Dissipation equals production in the log layer of wall-induced turbulence

Asymptotic analysis is presented of the energy balance equations derived from statistically averaged Navier-Stokes equations pertinent to wall-induced turbulence. Attention is focused on the inertial sublayer, the region outside the viscous sublayer, and the buffer layer where the log-law for mean flow holds. Production and dissipation of turbulence are shown to be equal with a relative error of O(x(2)/L), where x(2) is the distance from the wall and L is the external length (pipe radius, channel half-height, boundary layer thickness). Diffusion of pressure and kinetic energy together are only of relative magnitude O(x(2)/L). Pressure gradient terms are shown to redistribute longitudinal turbulence production in equal portions dissipated in the three orthogonal directions. (C) 2007 American Institute of Physics.