This volume contains eighteen contributions of work, conducted since 2000 in the French - German Research Programme "Numerical Flow Simulation," which was initiated in 1996 by the Centre National de la Recherche Scientifique (CNRS) and the Deutsche Forschungsgemeinschaft (DFG). The main purpose of this third publication on the research programme is again to give an overview over recent progress, and to make the obtained results available to the public. The reports are grouped, like those in the first and the second publi cation (NNFM 66, 1998, and NNFM 75, 2001), under the four headings "Devel opment of Solution Techniques," "Crystal Growth and Melts," "Flows of React ing Gases, Sound Generation" and "Turbulent Flows." All contributions to this publication were reviewed by a board consisting of T. Alziary de Roquefort (Poi tiers, France), H. W. Buggisch (Karlsruhe, Germany), S. Candel (Paris, France), U. Ehrenstein (Nice, France), Th. Gallouet (Marseille, France), W. Kordulla (Gottingen, Germany), A. Lerat (Paris, France), 1. Piquet (Nantes, France), R. Rannacher (Heidelberg, Germany), G. Warnecke (Magdeburg, Germany), and the editor. The responsibility for the contents of the reports nevertheless lies with the contributors."

Critical regimes of two-phase flows with a polydisperse solid phase form the basis of such widespread industrial processes as separation of various powdery materials and minerals dressing. It is impossible to describe such complicated flows analytically. Therefore, this study concentrates on invariants experimentally revealed and theoretically grounded for such flows.

This approach can be compared with the situation in gases, where in order to determine principal parameters of their state, one does not need to measure the kinetic energy and velocity of each molecule and find its contribution to the temperature and pressure. These parameters are determined in a simple way for the system on the whole.

A novel conception of two-phase flows allowing the formulation of their statistical parameters is physically substantiated. On the basis of the invariants and these parameters, a comprehensive method of estimating and predicting mass transfer in such flows is developed.

It is noteworthy that the presented results are mostly phenomenological. Such an approach can be successfully extended to the separation of liquids, gases and isotopes.

The book is intended for students and specialists engaged in chemical technology, mineral dressing, ceramics, microelectronics, pharmacology, power generation, thermal engineering and other fields in which flows carrying solid particles are used in the technological process.

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 field of shock compression science has a long and rich history involving contributions of mathematicians, physicists and engineers over approximately two hundred years. The middle of the nineteenth century was an especially ac tive period with the contributions of Riemann, Rankine and Hugoniot, among others. The middle of the twentieth century saw another increase in activity re lated to shock compression of condensed matter as a result of military applica tions. It was also recognized that shock compression provided a means of sub jecting solids and liquids to extreme states of temperature and pressure difficult to achieve by static means. It has thus become an academic study in its own right. The principal modem contributions to this science were summarized in the landmark paper by Rice, McQueen and Walsh [Solid State Physics, Vol. 6, pp. 1-63, 1958]. As this field has continued to mature, interest has increased in tracing the early papers that have served as the foundations of the field. Cheret [Shock Compression of Condensed Matter - 1989, Elsevier Sci. Pub. B. V. , pp 11-19, 1990) has contributed to this literature with his review of the life of Hugoniot on the one-hundredth anniversary of the publication of Hugoniot's classic paper on the propagation of discontinuous waves in gases. This contribution prompted additional historical investigation involving the precursors to Hugoniot.

Der Band enthalt den Abschlussbericht des DFG-Schwerpunktprogramms "Flusssimulation mit Hochstleistungsrechnern." Es fuhrt die Arbeiten fort, die schon als Band 38 in der Reihe "Notes on Numerical Fluid Mechanics" erschienen sind.Work is reported, which was sponsored by the Deutsche Forschungsgemeinschaft from 1993 to 1995. Scientists from numerical mathematics, fluid mechanics, aerodynamics, and turbomachinery present their work on flow simulation with massively parallel systems, on the direct and large-eddy simulation of turbulence, and on mathematical foundations, general solution techniques and applications. Results are reported from benchmark computations of laminar flow around a cylinder, in which seventeen groups participated."

The primary purpose of this text is to document many of the lessons that have been learned during the author s more than forty years in the field of blast and shock. The writing therefore takes on an historical perspective, in some sense, because it follows the author s experience. The book deals with blast waves propagating in fluids or materials that can be treated as fluids.

It begins by distinguishing between blast waves and the more general category of shock waves. It then examines several ways of generating blast waves, considering the propagation of blast waves in one, two and three dimensions as well as through the real atmosphere. One section treats the propagation of shocks in layered gases in a more detailed manner.

