On the asymptotic state of high Reynolds number, smooth-wall turbulent flows

Abstract

It is argued that the extrapolation of the log-wake law for the mean turbulent velocity profile to arbitrarily large Reynolds numbers, and also the similarity scaling for the intensity of stream-wise turbulent velocity fluctuations indicated by recent experimental measurements, are consistent with the hypothesis that smooth-wall turbulence is asymptotically transitory in the sense that these fluctuations almost everywhere decay with respect to the outer velocity scale when 1/log (Reτ) ≪ 1, where Reτ is the Reynolds number based on the skin-friction velocity uτ. The existence of one or more near-wall maxima in these turbulent velocity fluctuations whose value may grow with Reτ, does not invalidate the main scaling arguments. At gigantic Reτ, this paradigm suggests that nonlinear motions and “turbulent” energy production are still present immediately adjacent to the wall, but that their amplitude becomes vanishingly small compared to the outer velocity scale.