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

3Zero-pressure-gradientboundarylayerbeneathatur-

bulentfreestream:TheexperimentsofHancockandBradshaw

TheexperimentsofHancockandBradshaw(1989)revealedanewfeatureimportantforouranalysis.Examinationoftheseexperimentaldatasuggestedthatweseparatetheotherexperimentsintotwogroups.IntheHancockandBradshawexperimentsthefreestreamwasturbulizedbyagridinallseries,exceptone.Thus,processingthedatafromtheseexperimentswewereablenotonlytocomparethescalinglaw(5)withexperimentaldataonceagainbutalsotoinvestigatethein uenceoftheturbulenceoftheexternal owonthesecondself-similarintermediateregion.TheresultsoftheprocessingarepresentedinTable2andFigures7and8.InbothTable2andFigures7and8theintensityofturbulenceisshownbythevalueofu′/U,whereu′isthemeansquarevelocity uctuationinthefreestream.

Table2

Figure

Fig.8a

Fig.8b

Fig.8c

Fig.8d

Fig.8e

Fig.8f

Fig.8gReθ4,6802,9805,7604,3203,7103,1003,860αAlnRe1lnRe2lnReu′/UReθ/Re0.110.060.100.210.020.030.04β0.200.18––––Hancock,P.E.andBradshaw,P.(1989)0.1408.6610.6710.7110.690.00030.1388.7710.8610.9110.880.0240.1378.8010.9110.9510.930.0260.1508.229.9110.009.950.0410.1229.4912.1112.3012.200.0400.1289.1311.4811.7011.590.0580.1299.0711.3811.6311.500.058

Firstofall,ourprocessingshowedthatthe rstself-similarintermediatelayerisclearlyseeninalltheseexperiments,bothintheabsenceoftheexternalturbulence,andinitspresence.ThevaluesoflnRe1andlnRe2areclose.Thismeansthatthebasicscalinglaw

(5)isvalidintheintermediateregionadjacenttotheviscoussublayer.Atthesametime,thesecondself-similarregionisclearlyobservedandwell-de nedonlywhentheexternalturbulenceisweak(Figure8aandtoalesserextent,Figure8b)sothattheexternalturbu-lenceleadstoadrasticreductionofthepowerβ,andeventothedeteriorationofthesecondself-similarintermediateregionsothatβbecomesindeterminate.Weillustratethein uenceofthefreestreamturbulenceadditionallybyFigure7(b).