The book also details the interaction of shock waves with structures in particular reflections, progressing from simple to complex geometries, including planar structures, two-dimensional structures such as ramps or wedges, reflections from heights of burst, and three-dimensional structures.

Intended for those with a basic knowledge of algebra and a solid grasp of the concepts of conservation of mass and energy, the text includes an introduction to blast wave terminology and conservation laws as well as a discussion of units and the importance of consistency."

Some words about SCART 2000. SCART stands for science and art. SCART meetings are organized in a loose time sequence by an international group of scientists, most of them fluid-dynamicists. The first meeting was held in Hong-Kong, the second one in Berlin, and the third, and latest, one in Zurich. SCART meetings include a scientific conference and a number of art events. The intention is to restart a dialogue between scientists and artists which was so productive in the past. To achieve this goal several lectures given by scientists at the conference are intended for a broader public. In the proceedings they are denoted as SCART lectures. The artists in tum address the main theme of the conference with their contributions. The lectures at SCART 2000 covered the entire field of fluiddynamics, from laminar flows in biological systems to astrophysical events, such as the explosion of a neutron star. The main exhibition by Dutch and Swiss artists showed video and related art under the title 'Walking on Air'. Experimental music was performed in two concerts.

Aircraft concepts are always driven by the requirements of the desired m- sion. A di?erent purpose for the use of the aircraft consequently results in a di?erent design. Therefore, depending on the intended outcome, con?i- ing requirements need to be ful?lled, for example, e?cient cruise speed and greatercargocapabilities,in combinationwith shorttake-o?andlanding ?eld lengths, or high speed and agility combined with variable payload demands. Due to the highly complex, non-linear physical environment in which aircraft operate, this task demands that the most advanced methods and tools are employed, to gain the necessary understanding of ?ow phenomena, and to exploit the ?ow physics to achieve maximum aircraft e?ciency. Inthe naturalsciences,researcherstry to create andextend humankno- edge by understanding and explaining the mechanisms of physical processes. In engineering, a designer is limited by certain requirements, and in order to ful?l these requirements the necessary technical tools need to be designed. In general, for a given problem the corresponding scienti?c or technical solution is sought. In order to successfully advance from a problem towards a solution, three main methods may be used. The two classical methods include theory and experiment, which are now being complemented by a third method, - scribedasnumericalsimulation.Theexperimentalapproachis basedonph- ical observation, measurement of relevant values, and methodical variation of the subject matter. For example, such experiments are used to gain a ph- ical understanding as well as to validate and investigate design alternatives.

The homogenization of single phase gases or liquids with chemical reactive components by mixing belongs to one of the oldest basic operations applied in chemical engineering. The design of equipment for mixing processes is still derived from measurements of the mixing time which is related to the applied methods of measurement and the special design of the test equipment itself.

This book was stimulated by improved modern methods for experimental research and visualization, for simulations and numerical calculations of mixing and chemical reactions in micro and macro scale of time and local coordinates. It is aimed to improve the prediction of efficiencies and selectivities of chemical reactions in macroscopic scale. The results should give an understanding of the influence of the construction of different mixing equipment on to the momentum, heat and mass transfer as well as reaction processes running on microscopic scales of time and local coordinates.

Newly developed methods of measurement are adjusted to the scales of the selected special transport and conversion processes. They allow a more detailed modeling of the mixing processes by the formulation of an appropriate set of momentum-, heat- and mass balance equations as well as boundary conditions in time and local coordinates together with constitutive equations and reaction kinetics equations as closure laws for numerical and analytical calculations. The latter were empirically derived in the past and therefore of limited reliability only.

The improved and more detailed modeling leads to a major progress in predicting mixing processes on the different scales adjusted to transport and reaction processes in molecular, micro- and macro dimensions.

As a consequence improved numerical calculations are performed on the basis of newly derived experimental, measurement and modeling methods which are the basis for the prediction of mixing time as well as conversion rates and selectivities of chemical reactions during the mixing process. The research efforts are focused onto the design of the technical equipment for flow mixing processes. Mixing is performed inside velocity fields leading to deformation gradients from free or wall induced boundary layers. The different kinds of process equipment are jet mixer, static mixer and mixing vessels equipped with rotating stirrers. Especially in micro mixing newly developed constructions are investigated permitting the scale up from laboratory to technical dimensions.

