ALBERT

Notes: A temporally-growing mixing layer has been directly simulated with a pseudospectral technique, for initial bulk Richardson numbers from 0.0 to 0.2 and for Prandtl numbers from 0.00535 to 2.2. Several different initial conditions for the velocity fluctuations were imposed. For the two-dimensional (2-D) case only purely-deterministic conditions were used, whereas purely-deterministic, combined deterministic-random, or purely-random conditions were imposed in the three-dimensional (3-D) cases. The numerical procedure allowed fields with very different characteristic lengths to be resolved, with spectral accuracy maintained. The evolution of the velocity, active (temperature), and passive scalar fields were followed independently by adaptively redistributing collocation points in the regions of high shear and rapid scalar variations. The vertical boundary conditions were imposed at infinity to eliminate any boundary-layer effects and an exponential mapping was used to translate infinite physical space into finite computational space. The birth and time evolution of the longitudinal structures have been investigated. Variations in the initial modal forcing are reflected in different outcomes from the competition between core- and braid-centered instabilities in unstratified flow. For relatively strong fundamental forcing (compared to the 3-D forcing) the most unstable mode is braid-centered, whereas if the fundamental forcing is weak the most-unstable, core-centered mode determines the overall three-dimensionalization of the flow by generating large deformations of the main vortex cores. In subcritically-stratified air and water flow, instead, the braid-centered instability supersedes the core-centered instability, whatever the initial forcing. In stratified liquid sodium the shear-aligned convective instabilities observed in air and water are not excited. The conversion of potential into kinetic energy by convective overturning in the braid region does not occur because the high thermal conduction precludes the existence of the unstably-stratified regions necessary to drive the instabilities. The initial conditions, the Richardson, and the Prandtl numbers accordingly play a significant role in the free-shear-layer evolution and need to be explicitly considered for modeling purposes. © 1998 American Institute of Physics.

Notes: 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 flow. 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 Prandtl 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. © 1999 American Institute of Physics.

Notes: 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. © 2001 American Institute of Physics.