorsin?uid?ows. P. J. Mor- sondescribesthedynamicsofthecontinuousspectrumwhichoccursinshear ?ow. Theresultsareinterpretedinthecontextofin?nitedimensionalHam- toniansystemstheory. G. Chagelishvilipresentsnewlinearmechanismsof acousticwavegenerationinsmoothshear?owsusinganon-modalstudy. N. Peakepresents?uid-structureinteractionsinthepresenceofmean?ows, includingtheproblemsofinstabilityandcausality. Finally,W. Lauterborn presentsnonlinearacousticswithapplicationstosonoluminescenceandto acousticchaos. InthisCarg'eseSummerSchool,54studentsfrom12nations,and11l- turersfrom7nationsparticipated. Aknowledgements. TheSummerSchoolandthispublicationwouldnot havebeenpossiblewithout: *?nancialsupportfromtheEuropeanUnion,theCentreNationaldela RechercheScienti?que,theMinist'eredesA?airesEtrang'eres,theM- ist'eredel'EducationNationale,delaRechercheetdelaTechnologieand theGroupementdeRecherche"Turbulence"; *the guidance of Elisabeth Dubois-Violette, director of the Institut d'EtudesScienti?quesdeCarg'ese; *thehelpofChantalAriano,NathalieBedjai,BrigitteCassegrain,Pierre- EricGrossiandthewholeteaminpreparingandhostingofthisschool. Finally,wewishtothankthelecturersforgivingsomuchtimeinprep- ingthelecturesandwritingthemup,aswellasmakingthemselvesavailable fordiscussionsduringtheschool. 1 LeMans,Paris,Lyon YvesAur'egan , 2 September2001 Agn'esMaurel , 1 VincentPagneux , 3 Jean-Fran,coisPinton . 1 Laboratoired'Acoustiquedel'Universit'eduMaine,UMRCNRS6613, Av. OMessiaen,72085LeMansCedex9,France 2 LaboratoireOndesetAcoustique,UMRCNRS7587, ESPCI,10rueVauquelin,75005Paris,France 3 LaboratoiredePhysique,UMRCNRS1325, EcoleNormaleSup'erieuredeLyon,46all'eed'Italie,69007Lyon,France Preface VII SomeofthelecturersoftheCarg'eseSchool,fromlefttoright:M. S. Howe,A. Hirschberg,P. Morrison,W. Lauterborn,V. Ostashev,A. Fabrikant,N. Peake, T. Colonius(PhotoC. Schram) SomeoftheparticipantsoftheCarg'eseSchool(PhotoC. Schram) TableofContents APrimitiveApproachtoAeroacoustics AvrahamHirschberg,ChristopheSchram...1 1 Introduction ...1 2 FluidDynamics ...2 3 Lighthill'sAnalogy...4 4 JetNoise ...7 5 Thermo-Acoustics ...9 6 AcousticalEnergy ...10 7 Rijke-Tube...11 8 Vortex-SoundTheory ...14 9 ChoiceoftheGreen'sFunction...17 10 Howe'?owinteractions,andshareexpertiseandmethodologiesso astopromotecross-fertilisation. ThebasicknowledgeintheareaisintroducedbyA. HirschbergandC. Schram. Hepresentstheaeroacousticsofinternal?owinaverylivelyway withalotofillustrationdevices. Heintroducesaeroacousticanalogiesand applicationslikemusicalinstruments,theRijketube,speechproductionetc. M. S. Howeintroducesthetheoryofvortexsoundinaverydidacticway. From Lighthill'sacousticanalogy,heshowshowvorticityandentropy?uctuations canbeseenassourcesofsound. Then,usingthecompactGreen'sfunctions, heshowshowtocomputethevortexsound. Asanexampleofthemethod presented,heappliesthistheorytopressuretransientsgeneratedbyhi- speedtrains. F. Lundgivesthebasicequationsofsound-?owinteractions. Thenheintroducesveryclearlythescatteringofsoundbecauseofvorticity andgivesthemostrecentresultsonultrasoundpropagationthroughadis- dered?ow. V. Ostashevpresentsgeometricalacousticsinmovingmediaand theimportantpracticalproblemofsoundpropagationinturbulence(at- sphere,ocean). A. Fabrikantexaminestheplasma-hydrodynamicsanalogies