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...

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.

Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications. This volume, AMMA 2002, includes two parts with three articles by four subject experts. Part 1 deals with nonsmooth static and dynamic systems. A systematic mathematical theory for multibody dynamics with unilateral and frictional constraints and a brief introduction to hemivariational inequalities together with some new developments in nonsmooth semi-linear elliptic boundary value problems are presented. Part 2 provides a comprehensive introduction and the latest research on dendritic growth in fluid mechanics, one of the most profound and fundamental subjects in the area of interfacial pattern formation, a commonly observed phenomenon in crystal growth and solidification processes.

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 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.

The workshop "Nonhnear MHD Waves and Turbulence" was held at the - servatoire de Nice, December 1-4, 1998 and brought together an international group of experts in plasma physics, fluid dynamics and applied mathematics. The aim of the meeting was to survey the current knowledge on two main topics: (i) propagation of plasma waves (like Alfven, whistler or ion-acoustic waves), their instabilities and the development of a nonlinear dynamics lea ding to solitonic structures, wave collapse or weak turbulence; (ii) turbulence in magnetohydrodynamic flows and its reduced description in the presence of a strong ambient magnetic fleld. As is well known, both aspects play an important role in various geophysical or astrophysical media such as the - gnetospheres of planets, the heliosphere, the solar wind, the solar corona, the interplanetary and interstellar media, etc. This volume, which includes expanded versions of oral contributions pre sented at this meeting, should be of interest for a large community of resear chers in space plasmas and nonlinear sciences. Special effort was made to put the new results into perspective and to provide a detailed literature review. A main motivation was the attempt to relate more closely the theoretical un derstanding of MHD waves and turbulence (both weak and strong) with the most recent observations in space plasmas. Some papers also bring interesting new insights into the evolution of hydrodynamic or magnetohydrodynamic structures, based on systematic asymptotic methods."

In January 1992, the Sixth Workshop on Optimization and Numerical Analysis was held in the heart of the Mixteco-Zapoteca region, in the city of Oaxaca, Mexico, a beautiful and culturally rich site in ancient, colonial and modern Mexican civiliza tion. The Workshop was organized by the Numerical Analysis Department at the Institute of Research in Applied Mathematics of the National University of Mexico in collaboration with the Mathematical Sciences Department at Rice University, as were the previous ones in 1978, 1979, 1981, 1984 and 1989. As were the third, fourth, and fifth workshops, this one was supported by a grant from the Mexican National Council for Science and Technology, and the US National Science Foundation, as part of the joint Scientific and Technical Cooperation Program existing between these two countries. The participation of many of the leading figures in the field resulted in a good representation of the state of the art in Continuous Optimization, and in an over view of several topics including Numerical Methods for Diffusion-Advection PDE problems as well as some Numerical Linear Algebraic Methods to solve related pro blems. This book collects some of the papers given at this Workshop."

As computational fluid dynamics (CFD) is applied to ever more demanding fluid flow problems, the ability to compute numerical fluid flow solutions to a user specified tolerance as well as the ability to quantify the accuracy of an existing numerical solution are seen as essential ingredients in robust numerical simulation. Although the task of accurate error estimation for the nonlinear equations of CFD seems a daunting problem, considerable effort has centered on this challenge in recent years with notable progress being made by the use of advanced error estimation techniques and adaptive discretization methods. To address this important topic, a special course wasjointly organized by the NATO Research and Technology Office (RTO), the von Karman Insti tute for Fluid Dynamics, and the NASA Ames Research Center. The NATO RTO sponsored course entitled "Error Estimation and Solution Adaptive Discretization in CFD" was held September 10-14, 2002 at the NASA Ames Research Center and October 15-19, 2002 at the von Karman Institute in Belgium. During the special course, a series of comprehensive lectures by leading experts discussed recent advances and technical progress in the area of numerical error estimation and adaptive discretization methods with spe cific emphasis on computational fluid dynamics. The lecture notes provided in this volume are derived from the special course material. The volume con sists of 6 articles prepared by the special course lecturers."

This volume includes versions of papers selected from those presented at the THIESEL 2000 Conference on Thermofluidynamic Processes in Diesel Engines, held at the Universidad Politecnica de Valencia, during the period of September th th 13 to 15 , 2000. The papers are grouped into seven thematic areas: State of the Art and Prospective, Fuels for Diesel Engines, Injection System and Spray Formation, Combustion and Pollutant Formation, Modelling, Experimental Techniques, and Air Management. These areas cover most of the technologies and research strategies that may allow Light Duty and Heavy Duty Diesel engines to comply with current and forthcoming emission standards, while maintaining or improving fuel consumption. The main objectives of the conference were to bring together ideas and experience from Industry and Universities to facilitate interchange of information and to promote discussion of future research and development needs. The technical papers emphasised the use diagnostic and simulation techniques and their relationship to engineering practice and the advancement of the Diesel engine. We hope that this approach, which proved to be successful at the Conference, is reflected in this volume. We thank all those who contributed to the success of the Conference, and particularly the members of the Advisory Committee who assessed abstracts and chaired many of the technical sessions. Weare also grateful to participants who presented their work or contributed to the many discussions. Finally, the Conference benefitted from financial support from the organisations listed below and we are glad to have this opportunity to record our gratitude.

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.

