Fluid Dynamics Lecture Notes

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1、MTH-3D41FluidDynamicsLectureNotesDrMarkBlyth[1]D.J.AchesonElementaryfluiddynamics,Oxford.[2]D.J.TrittonPhysicalFluidDynamics,Oxford.[3]G.K.BatchelorAnintroductiontofluiddynamics,Cambridge.Toseethetheoryinaction,thefollowingisabookofphotographsoffluidmotion:[4]M.Van-Dyk

2、eAnalbumoffluidmotion,ParabolicPress.Contents0.Introduction1.Preliminaryideas2(a)Stressinfluids2(b)Straininfluids2(c)Stress-strainrelationshipforaNewtonianfluid3.TheNavier-Stokesequations4.Vorticitydynamicsandthestreamfunction5.ExactsolutionsoftheNavier-Stokesequations6

3、.Stokesflow7.Lubricationtheory8.Boundarylayers9.HydrodynamicstabilityAppendix:Invariantsofamatrixunderrotation.10.IntroductionThestudyoffluidmechanicsencompassesmanyvariedapplicationsinbothnaturalandengineeringprocesses.SomeexamplesareAerodynamics–flowpastwings;computa

4、tionofdragandlift;D’Alembert’sparadoxBiologicalfluiddynamics–fishswimming;flowinarteriesandveins;bloodflowinvasculartumours;KorotkoffsoundsGeophysicalfluiddynamics(GFD)–oceanographyandmeteorology;climateandweatherpredictionIndustrialfluiddynamics–flowpaststructuresandbuildi

5、ngs;coatingflows(e.g.depo-sitionofphotographicfilms);sprayingprocessesMagnetohydrodynamics(MHD)–flowofconductingfluids;Maxwell’sequationsPhysiochemicalfluiddynamics–flowundersurfacetensioninthepresenceofchemicalcontaminantsTurbulence–transitiontoturbulencefromlaminarflow;b

6、oundarylayerreceptivityAlloftheseareactiveareasofresearchWewillshowthattheNavier-Stokesequationsforanincompressiblefluidare:∂u2∇·u=0,+u·∇u=−∇p/ρ+(µ/ρ)∇u,∂twhereuisthevelocityinthefluidpisthepressureρisthedensityµistheviscosity.IfUandLaretypicalvelocityandlengthscalesf

7、ortheprobleminhand,wewillalsoseethatagivenflowmaybecharacterisedbythevalueofthedimensionlessReynoldsnumberULR=.νSimplificationscanbemadeifR≪1(seeSection6)orR≫1(seeSection8).1.PreliminaryideasWhatisafluid?Asimplefluidcannotwithstandanexternallyappliedstresswithoutdeformi

8、nginsomemanner.Thisdefinitionofafluidencompassesbothliquidsandgases.Inordertodevelopamathematicalbasisforthestudyoffluidmotion,weadoptthecont