Turbulent diffusion–cascade interaction

In the decay region around the centreline of three qualitatively different turbulent plane wakes, the turbulence is non-homogeneous and two-point turbulent diffusion counteracts the turbulence cascade all the way down to scales smaller than the Taylor length. It is found that the sum of the inter-space transfer rate and the horizontal part of the inter-scale transfer rate of horizontal two-point turbulent kinetic energy is approximately proportional to the turbulence dissipation rate in the inertial range with a constant of proportionality between $-0.6$ and $-1$ depending on wake and location within the wake, except at the near-field edge of the decay region.