includingtheresonantwave-?owinteractioninshear?ows,wavesofnegative VI Preface energyandover-re?ectionandacousticoscillatorsin?uid?ows. P. J. Mor- sondescribesthedynamicsofthecontinuousspectrumwhichoccursinshear ?ow. Theresultsareinterpretedinthecontextofin?nitedimensionalHam- toniansystemstheory. G. Chagelishvilipresentsnewlinearmechanismsof acousticwavegenerationinsmoothshear?owsusinganon-modalstudy. N. Peakepresents?uid-structureinteractionsinthepresenceofmean?ows, includingtheproblemsofinstabilityandcausality. Finally,W. Lauterborn presentsnonlinearacousticswithapplicationstosonoluminescenceandto acousticchaos. InthisCarg'eseSummerSchool,54studentsfrom12nations,and11l- turersfrom7nationsparticipated. Aknowledgements. TheSummerSchoolandthispublicationwouldnot havebeenpossiblewithout: *?nancialsupportfromtheEuropeanUnion,theCentreNationaldela RechercheScienti?que,theMinist'eredesA?airesEtrang'eres,theM- ist'eredel'EducationNationale,delaRechercheetdelaTechnologieand theGroupementdeRecherche"Turbulence"; *the guidance of Elisabeth Dubois-Violette, director of the Institut d'EtudesScienti?quesdeCarg'ese; *thehelpofChantalAriano,NathalieBedjai,BrigitteCassegrain,Pierre- EricGrossiandthewholeteaminpreparingandhostingofthisschool. Finally,wewishtothankthelecturersforgivingsomuchtimeinprep- ingthelecturesandwritingthemup,aswellasmakingthemselvesavailable fordiscussionsduringtheschool. 1 LeMans,Paris,Lyon YvesAur'egan , 2 September2001 Agn'esMaurel , 1 VincentPagneux , 3 Jean-FranccoisPinton . 1 Laboratoired'Acoustiquedel'Universit'eduMaine,UMRCNRS6613, Av. OMessiaen,72085LeMansCedex9,France 2 LaboratoireOndesetAcoustique,UMRCNRS7587, ESPCI,10rueVauquelin,75005Paris,France 3 LaboratoiredePhysique,UMRCNRS1325, EcoleNormaleSup'erieuredeLyon,46all'eed'Italie,69007Lyon,France Preface VII SomeofthelecturersoftheCarg'eseSchool,fromlefttoright:M. S. Howe,A. Hirschberg,P. Morrison,W. Lauterborn,V. Ostashev,A. Fabrikant,N. Peake, T. Colonius(PhotoC. Schram) SomeoftheparticipantsoftheCarg'eseSchool(PhotoC. Schram) TableofContents APrimitiveApproachtoAeroacoustics AvrahamHirschberg,ChristopheSchram...1 1 Introduction ...1 2 FluidDynamics ...2 3 Lighthill'sAnalogy...4 4 JetNoise ...7 5 Thermo-Acoustics ...9 6 AcousticalEnergy ...10 7 Rijke-Tube...11 8 Vortex-SoundTheory ...14 9 ChoiceoftheGreen'sFunction...17 10 Howe'sEnergyCorollary ...20 11 TheOpenPipeTerminationofanUn?angedPipe ...21 12 Whistler-NozzleandHumanWhistling ...25 13 Conclusion...27 References...28 LecturesontheTheoryofVortex-Sound MichaelS. Howe...31 1 AerodynamicSound...31 1. 1 Lighthill'sAcousticAnalogy(1952)...31 1. 2 AerodynamicSoundfromLow-Mach-NumberTurbulence ofUniformMeanDensity...34 1. 3 AerodynamicSoundfromLow-Mach-NumberTurbulence ofVariableMeanDensity...35 2 VorticityandEntropyFluctuations asSourcesofSound...37 2. 1 TheRoleofVorticityinLighthill'sTheory...37 2. 2 AcousticAnalogyinTermsoftheTotalEnthalpy...39 2. 3 VorticityandEntropySources...40 3 FundamentalSolutionsoftheWaveEquation...43 3. 1 TheHelmholtzEquation...43 3. 2 TheWaveEquation...46 4 GeneralSolutionoftheInhomogeneousWaveEquation...47 4. 1 GeneralSolutionintheFrequency-Domain...47 X TableofContents 4. 2 GeneralSolutionintheTime-Domain...49 5 CompactGreen'sFunctions...

