thelargerthesizeofthevorticeswouldbeandthequickerthevorticeswouldbegenerated.whenthefrequencyissmallerthan0.05,small-scalevorticeswouldbegenerated,andthelowerthefrequencyis,themorethesmall-scalevorticeswouldbe.thegenerationofthesmall-scalevortexesisinfavorofmixing.forpracticalequipmenthavingalimitedsize,theremustbeanoptimalfrequencyinregardwiththesizeandquickgenerationofthevortices.
ifubisfixed,thelargerthevalueofmais,theworsethemixingwouldbe.ifmaisgreaterthan1,thenlarge-scalevorticescanhardlybegeneratedforallfrequencies.ifmaisfixed,thenthesmallerthevalueofreis,theworsethemixingwillbe.
theaearanceofthean-wisevorticeswouldbequickerastheamplitudeoftheundulationgetslarger.butthesaturatedsizeofthean-wisevorticesdidnotkeepincreasingastheamplitudeoftheundulationbecomeslarger.itimpliesthattheevolutionwouldeventuallydependontheintriicpropertyofthemixinglayeritself.thispropertyisofcoursenon-linearinitsnature,notexplainablebythelinearstabilitytheory.forexample,eventheflowisstableaccordingtothelinearstabilitytheory,largescalevorticescanstillbegeneratedaslongastheamplitudeoftheintroducedt-swaveislargeenough.
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