Scale and Reynolds number dependence of stochastic subgrid energy transfer in turbulent channel flow

The forward and inverse cascades in turbulent channel flow are characterised by stochastic models developed from the statistics of reference direct numerical simulations (DNS) judiciously truncated into resolved and subgrid scales. The stochastic model consists of a meanfield shift, a deterministic drain dissipation acting on the resolved field and a stochastic backscatter force. The direction, magnitude and stochasticity of the energy transfer for the mean and fluctuating fields in scale space are determined from the spectral coefficients of the stochastic model. The meanfield is found to lose energy to the subgrid scales, whilst the fluctuating two-dimensional spanwise oriented wave receives a deterministic injection. For the three-dimensional fluctuations, there is a deterministic drain of energy out of the resolved scales, and a stochastic injection of energy into the system. Only the small vertical scales have a net injection of energy, where the stochastic backscatter overwhelms the drain dissipation. Results are presented for friction velocity based Reynolds numbers of 186, 546 and 945. The stochastic representation of the subgrid interactions are validated by producing large eddy simulations using these model coefficients that agree with the time averaged kinetic energy spectra of the DNS within the resolved scales.