The utilization of mathematical models to numerically describe the performance of internal combustion engines is of great significance in the development of new and improved engines. Today, such simulation models can already be viewed as standard tools, and their importance is likely to increase further as available com puter power is expected to increase and the predictive quality of the models is constantly enhanced. This book describes and discusses the most widely used mathematical models for in-cylinder spray and combustion processes, which are the most important subprocesses affecting engine fuel consumption and pollutant emissions. The relevant thermodynamic, fluid dynamic and chemical principles are summarized, and then the application of these principles to the in-cylinder processes is ex plained. Different modeling approaches for the each subprocesses are compared and discussed with respect to the governing model assumptions and simplifica tions. Conclusions are drawn as to which model approach is appropriate for a specific type of problem in the development process of an engine. Hence, this book may serve both as a graduate level textbook for combustion engineering stu dents and as a reference for professionals employed in the field of combustion en gine modeling. The research necessary for this book was carried out during my employment as a postdoctoral scientist at the Institute of Technical Combustion (ITV) at the Uni versity of Hannover, Germany and at the Engine Research Center (ERC) at the University of Wisconsin-Madison, USA."

The focus is on the main physical ideas and mathematical methods of the microscopic theory of fluids, starting with the basic principles of statistical mechanics. The detailed derivation of results is accompanied by explanation of their physical meaning. The same approach refers to several specialized topics of the liquid state, most of which are recent developments, such as: a perturbation approach to the surface tension, an algebraic perturbation theory of polar nonpolarizable fluids and ferrocolloids, a semi-phenomenological theory of the Tolman length and some others.

Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

The origins of turbulent flow and the transition from laminar to turbulent flow are among the most important unsolved problems of fluid mechanics and aerodynamics. Besides being a fundamental question of fluid mechanics, there are any number of applications for information regarding transition location and the details of the subsequent turbulent flow. The JUT AM Symposium on Laminar-Turbulent Transition, co-hosted by Arizona State University and the University of Arizona, was held in Sedona, Arizona. Although four previous JUT AM Symposia bear the same appellation (Stuttgart 1979, Novosibirsk 1984, Toulouse 1989, and Sendai 1994) the topics that were emphasized at each were different and reflect the evolving nature of our understanding of the transition process. The major contributions of Stuttgart 1979 centered on nonlinear behavior and later stages of transition in two-dimensional boundary layers. Stability of closed systems was also included with Taylor vortices in different geometries. The topics of Novosibirsk 1984 shifted to resonant wave interactions and secondary instabilities in boundary layers. Pipe- and channel-flow transition were discussed as model problems for the boundary layer. Investigations of free shear layers were presented and a heavy dose of supersonic papers appeared for the first time. The character of Toulouse 1989 was also different in that 3-D boundary layers, numerical simulations, streamwise vortices, and foundation papers on receptivity were presented. Sendai 1994 saw a number of papers on swept wings and 3-D boundary layers. Numerical simulations attacked a broader range of problems.

This book is devoted to recent developments in the field of rotating fluids, in particular the study of Taylor--Couette flow, spherical Couette flow, planar Couette flow, as well as rotating annulus flow. Besides a comprehensive overview of the current state of the art, possible future directions in this research field are investigated. The first part of this volume presents several new results in the classical Taylor--Couette system covering diverse theoretical, experimental and numerical work on bifurcation theory, influence of boundary conditions, counter-rotating flows, spiral vortices and many others. The second part focuses on spherical Couette flows, including isothermal flows, thermal convective motion, as well as magnetohydrodynamics in spherical shells. The remaining parts are devoted to Goertler vortices, rotating annulus flows, as well as superfluid Couette flows. The present book will be of interest to all researchers and graduate students working actively in the field.