The origins of turbulent ?ow and the transition from laminar to turbulent ?ow are the most important unsolved problems of ?uid mechanics and aerodynamics. - sides being a fundamental question of ?uid mechanics, there are numerous app- cations relying on information regarding transition location and the details of the subsequent turbulent ?ow. For example, the control of transition to turbulence is - pecially important in (1) skin-friction reduction of energy ef?cient aircraft, (2) the performance of heat exchangers and diffusers, (3) propulsion requirements for - personic aircraft, and (4) separation control. While considerable progress has been made in the science of laminar to turbulent transition over the last 30 years, the c- tinuing increase in computer power as well as new theoretical developments are now revolutionizing the area. It is now starting to be possible to move from simple 1D eigenvalue problems in canonical ?ows to global modes in complex ?ows, all - companied by accurate large-scale direct numerical simulations (DNS). Here, novel experimental techniques such as modern particle image velocimetry (PIV) also have an important role. Theoretically the in?uence of non-normality on the stability and transition is gaining importance, in particular for complex ?ows. At the same time the enigma of transition in the oldest ?ow investigated, Reynolds pipe ?ow tran- tion experiment, is regaining attention. Ideas from dynamical systems together with DNS and experiments are here giving us new insights.

Over the last decade, Computational Fluid Dynamics (CFD) has become a - ture technology for the development of new products in aeronautical industry. Aerodynamic design engineers have progressively taken advantage of the pos- bilities o?ered by the numericalsolutionof the Reynolds averagedNavier-Stokes (RANS) equations. Signi?cant improvements in physical modeling and solution algorithms as well as the enormous increase of computer power enable hi- ?delity numerical simulations in all stages of aircraft development. In Germany, the national CFD project MEGAFLOW furthered the dev- opment and availability of RANS solvers for the prediction of complex ?ow problemssigni?cantly. MEGAFLOWwasinitiated by the?rstaviationresearch programoftheFederalGovernmentin1995undertheleadershipoftheDLR(see Kroll, N. , Fassbender, J. K. (Eds). : MEGAFLOW - Numerical Flow Simulation for Aircraft Design; Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Volume 89, Springer, 2005). A network from aircraft industry, DLR and several universities was created with the goal to focus and direct development activities for numerical ?ow simulation towards a common aerodynamic si- lation system providing both a block-structured (FLOWer-Code) and a hybrid (TAU-Code) parallel ? ow prediction capability. Today, both codes have reached a high level of maturity and reliability. They are routinely used at DLR and German aeronautic industry for a wide range of aerodynamic applications. For many universities the MEGAFLOW software represents a platform for the - provementofphysicalmodelsandfortheinvestigationofcomplex?owproblems. The network was established as an e?cient group of very closely co-operating partners with supplementing expertises and experience.

This short but complicated book is very demanding of any reader. The scope and style employed preserve the nature of its subject: the turbulence phe nomena in gas and liquid flows which are believed to occur at sufficiently high Reynolds numbers. Since at first glance the field of interest is chaotic, time-dependent and three-dimensional, spread over a wide range of scales, sta tistical treatment is convenient rather than a description of fine details which are not of importance in the first place. When coupled to the basic conserva tion laws of fluid flow, such treatment, however, leads to an unclosed system of equations: a consequence termed, in the scientific community, the closure problem. This is the central and still unresolved issue of turbulence which emphasizes its chief peculiarity: our inability to do reliable predictions even on the global flow behavior. The book attempts to cope with this difficult task by introducing promising mathematical tools which permit an insight into the basic mechanisms involved. The prime objective is to shed enough light, but not necessarily the entire truth, on the turbulence closure problem. For many applications it is sufficient to know the direction in which to go and what to do in order to arrive at a fast and practical solution at minimum cost. The book is not written for easy and attractive reading."

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.

1. Objective and Scope Bubbles, drops and rigid particles occur everywhere in life, from valuable industrial operations like gas-liquid contracting, fluidized beds and extraction to such vital natural processes as fermentation, evaporation, and sedimentation. As we become increasingly aware of their fundamental role in industrial and biological systems, we are driven to know more about these fascinating particles. It is no surprise, therefore, that their practical and theoretical implications have aroused great interest among the scientific community and have inspired a growing number of studies and publications. Over the past ten years advances in the field of small Reynolds numbers flows and their technological and biological applications have given rise to several definitive monographs and textbooks in the area. In addition, the past three decades have witnessed enormous progress in describing quantitatively the behaviour of these particles. However, to the best of our knowledge, there are still no available books that reflect such achievements in the areas of bubble and drop deformation, hydrodynamic interactions of deformable fluid particles at low and moderate Reynolds numbers and hydrodynamic interactions of particles in oscillatory flows. Indeed, only one more book is dedicated entirely to the behaviour of bubbles, drops and rigid particles ["Bubbles, Drops and Particles" by Clift et al. (1978)] and the authors state its limitations clearly in the preface: "We treat only phenomena in which particle-particle interactions are of negligible importance. Hence, direct application of the book is limited to single-particle systems of dilute suspensions.

