Self-Similar Intermediate Structures in Turbulent Boundary Layers At Large Reynolds Numbers

authors(Barenblatt,Chorin(1996,1997)),itwasdemonstratedthatthescalinglaw(2)iscompatiblewiththeproperly

modi ed

IMMprocedure.Themethodofvanishingviscosity(Chorin,(1988,1994))wasusedinthismodi cation.

Letusturnnowtoshear owsotherthan owsinpipes.Bythesamelogic,thescalinglaw(5)shouldbealsovalidforanintermediateregionadjacenttotheviscoussublayerforallgoodqualityexperimentsperformedinturbulentshear owsatlargeRe.

The rstquestionis,whatistheappropriatede nitionoftheReynoldsnumberforthese owswhichwillmaketheformula(5)applicable?Thisisaveryimportantpoint—iftheuniversalReynolds-number-independentlogarithmiclawwerevalid,thede nitionoftheReynoldsnumberwouldbeirrelevantprovideditweresu cientlylarge.Forthescalinglaw

(5)thisisnotthecase.Indeed,ifthescalinglaw(5)hasgeneralapplicabilityitshouldbepossibleto nd,foreveryturbulentshear owatlargeReynoldsnumber,anappropriatede nitionoftheReynoldsnumberwhichwillmakethescalinglaw(5)valid.

Thereexistsnowadaysalargeamountofdataforanimportantclassofwall-boundedturbulentshear ows:turbulentzero-pressure-gradientboundarylayers.Thesedatawereobtainedoverthelast25yearsbyvariousauthorsusingvariousset-ups.Forboundarylayersthetraditionalde nitionoftheReynoldsnumberis

UθReθ=

(9)ν

isproperlydetermined.Moreover,weshowthatforallthe owswheretheturbulenceintheexternal owissmall,thereexistsasharplydistinguishablesecondintermediateregion