A stochastic model for turbulence at small scales - Generation of a stochastic process

Inverse energy transfers are considered for adding subgrid scale features to account for small scale turbulence energy input to large eddies in numerical flow simulations. The transfers occur at high Reynolds numbers and influence the structures in the large eddies. The subgrid structures are generated stochastically in spectral space at steady temporal intervals. A system of three random variables governs the symmetric tensor for the time dependent wave vector emitted by the small scale turbulence. It is shown that equivalent results can be obtained using either Gaussian or stochastic models for the subgrid scale inputs.