Dynamics of turbulent energy and dissipation in channel flow

The dynamics of turbulent kinetic energy (TKE), turbulence dissipation rate (TDR) and turbulence production rate (TPR) are explored in fully developed turbulent channel flow using direct numerical simulations up to $\textit {Re}_\tau \approx 2000$ with minimal computational box for large-scale structures. Time correlation analysis based on volume-averaged TKE and TDR shows a well-defined average time lag, as in periodic/homogeneous turbulence, which, unlike periodic/homogeneous turbulence, appears to be Reynolds-number-dependent. On the basis of a spatio-temporal correlation analysis, we show that plane-averaged TKE fluctuations in the near-equilibrium region are transported towards both the core and near-wall regions, and are positively correlated with plane-averaged TDR fluctuations there with combined wall-distance and time lags. In the path towards the core region, the wall-distance lag is very close to the time lag multiplied by the friction velocity. The path towards the near-wall region has a wide spread of time lags, which increases with Reynolds number. The spatio-temporal correlation paths both towards the core and towards the wall are reproduced when the reference plane TKE is conditionally averaged on either ejections or sweeps, and are in fact stronger in correlation values in the case of ejections, which are better organised than sweeps. While volume-averaged TPR evidently precedes volume-averaged TKE, a more complex picture of non-local space–time correlations between reference plane TKE and TPR is revealed. A mechanistic model is proposed to elucidate these correlations between TKE and TPR through the interaction between the mean shear and the Reynolds shear stress.