Interscale transfer of turbulent energy in grid-generated turbulence with low Reynolds numbers

Direct numerical simulations are performed for grid-generated turbulence with low Reynolds numbers to study the interscale transfer of turbulent energy. The Reynolds numbers based on the uniform velocity and grid mesh size, M, are set to Re-M = 5000, 9000, and 15000. The results show that, for Re-M = 9000 and Re-M = 15000, the turbulent dissipation constant increases in the upstream region but it becomes nearly constant in the region of x/M > 15. In contrast, for Re-M = 5000, it continues to increase and do not level off even in the downstream region. Scale-by-scale analysis using the Karman-Howarth-Monin-Hill equation indicates that, the non-linear transfer term balances with the dissipation term for all the cases. Instead, it is found that, in the downstream region of the Re-M = 5000 case, where the turbulent Reynolds number becomes Re-lambda < 25, the contribution of the advection term varies depending on the streamwise positions. Further analysis for the onepoint statistics indicates that, in such conditions, the coherences among the advection term, dissipation term, and diffusion term become small at small scales, while they are generally large in the other cases including the upstream region for Re-M = 5000. These indicate that energy cascade mechanism in the downstream region for Re-M = 5000 is different from the cases of 30 < Re-lambda < 60, even though both of them are generally considered as small Re-lambda, and it is caused by the increase of the dissipation scale range appearing in the transition period to the final decay.