Delayed correlation between turbulent energy injection and dissipation

The dissipation rate of mean turbulent kinetic energy, which is independent of viscosity for both numerical simulations of statistically stationary isotropic turbulence and experiments was studied. The numerical simulations were achieved with a random phase forcing applied at low wave numbers. It was demonstrated that C_ε should be estimated only with ensemble averaged quantities from the entire time series, for which the statistics are stationary. It was also demonstrated that if C_ε is to be estimated at each time snapshot it is necessary to correctly account for the time lag that occurs from the large scale energy injection to the fine scale energy dissipation.