Unsteady self-similarity of jet fluid age and mass fraction

Scalar mixing is investigated in a decelerating turbulent round jet using direct numerical simulation. The mass fraction of jet fluid and the fluid residence time, measured by the mass-weighted stream age of the jet fluid, both exhibit self-similar radial profiles in statistically-stationary turbulent jets. Upon stopping the inflow, a deceleration wave passes through the jet, behind which a new self-similar state is observed for the two scalar variables. The self-similar state during the jet deceleration is different from that in the statistically-stationary jet. Contrary to the steady-state behaviour, the jet fluid mass fraction exhibits a linear increase with downstream distance in the decelerating jet, whereas the centreline mass-weighted stream age of jet fluid remains proportional to downstream distance. Scalar transport budget analysis shows that the radial transport term increases for both scalars, and the contribution of the streamwise transport term of jet mass fraction changes sign between steady and unsteady cases.