Revisit of viscous sublayer scaling law

Abstract

Recent study has shown that the valid region of linear velocity profile in the viscous sublayer of turbulent channel flow is only the asymptotic limit y(+)-->0 even at a very high Reynolds number. In the view of similarity, this result implies that the conventional complete similarity assumption, which is the basis of linear velocity profile, is not valid. In terms of extended similarity argument of G. I. Barenblatt [J. Eng. Math. 36, 361 (1999)], it is shown that the plausible similarity assumption for the viscous sublayer is the incomplete similarity in y(+) and the complete similarity in h(+)(=hu(tau)/nu), where h is channel half width. The resulting velocity profile based on these assumptions has a quartic term of y(+) from Reynolds stress in addition to a linear term of y(+) from viscous stress, which greatly enlarges the extent of valid region of similarity. (C) 2004 American Institute of Physics.