Scalar entrainment in the mixing layer

New definitions of entrainment and mixing based on the passive scalar field in the plane mixing layer are proposed. The definitions distinguish clearly between three fluid states: (1) unmixed fluid, (2) fluid engulfed in the mixing layer, trapped between two scalar contours, and (3) mixed fluid. The difference betwen (2) and (3) is the amount of fluid which has been engulfed during the pairing process, but has not yet mixed. Trends are identified from direct numerical simulations and extensions to high Reynolds number mixing layers are made in terms of the Broadwell-Breidenthal mixing model. In the limit of high Peclet number (Pe = ReSc) it is speculated that engulfed fluid rises in steps associated with pairings, introducing unmixed fluid into the large scale structures, where it is eventually mixed at the Kolmogorov scale. From this viewpoint, pairing is a prerequisite for mixing in the turbulent plane mixing layer.