湍流流动的基础理论与数值模拟研究（Pope.turbulent.flows）

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摘要：

本文是 Pope《Turbulent Flows》核心章节节选，系统搭建湍流统计理论基础体系。开篇阐释湍流随机性源于初始与边界微小扰动，借助洛伦兹系统直观说明混沌敏感性；引入概率密度、均值、协方差等统计工具，介绍均匀、高斯、对数正态等常用分布，定义随机场、自相关与能谱。推导雷诺分解与雷诺平均 N-S 方程，点明湍流封闭难题，阐述布辛涅斯克涡粘假设、梯度扩散假设及其局限性。以圆形射流为典型自由剪切流案例，结合实验数据论证自相似特性，分析射流速度衰减、展宽规律与雷诺数无关的核心特征，为湍流建模、CFD 数值模拟提供完备理论根基。

Preface

knowledge of probability theory,and consequently the necessary material is provided in the text (e.g.,Sections 3.2-3.5).

For a less demanding pace,Parts I and II can be covered in two semesters

-there is ample material.Alternatively,if a coverage of modelling is not required,Part I by itself provides a reasonably complete introduction to turbulent flows.

Many of the exercises ask the reader to 'show that..,'and thereby intro- duce additional results and observations.Consequently,it is recommended that all the exercises be read,even if they are not performed.The book is designed to be a self-contained text,but sufficient references are given to provide an entry into the research literature.

However much care is taken in the preparation of a book of this nature, it is inevitable that there will be errors in the first printing.A list of known corrections is given at http://mae.cornell.edu/~pope/TurbulentFlows. The reader is asked to report any further corrections to the author at pope@mae.cornell.edu.

I am profoundly grateful to many people for their help in the prepa- ration of this work.For their support and technical input I thank my colleagues at Cornell,David Caughey,Sidney Leibovich,John Lumley,Di- etmar Rempfer,and Zellman Warhaft.For their valuable suggestions based on reading draft chapters,I am grateful to Peter Bradshaw,Paul Durbin, Rodney Fox,Kemo Hanjalic,Charles Meneveau,Robert Moser,Blair Perot, Ugo Piomelli,P.K.Yeung,and Norman Zabusky.Similarly,I am grateful to the following Cornell graduates for their feedback on drafts of the book: Bertrand Delarue,Thomas Dreeben,Matthew Overholt,Paul Van Slooten, Jun Xu,Cem Albukrek,Dawn Chamberlain,Timothy Fisher,Laurent Myd- larski,Gad Reinhorn,Shankar Subramaniam,and Walter Welton.The first five mentioned are also thanked for their assistance in producing the figures. Most of the typescript was prepared by June Meyermann,whose patience, accuracy,and enthusiasm are greatly appreciated.The accuracy of the bib- liography has been much improved by the careful checking performed by Sarah Pope.Above all,I wish to thank my wife,Linda,for her patience, support,and encouragement during this project and over the years.

Nonenclature

The notation used is given here in the following order:upper-case Roman, lower-case Roman,upper-case Greek,lower-case Greek,superscripts,sub- scripts,symbols,and abbreviations.Then the symbols O(),o(),and～ that are used to denote the order of a quantity are explained.

Use of symbols for order and scaling

The statement that ‘the variable f is of order g'has different meanings depending on the context and the type of 'order'implied.The symbols O(h) (read 'big order h’or 'big O of h')and o(h)(read 'little order h’or little O of h’)indicate quantities,dependent on h,such that

Thus,for example,the Taylor series for a function f(x)can be written

In the expression f(h)～hP,the symbol～ can be read ‘varies as'or 'scales with’,and it indicates that the quantity f(h)/h is approximately constant (possibly over a limited range of h).In some contexts this type of relation is also stated as 'f(h)is of order h?”:for example,the FFT of N data points can be computed in of order Nlog N operations.

A statement such as 'f is of order 100'is used to indicate the approximate magnitude of f to the nearest power of ten.Thus,in this case,the value of f is roughly between 30 and 300.

