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1IntroductionOurconcerniswiththerelationshipbetweenstationarystreamwisevortexstructuresandwavesystemsinshearrowsThesecondaryinstabilityofstreamwisevortexrowsisnowwellunderstoodandtheagreementfoun

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InconsiderationforpublicationinJ.FluidMech.1Streamwisevorticesinshear\: Transcript

1IntroductionOurconcerniswiththerelationshipbetweenstationarystreamwisevortexstructuresandwavesystemsinshearrowsThesecondaryinstabilityofstreamwisevortexrowsisnowwellunderstoodandtheagreementfoun. 1.Gobbling:IntroductionandPhysicalPictureApeculiarandapparentlynewpatternofbreakuphasbeenobservedinexperimentswithjetsofdilutepolymersolutionsat\rowratesclosetothecriticalratescorrespondingtoatransiti J.M.OttinoandD.V.KhakharDepartmentofChemicalEngineering,NorthwesternUniversity,Evanston,Illinois60203;e-mail:ottino@chem-eng.nwu.eduDepartmentofChemicalEngineering,IndianInstituteofTechnology 1.IntroductionJet-propelledswimmingisacommonmodeofaquaticlocomotion,performedbyjellysh,squidsandoctopuses.Onthepowerstroke,amuscularcavitycontracts,ejectingwaterinonedirectionandpropellingthebodyinth 1.IntroductionTheinstability,causedbythepassageofashockwave,ofaninterfacebetweentwogaseswasrststudiedbyRichtmyer(1960)nearlyftyyearsago.Histheoreticalpredictionsandnumericalcalculationswereconrmede InstabilityofachemicallydenselayerheatedfrombelowHerewediscussmarginalstabilityanddescribelaboratoryexperiments,whichareofgeneralinterestbecausetheybothillustratewellaformofoscillatoryconvection.Altho [5]J.deJong,R.Jeurissen,H.Borel,M.vandenBerg,H.Wijshoff,H.Reinten,M.Versluis,A.Prosperetti,andD.Phys.Fluids,121511(2006)[6]D.D.Joseph,J.Nelson,M.Renardy,andY.Renardy,FluidMech.,383(1991)[7]J.-T.Jeonga 1.Introduction Bourouiba1,2,†,Eline Dehandschoewercker3andJohnW.M. Bush11DepartmentofMathematics,MassachusettsInstituteofTechnology,Cambridge,MA02130,USA2DepartmentofCivilandEnvironmentalEngineering,Massachuset 1.IntroductionCollidingplumesoccurwhentherearetwoopposingsourcesofbuoyancyincloseproximity.Forexample,anairconditioningventplacedaboveelectronicequipment,suchasacomputer,willresultinplumesthatcollide. 1.IntroductionLeaves,treeseeds,andpapercardswhich 1.IntroductionImpingingjetshavebeenthesubjectofextensiveresearchbecauseoftheirwidespreadindustrialapplicationasecientpromotersofheatandmass-transfer Vorticalstructuresandheattransferinaroundimpinging 324Z.J.Wanginsteadfocusontheroleoftheunsteadyaerodynamicsandaskwhetherandhowaerodynamicsmightselectarangeofpreferredfrequencies.Toseparatethebiologyfromthiscomplexproblem,wechoosetostudyatwo-dimension 4th thpowerofthepipediameter,buttheconstantofproportionalityisabout10to20timeslargerthanthatforwateralone.WeusedReichardt WeinsteinRuschak2004Quere1999seeFig1TobeabletocoatasquicklyaspossibleonewantstooperateatthehighestspeedspossiblewithoutwettingfailureoccurringinotherwordsweareinterestedinthecriticalspeedUcrabovewhich

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