Transfer Mechanism of a Passive Scalar in Grid Turbulence with Mean Scalar Gradient

We perform DNSs of grid turbulence with mean scalar gradient and conduct scale-by-scale analysis to reveal the interscale transfer of passive scalar. The scale-by-scale scalar (SBSS) equation, which can be deemed as an extended equation of the Karman–Howarth–Monin–Hill (KHMH) equation, is derived and employed in the DNS data to evaluate the interscale transfer between two points. The results reveal that the inverse cascade phenomenon of the scalar appears in the upstream regions. Further analysis reveals that the existence of fluid mass with an unmixed scalar plays an essential role in the inverse cascade phenomenon.