A gentle introduction to the physics and mathematics of incompressible flow.pdf

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1、AGentleIntroductiontothePhysicsandMathematicsofIncompressibleFlowCourseNotes,Fall2000PaulFifeContents1Primaryconceptsinmodelingfluids31.1Fluid“particles”......................................31.2Propertiesofthefluidparticles..............................41.3Blobs......

2、......................................41.4Stresses...........................................41.5Fields............................................51.6Backtotheconceptofafluid...............................52Kinematics62.1Particlepaths.................................

3、.......62.2EulerianandLagrangiancoordinates...........................62.3Rateofchange“followingthefluid”;convection.....................72.4Streamlines.........................................82.4.1Examples......................................82.5Changesininfinitesim

4、alvolume..............................92.5.1Volumechangesinanevolvingbloboffluid...................92.5.2Incompressibility..................................102.5.3EvolutionoftheJacobian.............................103Conservationofmass113.1ThePDE......................

5、....................113.2Anotherformofthelaw..................................113.3Examples..........................................114Idealfluids.124.1Definition;viscosity.....................................124.2Thenormalforceisindependentoforientation..............

6、.......124.3Digressionintoclassicalparticlemechanics........................134.4Conservationofmomentum................................134.5Energeticconsiderations..................................144.5.1TheBernoullirelation...............................144.5.2Astri

7、cterderivationoftheBernoullirelation..................154.6ThecompletesystemofEuler’sequations........................154.7Thequestionofboundaryconditions...........................154.7.1Examples......................................164.8Vorticity...................

8、........................174.8.1Vorticityformofthemomentumequation....................184.8.2Examples...............................