Numerical investigation of the scalar probability density function distribution in neutral and stably stratified mixing layers

Direct numerical simulations of a temporally-growing mixing layer are performed to examine how the resulting concentration probability density function (PDF) of an advected, nearly nondiffusive, passive scalar (numerical dye) varies under the combined effects of stable stratification, thermal conductivity, and perturbation of the initial velocity field. In stably-stratified mixing layers convective instabilities are responsible for the development of streamwise vortices or ribs. These exhibit shorter spanwise separation than in nonstratified shear layers and lead to differences in the subsequent three-dimensionalization of the flow field. Furthermore, vortex development is very efficiently suppressed by stratification in high-thermally-conducting fluids, because only small temperature gradients arise and thus negligible baroclinic vorticity reinforcement is available to counterbalance the stabilizing effects of buoyancy. This is reflected in smaller mixed-fluid total PDF areas with decreasing Prandtl number. The effect of coherent structures on the PDF distribution is seen to be significant. The main rolls are the cause of "global-concentration" mixing, i.e., mixing of fluid lumps with vastly different species concentration, reflected in nonmarching PDF peaks, where the peak of the PDF is located at a constant concentration value. Ribs, on the other hand, having shorter spatial extent and engendering mixing on a narrower concentration range, cause "local-concentration" mixing, which translates into marching PDF peaks. The combined action of the spanwise vortices rolling up, or pairing, and the ribs, may then give rise to tilted PDF distributions, which are intermediate between nonmarching and marching. The "pairing parameter," used to predict the transition from nonmarching to marching PDFs, was found not to be reliable, small values being sufficient to allow the PDF to be marching in stratified flow. The scalar mean, and the scalar mean-mixed-fluid, concentrations are also investigated and are seen to deviate considerably from each other, depending on the strength and coherence of the vortical structures, the imposed stratification, and the thermal conductivity. (C) 2001 American Institute of Physics.