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."

The survival of the Aeronautical Industries of Europe in the highly competitive World Aviation Market is strongly dependent on such factors as time-to-market of a new or derivative aircraft and on its manufacturing costs but also on the achievement of a competitive technological advantage by which an increased market share can be gained. Recognizing this, cooperative research is continuously encouraged and co-financed by the European Union in order to strengthen the scientific and technological base of the Aeronautical Industries thus providing - among others - the technological edge needed for survival. Corresponding targets of research within Area 3, Technologies for Transport Means, and here in particular Area 3A, Aeronautics Technologies, of the Industrial and Materials Technologies Program ( Brite -EuRam III, 1994 -1998) have been identified to be aircraft efficiency, cost effectiveness and environmental impact. Concerning aircraft efficiency - relevant to the present research - a reduction in aircraft drag of 10%, a reduction in aircraft fuel consumption of 30%, and a reduction in airframe, engine and system weight of 20% are envisaged. Meeting these objectives has, of course, also a strong positive impact on the environment.

The need to predict, understand, and optimize complex physical and c- mical processes occurring in and around the earth, such as groundwater c- tamination, oil reservoir production, discovering new oil reserves, and ocean hydrodynamics, has been increasingly recognized. Despite their seemingly disparate natures, these geoscience problems have many common mathe- tical and computational characteristics. The techniques used to describe and study them are applicable across a broad range of areas. The study of the above problems through physical experiments, mat- matical theory, and computational techniques requires interdisciplinary col- boration between engineers, mathematicians, computational scientists, and other researchers working in industry, government laboratories, and univ- sities. By bringing together such researchers, meaningful progress can be made in predicting, understanding, and optimizing physical and chemical processes. The International Workshop on Fluid Flow and Transport in Porous - dia was successfully held in Beijing, China, August 2{6, 1999. The aim of this workshop was to bring together applied mathematicians, computational scientists, and engineers working actively in the mathematical and nume- cal treatment of ?uid ?ow and transport in porous media. A broad range of researchers presented papers and discussed both problems and current, state-of-the-art techniques.

Results of experimental research on aerodynamic and acoustic control of subsonic turbulent jets by acoustic excitation are presented. It was demonstrated that these control methods, originated by authors, not only can intensify mixing (by acoustic irradiation at low frequency), but also notably ease it (at high-frequency irradiation). This research monograph presents the updated results of the authors supplemented by other investigations conducted in USA, Germany and Great Britain. The methods for the numerical simulation of subsonic turbulent jets under acoustic excitation are described in detail, and examples are reviewed of practical applications, including reduction of turbojet engine noise and acoustic control of self-sustained oscillations in wind tunnels.

This volume contains the proceedings of the CEASlDragNet European Drag Reduction Conference held on 19-21 June 2000 in Potsdam, Germany. This conference, succeeding the First and Second European Forum on Laminar Flow Technology 1992 and 1996 respectively, was initiated by the European Drag Reduction Network (DragNet) and organised by DGLR (Deutsche Gesellschaft fUr Luft- und Raumfahrt - Lilienthal Oberth e. V. ) under the auspices ofCEAS (Confederation of European Aerospace Societies). The development of aerodynamic drag reduction technologies is driven by predictions of remarkable fuel savings, promising substantial improvements not only of aircraft efficiency but also of environmental compatibility. However, considerable efforts on an European scale are needed in order to develop, qualifY and demonstrate the means for their practical realisation. The primary aim of this conference was to provide a comprehensive survey of the current status of research, development and application in all disciplines of aerodynamic drag re- duction including laminar flow technology, adaptive wing concepts, turbulence and se- paration control, induced drag reduction and supersonic flow aspects. Besides aerodynamic topics the Call for Papers addressed also interdisciplinary aspects of design & system inte- gration, structures, materials, manufacturing, operations and maintenance. The Programme Committee (PC), responsible for the scientific preparation of the conference, consisted of CEAS representatives and DragNet board members (see following page).

