The three-dimensional mixing layer is characterized by both two-dimensional
and
streamwise large-scale structures. Understanding the effects of those large-scale
structures
on the dispersion of particles is very important. Using a pseudospectral
method,
the large-scale structures of a three-dimensional temporally developing
mixing layer
and the associated dispersion patterns of particles were simulated. The
Fourier expansion
was used for spatial derivatives due to the periodic boundary conditions
in the streamwise and the spanwise directions and the free-slip boundary
condition
in the transverse direction. A second-order Adam–Bashforth scheme
was used in
the time integration. Both a two-dimensional perturbation, which was based
on the
unstable wavenumbers of the streamwise direction, and a three-dimensional
perturbation,
derived from an isotropic energy spectrum, were imposed initially. Particles
with
different Stokes numbers were traced by the Lagrangian approach based on
one-way
coupling between the continuous and the dispersed phases.The time scale and length scale for the pairing were found to be twice
those for the
rollup. The streamwise large-scale structures develop from the initial
perturbation and
the most unstable wavelength in the spanwise direction was found to be
about two
thirds of that in the streamwise direction. The pairing of the spanwise
vortices was also
found to have a suppressing effect on the development of the three-dimensionality.
Particles with Stokes number of the order of unity were found to have the
largest
concentration on the circumference of the two-dimensional large-scale structures.
The presence of the streamwise large-scale structures causes the variation
of the
particle concentrations along the spanwise and the transverse directions.
The extent
of variation also increases with the development of the three-dimensionality,
which
results in the ‘mushroom’ shape of the particle distribution.
Formation of large-scale structures with sharp density gradient through Rayleigh-Taylor growth in a two-dimensional slab under the two-fluid and finite Larmor radius effects
