ntistotheleftoftheshockletfortheloweedsideofthelayer.iftheflowvelocityandsoundeedaredenotedbyu(t,x,y)anda(t,x,y)reectively,thent
heshockcanbedeterminedasthesetofthepointssatisfyingthefollowingrelation:
inwhich,εisacertainparameteranditsvaluewillaffectthenumericalthickneoftheshocklets.itwasfoundthatforourcasesavaluebetween0.005to0.01forεmightyieldgoodresults.then,εisfixedas0.01.u(t,x,y)anda(t,x,y)wereobtainedfromnumericalcomputation.itisconfirmedfromthecomputationthatifthemachnumberisnottoolarge,forawiderangeofra,themostutablet-swaveintroducedyieldedac≈1aspredictedbystabilityanalysis.thelocationofshockletsestablishedbythemethodaboveiscoistenttothedeestpartoftheiso-deitycontoursplot.
inordertomakeitevenmorereliable,oneeffectivemethodtoexaminewhetheritisashockletornotisasfollows:afterthelocationofashocklethasbeendeterminedby,say,theabovemethod,whichischangingwiththetime,onecanfollowafluidparticle,startingsomewherenearandinfrontoftheshocklet,toseetheentropychangeofthatparticle.theentropyoftheparticleremainedalmostunchangedwhenitdidnotmeettheshockletasinanadiabatic,isoentropicflow,butwouldunambiguouslyhaveanentropyjumpwhentheparticlepaedthroughtheshocklet.bythiscriterion,shockletsfoundbythepreviousmethodwereprovedtobecorrect.
2.theinfluencesofshockletsonflowcharacteristicsandtherelatiohipbetweenthestrengthofinducedshockletsandtheamplitudeofdisturbancetheinlethasbeenstudied.
inrecentyears,attemptshavebeenmadeinalyingthenonlineartheoryofhydrodynamicstabilitygoo
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