In this book, the necessary background for understanding viscoelasticity is covered; both the continuum and microstructure approaches to modelling viscoelastic materials are discussed, since neither approach alone is sufficient.

The book describes recent developments in aeroacoustic measurements in wind tunnels and the interpretation of the resulting data. The reader will find the latest measurement techniques described along with examples of the results.

This well-written book explains the theory of spectral methods and their application to the computation of viscous incompressible fluid flows in clear and elementary terms. It begins with an introduction to the fundamentals of spectral methods and then moves on to cover, in particular, the Fourier and Chebyshev methods. Examples are included. Chapters 6 and 7 handle streamfunction-vorticity and velocity-pressure fomulations of the Navier-Stokes equations. Chapter 8 and 9 address special topics such as self- adaptive coordinate transform, treatment of singularities, and domain decomposition. The work will be useful to those teaching in the field at the graduate level, as well as to researchers working in the area.

Experts in rheology and polymer processing present up-to-date, fundamental and applied information on the rheological properties of polymers, in particular those relevant to processing, contributing to the physical understanding and the mathematical modelling of polymer processing sequences. Basic concepts of non-Newtonian fluid mechanics, micro-rheological modelling and constitutive modelling are reviewed, and rheological measurements are described. Topics with practical relevance are debated, such as linear viscoelasticity, converging and diverging flows, and the rheology of multiphase systems. Approximation methods are discussed for the computer modelling of polymer melt flow. Subsequently, polymer processing technologies are studied from both simulation and engineering perspectives. Mixing, crystallization and reactive processing aspects are also included. Audience: An integrated and complete view of polymer processing and rheology, important to institutions and individuals engaged in the characterisation, testing, compounding, modification and processing of polymeric materials. Can also support academic polymer processing engineering programs.

Segregation is a pervasive phenomenon whereby a flowing granular mass consisting of particles with diverse physical properties becomes spatially inhomogeneous. In the industrial sector that deals with the handling and processing of bulk solids, this non-uniformity is highly undesirable since blend homogeneity is generally a stringent requirement of most products. In the arena of geophysical flows, segregation can enhance the destructive capabilities of natural events such as avalanches and landslides. During the last 15 years, these issues have provided motivation and fostered collaborations between the communities of mathematicians, engineers, industrial researchers, and physicists to develop predictive models of segregation by integrating the perspectives and approaches of each. The collection of unique papers brings to light many of the perplexing scientific and technical issues in our current understanding of this complex phenomenon. It addresses advances in experiment, computational modeling and theory. This volume is one of the very few books devoted entirely to problems of segregation of particulate solids.

Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.

This volume contains the proceedings of the 2001 DLES4 workshop. It describes and discusses state-of-the-art modeling and simulation approaches for complex flows. Fundamental turbulence and modeling issues but also elements from modern numerical analysis are at the heart of this field of interest.

The purpose of this volume is to present a clear and systematic account of the mathematical methods of wave phenomena in solids, gases, and water that will be readily accessible to physicists and engineers. The emphasis is on developing the necessary mathematical techniques, and on showing how these mathematical concepts can be effective in unifying the physics of wave propagation in a variety of physical settings: sound and shock waves in gases, water waves, and stress waves in solids. Nonlinear effects and asymptotic phenomena will be discussed. Wave propagation in continuous media (solid, liquid, or gas) has as its foundation the three basic conservation laws of physics: conservation of mass, momentum, and energy, which will be described in various sections of the book in their proper physical setting. These conservation laws are expressed either in the Lagrangian or the Eulerian representation depending on whether the boundaries are relatively fixed or moving. In any case, these laws of physics allow us to derive the "field equations" which are expressed as systems of partial differential equations. For wave propagation phenomena these equations are said to be "hyperbolic" and, in general, nonlinear in the sense of being "quasi linear" . We therefore attempt to determine the properties of a system of "quasi linear hyperbolic" partial differential equations which will allow us to calculate the displacement, velocity fields, etc.