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流体力学基础（第六版）核心内容整理（Fundamentals of FluidMechanics）

流体力学基础（第六版）核心内容整理（FundamentalsofFluidMechanics）摘要：本文为流体力学经典教材《FundamentalsofFluidMechanics》第六版，面向工科本科入门课程。全书分流体静力学、伯努利方程、控制体积分析、可压缩流、叶轮机械等十二核心章节，系统讲解流体基础物性、量纲分析、边界层、管道流动等核心理论。教材配套159段流体实景视频、超1300道分层习题，创新采用“已知-求解-点评”标准化例题格式，同时提供WileyPLUS线上数字化学习平台，内置交互式动画、自动批改题库与FlowLab简易CFD工具。书中兼顾SI与英制两套单位，结合冰山、水黾、空化等工程实例，兼顾理论推导与工程仿真实操，是流体力学入门权威教学用书。AchievePositiveLearningOutcomesWileyPLUScombinesrobustcoursewithinteractiveteachingandlearningresourcesallinoneeasy-to-usesystem.Ithashelpedoverhalfamillionstudentsandinstructorsachievepositivelearningoutcomesintheircourses.WileyPLUScontainseverythingyouandyourstudentsneed—andnothingmore,including:Theentiretextbookonline—withdynamiclinksfromhomeworktorelevantsections.Studentscanusetheonlinetextandsaveuptohalfthecostofbuyinganewprintedbook.Automatedassigning&gradingofhomework&quizzes.Aninteractivevarietyofwaystoteachandlearnthematerial.Instantfeedbackandhelpforstudents…available24/7.“WileyPLUShelpedmebecomemoreprepared.ThereweremoreresourcesavailableusingWileyPLUSthanjustusingaregular[printed]textbook,whichhelpedoutsigniﬁcantly.Veryhelpful...andveryeasytouse.”—StudentVictoriaCazorla,DutchessCountyCommunityCollegeSeeandtryWileyPLUSinaction!DetailsandDemo:www.wileyplus.comWhyWileyPLUSforEngineering?WileyPLUSofferstoday’sEngineeringstudentstheinteractiveandvisuallearningmaterialstheyneedtohelpthemgraspdifﬁcultconcepts—andapplywhatthey’velearnedtosolveproblemsinadynamicenvironment.Arobustvarietyofexamplesandexercisesenablestudentstoworkproblems,seetheirresults,andobtaininstantfeedbackincludinghintsandreadingreferenceslinkeddirectlytotheonlinetext.Studentscanvisualizeconceptsfromthetextbylinkingtodynamicresourcessuchasanimations,videos,andinteractiveLearningWare.SeeandtryWileyPLUSinaction!DetailsandDemo:www.wileyplus.comWileyPLUScombinesrobustcoursemanagementtoolswiththecompleteonlinetextandalloftheinteractiveteaching&learningresourcesyouandyourstudentsneedinoneeasy-to-usesystem.“Ilovedthisprogram[WileyPLUS]andIhopeIcanuseitinthefuture.”—AnthonyPastin,WestVirginiaUniversityAlgorithmicquestionsallowagroupofstudentstoworkonthesameproblemwithdifferingvalues.Studentscanalsoreworkaproblemwithdifferingvaluesforadditionalpractice.MultiPartProblemsandGoTutorialsleadstudentsthroughaseriesofsteps,providinginstantfeedbackalongtheway,tohelpthemdevelopalogical,structuredapproachtoproblemsolving.Or,theycanlinkdirectlytotheonlinetexttoreadaboutthisconceptbeforeattemptingtheproblemagain—withorwithoutthesamevalues.WileyiscommittedtomakingyourentireWileyPLUSexperienceproductive&enjoyablebyprovidingthehelp,resources,andpersonalsupportyou&yourstudentsneed,whenyouneedit.It’sallhere:www.wileyplus.comTECHNICALSUPPORT:AfullysearchableknowledgebaseofFAQsandhelpdocumentation,available24/7LivechatwithatrainedmemberofoursupportstaffduringbusinesshoursAformtoﬁlloutandsubmitonlinetoaskanyquestionandgetaquickresponseInstructor-onlyphonelineduringbusinesshours:1.877.586.0192FACULTY-LEDTRAININGTHROUGHTHEWILEYFACULTYNETWORK:Registeronline:www.wherefacultyconnect.comConnectwithyourcolleaguesinacomplimentaryvirtualseminar,withapersonalmentorinyourﬁeld,orataliveworkshoptosharebestpracticesforteachingwithtechnology.1STDAYOFCLASSANDBEYOND!ResourcesYou&YourStudentsNeedtoGetStarted&UseWileyPLUSfromthefirstdayforward.2-MinuteTutorialsonhowtosetup