The interest in the field of active flow control (AFC) is steadily increasing. In - cent years the number of conferences and special sessions devoted to AFC org- ized by various institutions around the world continuously rises. New advanced courses for AFC are offered by the American Institute of Aeronautics and Ast- nautics (AIAA), the European Research Community on Flow, Turbulence and Combustion (ERCOFTAC), the International Centre for Mechanical Sciences (CISM), the von Karman Institute for Fluid Dynamics (VKI), to name just a few. New books on AFC are published by prominent colleagues of our field and even a new periodical, the 'International Journal of Flow Control', appeared. Despite these many activities in AFC it was felt that a follow-up of the highly successful 'ACTIVE FLOW CONTROL' Conference held in Berlin in 2006 was appropriate. As in 2006, 'ACTIVE FLOW CONTROL II' consisted only of invited lectures. To sti- late multidisciplinary discussions between experimental, theoretical and numerical fluid dynamics, aerodynamics, turbomachinary, mathematics, control engineering, metrology and computer science parallel sessions were excluded. Unfortunately, not all of the presented papers made it into this volume. As the preparation and printing of a book takes time and as this volume should be available at the conf- ence, the Local Organizing Committee had to set up a very ambitious time sch- ule which could not be met by all contributors.

Ludwig Prandtl, with his fundamental contributions to hydrodynamics, ae- dynamics, and gas dynamics, greatly in?uenced the development of ?uid - chanics as a whole, and it was his pioneering research in the ?rst half of the last century that founded modern ?uid mechanics. His book Fu]hrer durch die Str]omungslehre, which appeared in 1942, originated from previous pub- cations in 1913, Lehre von der Flu]ssigkeit und Gasbewegung, and 1931, Abriss der Str]omungslehre. The title Fu]hrer durch die Str]omungslehre, or Essentials of Fluid Mechanics, is an indication of Prandtl's intentions to guide the reader on a carefully thought-out path through the di?erent areas of ?uid mech- ics. On his way, the author advances intuitively to the core of the physical problem, without extensive mathematical derivations. The description of the fundamental physical phenomena and concepts of ?uid mechanics that are needed to derive the simpli?ed models has priority over a formal treatment of the methods. This is in keeping with the spirit of Prandtl's research work. The ?rst edition of Prandtl's Fu]hrer durch die Str]omungslehre was the only book on ?uid mechanics of its time and, even today, counts as one of the most important books in this area. After Prandtl's death, his students Klaus Oswatitsch and Karl Wieghardt undertook to continue his work, and to add new ?ndings in ?uid mechanics in the same clear manner of presentation."

This volume constitutes the Proceedings of the IUTAM Symposium on "Analytical and Computational Fracture Mechanics of Non-homogeneous Materials," held in Cardiff from 18th to 22nd June 2001. The Symposium was convened to address and place on record topical issues in analytical and computational aspects of the fracture of non-homogeneous materials as they are approached by specialists in mechanics, materials science and related fields. The expertise represented in the Symposium was accordingly very wide, and many of the world's greatest authorities in their respective fields participated. Given the extensive range and scale of non-homogeneous materials, it had to be focussed to enhance the quality and impact of the Symposium. The range of non-homogeneous materials was limited to those that are inhomogeneous at the macroscopic level and/or exhibit strain softening. The issues of micro to macro scaling were not excluded even within this restricted range which covered materials such as rock, concrete, ceramics and composites on the one hand, and, on the other, those metallic materials whose ductile fracture is strongly influenced by the presence of inhomogeneities. The Symposium remained focussed on fundamental research issues of practical significance. These issues have many common features among seemingly disparate non-homogeneous materials.

The present set of lectures and tutorial reviews deals with various topical aspects related to instabilities of interfacial processes and driven flows from both the theoretical and experimental point of views. New research has been spurred by demands for many applications in material sciences (melting, solidification, electro deposition), biomedical engineering and processing in microgravity environments. This book is intended as both a modern source of reference for researchers in the field as well as an introduction to postgraduate students and non-specialists from related areas.

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."

This book is an effort to explore the technical aspects associated with bird flight and migration on wings. After a short introduction on the birds migration, the book reviews the aerodynamics and Energetics of Flight and presents the calculation of the Migration Range. In addition, the authors explains aerodynamics of the formation flight and finally introduces great flight diagrams.

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 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.