Numerical investigation of the entrainment and mixing processes in neutraland 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 Richar dson and Prandtl numbers, by means of a pseudo-spectral technique; the main objective being to elucidate how the entrainment and mixing processes in m ixing-layer turbulence are altered under the combined influence of stable s tratification and thermal conductivity. Stratification is seen to significa ntly modify the way by which entrainment and mixing occur by introducing hi ghly-localized, convective instabilities, which in turn cause a substantial ly different three-dimensionalization of the flow compared to the unstratif ied situation. Fluid which was able to cross the braid region mainly undist urbed (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 efficient ly mix the fluid crossing the braid region. More efficient entrainment and mixing has been noticed for high PrandtI number computations, where vortici ty is significantly reinforced by the baroclinic torque. In liquid sodium, however, for which the Prandtl number is very low, the generation of vortic ity is very effectively suppressed by the large thermal conduction, since o nly small temperature gradients, and thus negligible baroclinic vorticity r einforcement, are then available to counterbalance the effects of buoyancy. This is then reflected in less efficient entrainment and mixing. The influ ence of the stratification and the thermal conductivity can also be clearly identified from the calculated entrainment coefficients and turbulent Pran dtl numbers, which were seen to accurately match experimental data. The tur bulent Prandtl number increases rapidly with increasing stratification in l iquid sodium, whereas for air and water the stratification effect is less s ignificant. A general law for the entrainment coefficient as a function of the Richardson and Prandtl numbers is proposed, and critically assessed aga inst experimental data. (C) 1999 American Institute of Physics. [S1070-6631 (99)01201-5].