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

Asymptotic analysis is presented of the energy balance equations derived from statistically averagedNavier-Stokes equations pertinent to wall-induced turbulence. Attention is focused on the inertialsublayer, the region outside the viscous sublayer, and the buffer layer where the log-law for meanflow holds. Production and dissipation of turbulence are shown to be equal with a relative error of order(x2 /L), where x2 is the distance from the wall and L is the external length (pipe radius, channelhalf-height, boundary layer thickness). Diffusion of pressure and kinetic energy together are only ofrelative magnitude order (x2 /L). Pressure gradient terms are shown to redistribute longitudinalturbulence production in equal portions dissipated in the three orthogonal directions.