Integral properties of turbulent-kinetic-energy production and dissipation in turbulent wall-bounded flows

Integral properties of TKE production and dissipation are investigated in turbulent wall-bounded flows. The main findings include 1) the global integral identity for the TKE production is derived from the mean momentum balance equation. 2) At sufficiently high Reynolds number, the integrals of TKE production and dissipation are equally partitioned around the peak Reynolds shear stress location. 3) The integral of the TKE production and the integral of the TKE dissipation exhibit a logarithmic-like layer similar to that of the mean streamwise velocity. The logarithmic-like scaling of the global integral of TKE production and dissipation, the equal partition of the integrals of TKE production and dissipation around the peak Reynolds shear stress location, and the logarithmic-like layer in the integral of TKE production and dissipation are intimately related. The equal partition of the integral of the TKE production and dissipation around the peak Reynolds shear stress location underlines the important role of the meso-layer and meso-length scale in the dynamics of turbulent wall-bounded flows.