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000231554 001__ 231554 000231554 005__ 20180913064524.0 000231554 0247_ $$2doi$$a10.1103/PhysRevFluids.2.094602 000231554 022__ $$a2469-990X 000231554 02470 $$2ISI$$a000410594800001 000231554 037__ $$aARTICLE 000231554 245__ $$aRevisiting the quest for a universal log-law and the role of pressure gradient in "canonical" wall-bounded turbulent flows 000231554 260__ $$aCollege Pk$$bAmer Physical Soc$$c2017 000231554 269__ $$a2017 000231554 300__ $$a17 000231554 336__ $$aJournal Articles 000231554 520__ $$aThe trinity of so-called "canonical" wall-bounded turbulent flows, comprising the zero pressure gradient turbulent boundary layer, abbreviated ZPG TBL, turbulent pipe flow, and channel/duct flows has continued to receive intense attention as new and more reliable experimental data have become available. Nevertheless, the debate on whether the logarithmic part of the mean velocity profile, in particular the Karman constant kappa, is identical for these three canonical flows or flow-dependent is still ongoing. In this paper, the asymptotic matching requirement of equal. in the logarithmic overlap layer, which links the inner and outer flow regions, and in the expression for the centerline/free-stream velocity is reiterated and shown to preclude a universal logarithmic overlap layer in the three canonical flows. However, the majority of pipe and channel flowstudies at friction Reynolds numbers Re-tau below approximate to 10(4) extract from near-wall profiles the same kappa of 0.38-0.39 as in the ZPG TBL. This apparent contradiction is resolved by a careful reanalysis of high-quality mean velocity profiles in the Princeton "Superpipe" and other pipes, channels, and ducts, which shows that the mean velocity in a near-wall region extending to around 700 "+" units in channels and ducts and 500 "+" units in pipes is the same as in the ZPG TBL. In other words, all the "canonical" flow profiles contain the lower end of the ZPG TBL log-region, which starts at a wall distance of 150-200 "+" units with a universal kappa of kappa(ZPG) approximate to 0.384. This interior log-region is followed by a second logarithmic region with a flow specific. > kappa(ZPG), which increases monotonically with pressure gradient. This second, exterior log-layer is the actual overlap layer matching up to the outer expansion, which implies equality of the exterior. and kappa(CL) obtained from the evolution of the respective centerline velocity with Reynolds number. The location of the switch-over point implies furthermore that this second log-layer only becomes clearly identifiable, i.e., separated from the wake region, for Re-tau well beyond 10(4) (see Fig. 1). This explains the discrepancies between the Karman constants of 0.38-0.39, extracted from near-wall pipe profiles below Re-tau approximate to 10(4) and the kappa's obtained from the evolution of the centerline velocity with Reynolds number. The same analysis is successfully applied to velocity profiles in channels and ducts even though experiments and numerical simulations have not yet reached Reynolds numbers where the different layers have even started to clearly separate. 000231554 700__ $$0240474$$aMonkewitz, Peter A.$$g105889 000231554 773__ $$j2$$k9$$q094602$$tPhysical Review Fluids 000231554 909C0 $$0252381$$pLMF$$xU10317 000231554 909CO $$ooai:infoscience.tind.io:231554$$particle 000231554 937__ $$aEPFL-ARTICLE-231554 000231554 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED 000231554 980__ $$aARTICLE