The limiting behaviour of turbulence near a wall

Three different Navier-Stokes computational models of incompressible viscoussublayer turbulence have been developed. Comparison of computed turbulence quantities with experiment is made for the mean streamwise velocity, Reynolds stress, correlation coefficient and dissipation; for the r.m.s. fluctuation intensities of streamwise vorticity, Reynolds stress and three velocity components; and for the skewness and flatness of fluctuating streamwise velocity and Reynolds stress. The comparison is good for the first three of these quantities, and reasonably good for most of the remainder. Special computer runs with a very fine mesh and small Courant number were made to define the limiting power-law behaviour of turbulence near a wall. Such behaviour was found to be confined to about 0.3 wall units from the wall, and to be: linear for streamwise turbulence, spanwise turbulence, vorticity normal to the wall, and for the departures from their respective wall values of dissipation, streamwise vorticity and spanwise vorticity; second power for turbulence normal to the wall; third power for Reynolds stress; and a constant value of the correlation coefficient for Reynolds stress. A simple physical explanation is given for the third-power variation of Reynolds stress and for the broad generality of this limiting variation. Applications are made to Reynolds-average turbulence modelling: damping functions for Reynolds stress in eddy-viscosity models are derived that are compatible with the near-wall limiting behaviour; and new wall boundary conditions for dissipation in k -e models are developed that are similarly compatible.