Numerical investigation of the entrainment and mixing processes in neutral and stably-stratified mixing layers

The direct numerical simulation (DNS) of a temporally-growing mixing layer has been carried out, for a variety of initial conditions at various Richardson and Prandtl numbers, by means of a pseudo-spectral technique; the main objective being to elucidate how the entrainment and mixing processes in mixing-layer turbulence are altered under the combined influence of stable stratification and thermal conductivity. Stratification is seen to significantly modify the way by which entrainment and mixing occur by introducing highly-localized, convective instabilities, which in turn cause a substantially different three-dimensionalization of the flow compared to the unstratified situation. Fluid which was able to cross the braid region mainly undisturbed (unmixed) in the unstratified case, pumped by the action of rib pairs and giving rise to well-formed mushroom structures, is not available with stratified how. This is because of the large number of ribs which efficiently mix the fluid crossing the braid region. More efficient entrainment and mixing has been noticed for high PrandtI number computations, where vorticity is significantly reinforced by the baroclinic torque. In liquid sodium, however, for which the Prandtl number is very low, the generation of vorticity is very effectively suppressed by the large thermal conduction, since only small temperature gradients, and thus negligible baroclinic vorticity reinforcement, are then available to counterbalance the effects of buoyancy. This is then reflected in less efficient entrainment and mixing. The influence of the stratification and the thermal conductivity can also be clearly identified from the calculated entrainment coefficients and turbulent Prandtl numbers, which were seen to accurately match experimental data. The turbulent Prandtl number increases rapidly with increasing stratification in liquid sodium, whereas for air and water the stratification effect is less significant. A general law for the entrainment coefficient as a function of the Richardson and Prandtl numbers is proposed, and critically assessed against experimental data. (C) 1999 American Institute of Physics. [S1070-6631(99)01201-5].