Introductory Lectures on Turbulence

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1、INTRODUCTORYLECTURESonTURBULENCEPhysics,MathematicsandModelingJ.M.McDonoughDepartmentsofMechanicalEngineeringandMathematicsUniversityofKentuckyc2004,2007Contents1FundamentalConsiderations11.1WhyStudyTurbulence?......................................11.2SomeD

2、escriptionsofTurbulence.................................11.3ABriefHistoryofTurbulence...................................61.3.1Generaloverview......................................61.3.2Threeerasofturbulencestudies.............................101.4Definitions

3、,MathematicalTools,BasicConcepts........................111.4.1Definitions.........................................111.4.2Mathematicaltools.....................................271.4.3Furtherbasicconcepts...................................371.5Summary........

4、......................................572StatisticalAnalysisandModelingofTurbulence592.1TheReynolds-AveragedNavier–StokesEquations........................592.1.1DerivationoftheRANSequations............................602.1.2Time-dependentRANSequations......

5、.......................632.1.3Importanceofvorticityandvortexstretchingtoturbulence..............652.1.4SomegeneralproblemswithRANSformulations....................682.1.5Reynolds-averagedNavier–StokesModels........................782.2TheKolmogorovTheoryofTu

6、rbulence..............................972.2.1Kolmogorov’s“universality”assumptions........................972.2.2HypothesesemployedbyFrisch[80]...........................982.2.3PrincipalresultsoftheK41theory............................992.3Summary..........

7、....................................1043Large-EddySimulationandMulti-ScaleMethods1073.1Large-EddySimulation.......................................1073.1.1ComparisonofDNS,LESandRANSmethods.....................1083.1.2TheLESdecomposition......................

8、............1103.1.3DerivationoftheLESfilteredequations.........................1113.1.4Subgrid-scalemodelsforLES...............................1143.1.5SummaryofbasicLESmethods..........................