Scale-by-scale analysis of interscale scalar transfer in grid turbulence with mean scalar gradient

Direct numerical simulations were carried out on grid turbulence with a mean scalar gradient to reveal interscale scalar transport. Two-point statistical analysis using the structure function and the scale-by-scale scalar equation was performed. Results show that the third-order structure function becomes negative at large scales in the upstream region (inverse cascade occurs), while such distributions do not appear for turbulence energy. This phenomenon in scalars gradually disappears in the downstream region. Budget analysis of the structure function reveals that this is mainly caused by the non-linear scalar transfer term in the direction of the mean scalar gradient (vertical direction here). When the separation distance is smaller than Taylor's microscale, where the interscale scalar transfer is normal (large to small scales), the direction of the scalar flux is determined by the vertical velocity fluctuation difference between two points. However, when separation is larger than Taylor's microscale and inverse cascading occurs, the direction is determined by derivative of the scalar fluctuation rather than the velocity fluctuation difference. Further analysis reveals that the existence of fluid mass with an unmixed scalar plays an important role in the inverse cascade phenomenon.