Erratum: "Generalized Law of the Wall and Eddy-Viscosity Model for Wall Boundary Layers"

Abstract

Based on the logarithmic velocity distribution at distances not so far from the wall, and a turbulent shear variation proportional to the cubic power of the wall distance in the immediate proximity of the wall, an analytical model for an eddy viscosity through the wall region is derived leading to a closed-form expression for the velocity distribution. An extension of the preceding analysis to include shear variation results in a generalized law of the wall which admits a Reynolds number effect on the velocity distribution. While many applications of the generalized solution are envisaged, as an example the velocity distribution for the case of injection or suction is considered. The theoretical results are shown to be in agreement with available experimental data. Nomenclature u — mean flow velocity (streamwise component) UT = friction velocity (local) UT = [r(y)/p]1/2 u* = wall friction velocity w* = (UT)W = [r(0)/p]1/2 u + = dimensionless mean flow velocity u + — u/u* u' = dummy variable for u + UT* — dimensionless friction velocity UT+ = ur/u* U = defined by Eq. (18) U' = dummy variable for U e = eddy viscosity e+ = dimensionless eddy viscosity e/v y = normal coordinate y+ = dimensionless normal coordinate y+ = yu*/v vw+ = dimensionless injection velocity vw+ = vw/u*