REYNOLDS-NUMBER-DEPENDENCE OF THE MAXIMUM IN THE STREAMWISE VELOCITY FLUCTUATIONS IN WALL TURBULENCE

A survey is made of the standard deviation of the streamwise velocity fluctuations in near-wall turbulence and in particular of the Reynolds -number-dependency of its peak value. The following canonical flow geo metries are considered: an incompressible turbulent boundary layer und er zero pressure gradient, a fully developed two-dimensional channel a nd a cylindrical pipe flow. Data were collected from 47 independent ex perimental and numerical studies, which cover a Reynolds number range of R(0) = U-proportional to theta/nu = 300-20,920 for the boundary lay er with theta the momentum thickness and R(+) = u(star)R/nu = 100-4,30 0 for the internal flows with R the pipe radius or the channel half-wi dth. It is found that the peak value of the rms-value normalised by th e friction velocity, u(star), is within statistical errors independent of the Reynolds number. The most probable value for this parameter wa s found to be 2.71 +/- 0.14 and 2.70 +/- 0.09 for the case of a bounda ry layer and an internal flow, respectively. The present survey also i ncludes some data of the streamwise velocity fluctuations measured ove r a riblet surface. We find no significant difference in magnitude of the normalised peak value between the riblet and smooth surfaces and t his property of the normalised peak value may for instance be exploite d to estimate the wall shear stress from the streamwise velocity fluct uations. We also consider the skewness of the streamwise velocity fluc tuations and find its value to be close to zero at the position where the variance has its peak value. This is explained with help of the eq uations of the third-order moment of velocity fluctuations. These resu lts for the peak value of the rms of the streamwise velocity fluctuati ons and also the coincidence of this peak with the zero value of the t hird moment can be interpreted as confirmation of local equilibrium in the near-wall layer, which is the basis of inner-layer scaling. Furth ermore, these results can be also used as a requirement which turbulen ce models for the second and triple velocity correlations should satis fy.