A comment on the "linear" law of the wall for fully developed turbulent channel flow

In fully developed turbulent channel or pipe flows, the validity of a viscous sublayer with a quadratic mean velocity profile strictly requires the gradient of the Reynolds shear stress to be negligible compared to the gradient of the viscous shear stress. Direct numerical simulations suggest that this requirement is satisfied only in the limit y(+) --> 0. The use of a quartic, instead of quadratic, profile represents the available numerical and experimental mean velocity data satisfactorily in the region y(+) < 10.