This book is an introduction to current research on the N- vortex problem of fluid mechanics. Its goal is to describe the Hamiltonian aspects of vortex dynamics so that graduate students and researchers can use the book as an entry point into the rather large literature on integrable and non-integrable vortex problems within the broader context of dynamical systems. It is as self-contained as possible: the only training required of the reader is a good background in advanced calculus and ordinary and partial differential equations at the level of a typical undergraduate engineering, physics, or applied mathematics major. Exercises of varying difficulty are found at the end of each chapter which often require the reader to fill in details of proofs or complete examples.

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.

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.

Explains the motivation and reviewing the classical theory in a new form; Discusses conservation laws and Euler equations; For one-dimensional cases, the models presented are completely integrable

"Nanotechnology" isa broad term that includes aspects of materials science, mesoscopicphysics, organicandinorganicchemistry, na- electronics, atmosphericchemistry, airpollution, and other?elds. The technology is very muchincurrent focus-at the beginning of the Third Millennium-and raises hopes for environmentally benign, resource-lean manufacturing of products of manykinds. One precursor to present-day nanotechnology used porous coatings, comprised of "ultra?ne" particles withdimensions inthe nanometer range, for absorption of thermal radiation on thermocouples, bolometers, and the like. These particles were prepared by gas-phase syntheses, speci?cally using species formed by nucleation andgrowth from a metalvapor - dergoing coolingby collisions withinert gas molecules. Such "inert gas evaporation" was explored inthe 1920s and 1930s see, for example, A.H. Pfund, Phys. Rev. 35 (1930) 1434]andwas investigated in moredetail in the 1960s and 1970s see, for example, K. Kimoto et al., Jpn. J. Appl. Phys. 2 (1963) 702; C.G. Granqvist and R.A. Buhrman, J. Appl. Phys.47 (1976) 2200]. Improved analytical capabilities(electron microscopy)as well as new applications (selective absorption of solar energy) were twoofthe r- sons for the renewed interest. Today, gas-phase synthesis of nanoparticles constitutesthe foundation for a pro?table butstill small industry. Aerosols, i.e., dispersions or suspensions of particles ina gas, form the background ?eld for contemporaryefforts in gas-phase nanotechnology. Interest inaerosol researchhistorically arose from the issues of atmospheric chemistry and physics, human health protection, and airpollution. Today, aerosol researchengagesa vast array of efforts inthese and related ?elds, andelsewherein work identi?ed as nanotechnology.

The simulation of technological and environmental flows is very important for many industrial developments. A major challenge related to their modeling is to involve the characteristic turbulence that appears in most of these flows. The traditional way to tackle this question is to use deterministic equations where the effects of turbulence are directly parametrized, i. e. , assumed as functions of the variables considered. However, this approach often becomes problematic, in particular if reacting flows have to be simulated. In many cases, it turns out that appropriate approximations for the closure of deterministic equations are simply unavailable. The alternative to the traditional way of modeling turbulence is to construct stochastic models which explain the random nature of turbulence. The application of such models is very attractive: one can overcome the closure problems that are inherent to deterministic methods on the basis of relatively simple and physically consistent models. Thus, from a general point of view, the use of stochastic methods for turbulence simulations seems to be the optimal way to solve most of the problems related to industrial flow simulations. However, it turns out that this is not as simple as it looks at first glance. The first question concerns the numerical solution of stochastic equations for flows of environmental and technological interest. To calculate industrial flows, 3 one often has to consider a number of grid cells that is of the order of 100 .

Transports in fluids can be approached from two complementary perspectives. In the Eulerian view of mixing, the focus is on the concentration field. In the Langrangian view, fluid parcels are followed around as they move with the flow, experiencing chaotic or stochastic motion. This book examines both pictures, presenting a number of theoretical and experimental lectures on various aspects of transport and mixing of active and passive particles in geophysical flows.

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."

Six new chapters (14-19) deal with topics of current interest: multi-component convection diffusion, convection in a compressible fluid, convenction with temperature dependent viscosity and thermal conductivity, penetrative convection, nonlinear stability in ocean circulation models, and numerical solution of eigenvalue problems.

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.

This IMA Volume in Mathematics and its Applications PARTICULATE FLOWS: PROCESSING AND RHEOLOGY is based on the proceedings of a very successful one-week workshop with the same title, which was an integral part of the 1995-1996 IMA program on "Mathematical Methods in Materials Science." We would like to thank Donald A. Drew, Daniel D. Joseph, and Stephen L. Passman for their excellent work as organizers of the meeting. We also take this opportunity to thank the National Science Foun dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE The workshop on Particulate Flows: Processing and Rheology was held January 8-12, 1996 at the Institute for Mathematics and its Applications on the University of Minnesota Twin Cities campus as part of the 1995- 96 Program on Mathematical Methods in Materials Science. There were about forty participants, and some lively discussions, in spite of the fact that bad weather on the east coast kept some participants from attending, and caused scheduling changes throughout the workshop. Heterogeneous materials can behave strangely, even in simple flow sit uations. For example, a mixture of solid particles in a liquid can exhibit behavior that seems solid-like or fluid-like, and attempting to measure the "viscosity" of such a mixture leads to contradictions and "unrepeatable" experiments. Even so, such materials are commonly used in manufacturing and processing."

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.

This book presents two reviews from the cutting-edge of Russian plasma physics research. The first review is devoted to the mechanisms of transverse conductivity and generation of self-consistent electric fields in strongly ionized magnetized plasma. The second review considers numerous aspects of turbulent transport in plasma and fluids. This second review is focused on scaling arguments for describing anomalous diffusion in the presence of complex structures.