The book provides a broad overview of the full spectrum of state-of-the-art computational activities in multiphase flow as presented by top practitioners in the field. It starts with well-established approaches and builds up to newer methods. These methods are illustrated with applications to a broad spectrum of problems involving particle dispersion and deposition, turbulence modulation, environmental flows, fluidized beds, bubbly flows, and many others.

obtained are still severely limited to low Reynolds numbers (about only one decade better than direct numerical simulations), and the interpretation of such calculations for complex, curved geometries is still unclear. It is evident that a lot of work (and a very significant increase in available computing power) is required before such methods can be adopted in daily's engineering practice. I hope to l"Cport on all these topics in a near future. The book is divided into six chapters, each. chapter in subchapters, sections and subsections. The first part is introduced by Chapter 1 which summarizes the equations of fluid mechanies, it is developed in C apters 2 to 4 devoted to the construction of turbulence models. What has been called "engineering methods" is considered in Chapter 2 where the Reynolds averaged equations al"C established and the closure problem studied ( 1-3). A first detailed study of homogeneous turbulent flows follows ( 4). It includes a review of available experimental data and their modeling. The eddy viscosity concept is analyzed in 5 with the l"Csulting alar-transport equation models such as the famous K-e model. Reynolds stl"Css models (Chapter 4) require a preliminary consideration of two-point turbulence concepts which are developed in Chapter 3 devoted to homogeneous turbulence. We review the two-point moments of velocity fields and their spectral transforms ( 1), their general dynamics ( 2) with the particular case of homogeneous, isotropie turbulence ( 3) whel"C the so-called Kolmogorov's assumptions are discussed at length."

The Origin of Species Charles Darwin The origin of turbulence in fluids is a long-standing problem and has been the focus of research for decades due to its great importance in a variety of engineering applications. Furthermore, the study of the origin of turbulence is part of the fundamental physical problem of turbulence description and the philosophical problem of determinism and chaos. At the end of the nineteenth century, Reynolds and Rayleigh conjectured that the reason of the transition of laminar flow to the 'sinuous' state is in stability which results in amplification of wavy disturbances and breakdown of the laminar regime. Heisenberg (1924) was the founder of linear hydrody namic stability theory. The first calculations of boundary layer stability were fulfilled in pioneer works of Tollmien (1929) and Schlichting (1932, 1933). Later Taylor (1936) hypothesized that the transition to turbulence is initi ated by free-stream oscillations inducing local separations near wall. Up to the 1940s, skepticism of the stability theory predominated, in particular due to the experimental results of Dryden (1934, 1936). Only the experiments of Schubauer and Skramstad (1948) revealed the determining role of insta bility waves in the transition. Now it is well established that the transition to turbulence in shear flows at small and moderate levels of environmental disturbances occurs through development of instability waves in the initial laminar flow. In Chapter 1 we start with the fundamentals of stability theory, employing results of the early studies and recent advances."

This volume contains 27 contributions to the Second Russian-German Advanced Research Workshop on Computational Science and High Performance Computing presented in March 2005 at Stuttgart, Germany. Contributions range from computer science, mathematics and high performance computing to applications in mechanical and aerospace engineering.

This volume features the contributions to the 15th Symposium of the STAB (German Aerospace Aerodynamics Association). Papers provide a broad overview of ongoing work in Germany, including high aspect ratio wings, low aspect ratio wings, bluff bodies, laminar flow control and transition, active flow control, hypersonic flows, aeroelasticity, aeroacoustics, mathematical fundamentals, numerical simulations, physical fundamentals, and facilities.

Capillary Forces in Microassembly discusses the use of capillary forces as a gripping principle in microscale assembly. Clearly written and well-organized, this text brings together physical concepts at the microscale with practical applications in micromanipulation. Throughout this work, the reader will find a review of the existing gripping principles, elements to model capillary forces as well as descriptions of the simulation and experimental test bench developed to study the design parameters. Using well-known concepts from surface science (such as surface tension, capillary effects, wettability, and contact angles) as inputs to mechanical models, the amount of effort required to handle micro-components is then predicted.

Researchers and engineers involved in micromanipulation and precision assembly will find this a highly useful reference for microassembly system design and analysis.