Ab. Cortesi et al., NUMERICAL INVESTIGATION OF THE FORMATION OF 3-DIMENSIONAL STRUCTURES IN STABLY-STRATIFIED MIXING LAYERS, Physics of fluids (1994), 10(6), 1998, pp. 1449-1473
A temporally-growing mixing layer has been directly simulated with a p
seudospectral 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 p
urely-random conditions were imposed in the three-dimensional (3-D) ca
ses. The numerical procedure allowed fields with very different charac
teristic lengths to be resolved, with spectral accuracy maintained. Th
e evolution of the velocity, active (temperature), and passive scalar
fields were followed independently by adaptively redistributing colloc
ation points in the regions of high shear and rapid scalar variations.
The vertical boundary conditions were imposed at infinity to eliminat
e any boundary-layer effects and an exponential mapping was used to tr
anslate infinite physical space into finite computational space. The b
irth and time evolution of the longitudinal structures have been inves
tigated. Variations in the initial modal forcing are reflected in diff
erent outcomes from the competition between core- and braid-centered i
nstabilities in unstratified flow. For relatively strong fundamental f
orcing (compared to the 3-D forcing) the most unstable mode is braid-c
entered, 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. I
n subcritically-stratified air and water flow, instead, the braid-cent
ered instability supersedes the core-centered instability, whatever th
e initial forcing. In stratified liquid sodium the shear-aligned conve
ctive instabilities observed in air and water are not excited. The con
version of potential into kinetic energy by convective overturning in
the braid region does not occur because the high thermal conduction pr
ecludes the existence of the unstably-stratified regions necessary to
drive the instabilities. The initial conditions, the Richardson, and t
he Prandtl numbers accordingly play a significant role in the free-she
ar-layer evolution and need to be explicitly considered for modeling p
urposes. (C) 1998 American Institute of Physics.