Delayed correlation between turbulent energy injection and dissipation

The dimensionless kinetic energy dissipation rate C_ε is estimated from numerical simulations of statistically stationary isotropic box turbulence that is slightly compressible. The Taylor microscale Reynolds number (Re_λ) range is 20Re_λ220 and the statistical stationarity is achieved with a random phase forcing method. The strong Re_λ dependence of C_ε abates when Re_λ≈100 after which C_ε slowly approaches ≈0.5, a value slightly different from previously reported simulations but in good agreement with experimental results. If C_ε is estimated at a specific time step from the time series of the quantities involved it is necessary to account for the time lag between energy injection and energy dissipation. Also, the resulting value can differ from the ensemble averaged value by up to ±30%. This may explain the spread in results from previously published estimates of C_ε.