&maintainyourWileyPLUScourseUserguides,linkstotechnicalsupport&trainingoptionsWileyPLUSforDummies:Instructors’quickreferenceguidetousingWileyPLUSStudenttutorials&instructiononhowtoregister,buy,anduseWileyPLUSYOURWileyPLUSACCOUNTMANAGER:YourpersonalWileyPLUSconnectionforanyassistanceyouneed!SETUPYOURWileyPLUSCOURSEINMINUTES!SelectedWileyPLUScourseswithQuickStartcontainpre-loadedassignments&presentationscreatedbysubjectmatterexpertswhoarealsoexperiencedWileyPLUSusers.Interested?SeeandtryWileyPLUSinaction!DetailsandDemo:www.wileyplus.comSixthEditionFundamentalsofFluidMechanicsBRUCER.MUNSONDONALDF.YOUNGDepartmentofAerospaceEngineeringandEngineeringMechanicsTHEODOREH.OKIISHIDepartmentofMechanicalEngineeringIowaStateUniversityAmes,Iowa,USAWADEW.HUEBSCHDepartmentofMechanicalandAerospaceEngineeringWestVirginiaUniversityMorgantown,WestVirginia,USAToErikandallotherswhopossessthecuriosity,patience,anddesiretolearnPublisher:DonFowleyEditorialAssistant:MarkOwensAcquistionsEditor:JenniferWelterMediaEditor:LaurenSapiraMarketingManager:ChristopherRuelProductionManager:DorothySinclairProductionEditor:SandraDumasSeniorDesigner:MadelynLesureProductionManagementServices:IngraoAssociates/SuzanneIngraoCover:photoshowsthedevelopmentofvorticeswhichthewaterstriderusesformovingonthesurfaceofwaterbythetransferofmomentumfromthemovementofitslegstotheshedvortices(i.e.rowing).Thefluiddynamicsarevisualizedbyaddingthymolbluetothewatersurface.Formoreonwaterstriders,seethefollowinginthistext:Problem1.103inChapter1;FluidsintheNewstitled“Walkingonwater”inSect.1.9;andVideoV10.3“Waterstrider”inChapter10.PhotocourtesyofDavidL.HuandJohnW.M.Bush,MIT.Thisbookwastypesetin10/12TimesRomanbyAptara®,Inc.,andprintedandboundbyR.R.Donnelley/JeffersonCity.ThecoverwasprintedbyR.R.Donnelley/JeffersonCity.Thepaperinthisbookwasmanufacturedbyamillwhoseforestmanagementprogramsincludesustainedyieldharvestingofitstimberlands.Sustainedyieldharvestingprinciplesensurethatthenumberoftreescuteachyeardoesnotexceedtheamountofnewgrowth.Thisbookisprintedonacid-freepaper.∞Copyright©2009,2006,2002,1999,1994,1990byJohnWiley&Sons,Inc.Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording,scanningorotherwise,exceptaspermittedunderSections107or108ofthe1976UnitedStatesCopyrightAct,withouteitherthepriorwrittenpermissionofthePublisherorauthorizationthroughpaymentoftheappropriateper-copyfeetotheCopyrightClearanceCenter,222RosewoodDrive,Danvers,MA01923,(978)750-8400,fax(978)646-8600.RequeststothePublisherforpermissionshouldbeaddressedtothePermissionDepartment,JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030-5774,(201)748-6011,fax(201)748-6008.Toorderbooksorforcustomerservicecall1-800-CALL-WILEY(225-5945).Munson,BruceR.,Young,DonaldF.,Okiishi,TheodoreH.,Huebsch,WadeW.FundamentalsofFluidMechanics,SixthEditionISBN978-0470-26284-9PrintedintheUnitedStatesofAmerica.10987654321AbouttheAuthorsBruceR.Munson,ProfessorEmeritusofEngineeringMechanicsatIowaStateUniversity,receivedhisB.S.andM.S.degreesfromPurdueUniversityandhisPh.D.degreefromtheAerospaceEngi-neeringandMechanicsDepartmentoftheUniversityofMinnesotain1970.PriortojoiningtheIowaStateUniversityfacultyin1974,Dr.MunsonwasonthemechanicalengineeringfacultyofDukeUniversityfrom1970to1974.From1964to1966,heworkedasanen-gineerinthejetenginefuelcontroldepartmentofBendixAerospaceCorporation,SouthBend,Indiana.Dr.Munson’smainprofessionalactivityhasbeenintheareaoffluidmechanicseducationandresearch.Hehasbeenresponsibleforthedevelopmentofmanyfluidmechanicscoursesforstudiesincivilengineering,mechanicalengineering,engineeringscience,andagriculturalengineeringandistherecipientofanIowaStateUniversitySuperiorEngineeringTeacherAwardandtheIowaStateUniversityAlumniAssociationFacultyCitation.Hehasauthoredandcoauthoredmanytheoreticalandexperimentaltechnicalpapersonhy-drodynamicstability,lowReynoldsnumberflow,secondaryflow,andtheapplicationsofviscousin-compressibleflow.HeisamemberofTheAmericanSocietyofMechanicalEngineers.DonaldF.Young,AnsonMarstonDistinguishedProfessorEmeritusinEngineering,receivedhisB.S.degreeinmechanicalengineering,hisM.S.andPh.D.degreesintheoreticalandappliedmechanicsfromIowaStateUiversity,andhastaughtbothundergraduateandgraduatecoursesinfluidmechanicsatIowaStateformanyyears.InadditiontobeingnamedaDistinguishedProfessorintheCollegeofEngineer-ing,Dr.YounghasalsoreceivedtheStandardOilFoundationOutstandingTeacherAwardandtheIowaStateUniversityAlumniAssociationFacultyCitation.Hehasbeenengagedinfluidmechanicsresearchformorethan35years,withspecialinterestsinsimilitudeandmodelingandtheinterdisciplinaryfieldofbiomedicalfluidmechanics.Dr.Younghascontributedtomanytechnicalpublicationsandistheauthororcoauthoroftwotextbooksonappliedmechanics.HeisaFellowofTheAmericanSocietyofMechan-icalEngineers.TedH.Okiishi,ProfessorEmeritusofMechanicalEngineeringatIowaStateUniversity,joinedthefacultytherein1967afterreceivinghisundergraduateandgraduatedegreesfromthatinstitution.From1965to1967,Dr.OkiishiservedasaU.S.ArmyofficerwithdutyassignmentsattheNationalAeronauticsandSpaceAdministrationLewisResearchCenter,Cleveland,Ohio,whereheparticipatedinrocketnozzleheattransferresearch,andattheCombinedIntelligenceCenter,Saigon,RepublicofSouthVietnam,wherehestudiedseasonalriverfloodingproblems.ProfessorOkiishiandhisstudentshavebeenactiveinresearchonturbomachineryfluiddy-namics.Someoftheseprojectshaveinvolvedsignificantcollaborationwithgovernmentandindus-triallaboratoryresearcherswithtwooftheirpaperswinningtheASMEMelvilleMedal(in1989and1998).Dr.Okiishihasreceivedseveralawardsforteaching.Hehasdevelopedundergraduateandgradu-atecoursesinclassicalfluiddynamicsaswellasthefluiddynamicsofturbomachines.Heisalicensedprofessionalengineer.HisprofessionalsocietyactivitiesincludehavingbeenavicepresidentofTheAmericanSocietyofMechanicalEngineers(ASME)andoftheAmericanSocietyforEngineeringEducation.HeisaLifeFellowofTheAmericanSocietyofMechanicalEn-gineersandpasteditorofitsJournalofTurbomachinery.HewasrecentlyhonoredwiththeASMER.TomSawyerAward.WadeW.Huebsch,AssociateProfessorintheDepartmentofMechanicalandAerospaceEngineer-ingatWestVirginiaUniversity,receivedhisB.S.degreeinaerospaceengineeringfromSanJoseStateUniversitywhereheplayedcollegebaseball.HereceivedhisM.S.degreeinmechanicalengi-neeringandhisPh.D.inaerospaceengineeringfromIowaStateUniversityin2000.Dr.Huebschspecializesincomputationalfluiddynamicsresearchandhasauthoredmultiplejournalarticlesintheareasofaircrafticing,roughness-inducedflowphenomena,andboundarylayerflowcontrol.Hehastaughtbothundergraduateandgraduatecoursesinfluidmechanicsandhasdevelopedanewundergraduatecourseincomputationalfluiddynamics.Hehasreceivedmulti-pleteachingawardssuchasOutstandingTeacherandTeacheroftheYearfromtheCollegeofEngi-neeringandMineralResourcesatWVUaswellastheRalphR.TeetorEducationalAwardfromSAE.HewasalsonamedastheYoungResearcheroftheYearfromWVU.HeisamemberoftheAmericanInstituteofAeronauticsandAstronautics,theSigmaXiresearchsociety,theSocietyofAutomotiveEngineers,andtheAmericanSocietyofEngineeringEducation.PrefaceThisbookisintendedforjuniorandseniorengineeringstudentswhoareinterestedinlearningsomefundamentalaspectsoffluidmechanics.Wedevelopedthistexttobeusedasafirstcourse.Theprinci-plesconsideredareclassicalandhavebeenwell-establishedformanyyears.However,fluidmechanicseducationhasimprovedwithexperienceintheclassroom,andwehavebroughttobearinthisbookourownideasabouttheteachingofthisinterestingandimportantsubject.Thissixtheditionhasbeenpre-paredafterseveralyearsofexperiencebytheauthorsusingthepreviouseditionsforintroductorycoursesinfluidmechanics.Onthebasisofthisexperience,alongwithsuggestionsfromreviewers,col-leagues,andstudents,wehavemadeanumberofchangesinthisedition.Thechanges(listedbelow,andindicatedbythewordNewindescriptionsinthispreface)aremadetoclarify,update,andexpandcer-tainideasandconcepts.NewtoThisEditionInadditiontothecontinualeffortofupdatingthescopeofthematerialpresentedandimprovingthepresentationofallofthematerial,thefollowingitemsarenewtothisedition.Withthewide-spreaduseofnewtechnologiesinvolvingtheweb,DVDs,digitalcamerasandthelike,thereisanincreasinguseandappreciationofthevarietyofvisualtoolsavailableforlearning.Thisfacthasbeenaddressedintheneweditionbytheinclusionofnumerousnewillustrations,graphs,photographs,andvideos.Illustrations:Thebookcontainsmorethan260newillustrationsandgraphs.Theseillustrationsrangefromsimpleonesthathelpillustrateabasicconceptorequationtomorecomplexonesthatillustratepracticalapplicationsoffluidmechanicsinoureverydaylives.Photographs:Thebookcontainsmorethan256newphotographs.Somephotosinvolvesituationsthataresocommontousthatweprobablyneverstoptorealizehowfluidsareinvolvedinthem.Othersinvolvenewandnovelsituationsthatarestillbafflingtous.Thephotosarealsousedtohelpthereaderbetterunderstandthebasicconceptsandexamplesdiscussed.Videos:Thevideolibraryforthebookhasbeensignificantlyenhancedbytheadditionof80newvideosegmentsdirectlyrelatedtothetextmaterial.Theyillustratemanyoftheinterestingandprac-ticalapplicationsofreal-worldfluidphenomena.Therearenow159videos.Examples:Alloftheexamplesarenewlyoutlinedandcarriedoutwiththeproblemsolvingmethodof“Given,Find,Solution,andComment.”Learningobjectives:Eachchapterbeginswithasetoflearningobjectives.Thisnewfeaturepro-videsthestudentwithabriefpreviewofthetopicscoveredinthechapter.Listofequations:Eachchapterendswithanewsummaryofthemostimportantequationsinthechapter.Problems:Approximately30%newhomeworkproblemshavebeenaddedforthisedition.Theyareallnewlygroupedandidentifiedaccordingtotopic.Typically,thefirstfewproblemsineachgrouparerelativelyeasyones.Inmanygroupsofproblemsthereareoneortwonewproblemsinwhichthestudentisaskedtofindaphotograph/imageofaparticularflowsituationandwriteaparagraphdescribingit.EachchaptercontainsnewLifeLongLearningProblems(i.e.,oneaspectofthelifelonglearningasinterpretedbytheauthors)thataskthestudenttoobtaininformationaboutagiven,newflowconceptandtowriteabriefreportaboutit.FundamentalsofEngineeringExam:AsetofFEexamquestionsisnewlyavailableonthebookwebsite.原资料见附件免责声明：本页面/内容部分素材来源于互联网公开信息，旨在传递更多信息，不代表本平台立场。版权归原作者或机构所有，如涉及侵权，请通过平台联系我们，我们将在核实后第一时间处理。本平台对转载内容的真实性、准确性不作任何保证，用户需自行判断并承担使用风险。

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