Small viscosity asymptotics for the inertial range of local structure and for the wall region of wall-bounded turbulent shear flow

The small viscosity asymptotics of the inertial range of local structure and of the wall region in wall-bounded turbulent shear flow are compared. The comparison leads to a sharpening of the dichotomy between Reynolds number dependent scaling (power-type) laws and the universal Reynolds number independent logarithmic law in wall turbulence. It further leads to a quantitative prediction of an essential difference between them, which is confirmed by the results of a recent experimental investigation, These results lend support to recent work on the zero viscosity limit of the inertial range in turbulence.