The effect of nonuniform seeding on the dispersion of fluid elements and heavy particles has been investigated in two-dimensional, incompressible mixing layers. The cross-stream dispersion of fluid elements can be enhanced using nonuniform seeding with most particles near the saddle point because of the greater lateral extent of streamlines in this region, though the increase in dispersion compared to a uniform seeding occurs only after a few vortex turnover times. Compared to fluid elements, additional mechanisms—ejection from vortex cores, separatrix crossing, and the effect of the initial particle velocity—must be considered in the analysis of nonuniform seeding on heavy particle dispersion. The influences of these additional mechanisms are first investigated in a Stuart vortex. With increasing response time, vortex ejection and separatrix crossing shift the streamwise position maximizing lateral transport towards the vortex core. While changes in the initial particle velocity increase/decrease displacement, lateral dispersion may still be enhanced by appropriate nonuniform seeding of particles near the saddle point. Numerical simulations of the incompressible Navier–Stokes equations are then used to study cross-stream dispersion in a temporally evolving two-dimensional mixing layer. Stokes numbers St in the calculations were 0.05, 1, 10, and 100 where St is defined as the ratio of the particle response time to the time scale formed using the vorticity thickness of the initial mean flow. Particles were initially distributed nonuniformly at the interface between the two streams or along a line parallel to the interface. Simulation results show that the seeding location maximizing lateral dispersion is both time and Stokes number dependent, with larger increases in dispersion for the interface seeding. For Stokes numbers of order unity cross-stream dispersion exhibits a weak dependence on initial position since particles are efficiently ejected from the vortex core with subsequent motion confined to the nearby region outside the separatrix in one of the freestreams. Simulation results also show that substantial increases in particle dispersion can be obtained using nonuniform seedings relative to that obtained from an initially uniform distribution.

1.
G. L.
Brown
and
A.
Roshko
, “
On density effect and large structure in turbulent mixing layers
,”
J. Fluid Mech.
64
,
775
(
1974
).
2.
C. D.
Winant
and
F. K.
Browand
, “
Vortex pairing, the mechanism of turbulent mixing layer growth at moderate Reynolds number
,”
J. Fluid Mech.
63
,
237
(
1974
).
3.
C.-M
Ho
and
P.
Huerre
, “
Perturbed free shear layers
,”
Annu. Rev. Fluid Mech.
16
,
365
(
1984
).
4.
B. J.
Lazaro
and
J. C.
Lasheras
, “
Particle dispersion in the developing free shear layer. Part 1. Unforced flow
,”
J. Fluid Mech.
235
,
143
(
1992
a).
5.
B. J.
Lazaro
and
J. C.
Lasheras
, “
Particle dispersion in the developing free shear layer. Part 2. Forced flows
,”
J. Fluid Mech.
235
,
179
(
1992
b).
6.
C. T.
Crowe
,
R. A.
Gore
, and
T. R.
Trout
, “
Particle dispersion by coherent structures in free shear flows
,”
Part. Sci. Technol.
3
,
149
(
1985
).
7.
R.
Chein
and
J. N.
Chung
, “
Effects of vortex pairing on particle dispersion in turbulent shear flows
,”
Int. J. Multiphase Flow
13
,
785
(
1987
).
8.
M.
Samimy
and
S. K.
Lele
, “
Motion of particles with inertia in a compressible free shear layer
,”
Phys. Fluids A
3
,
1915
(
1991
).
9.
K.
Hishida
,
A.
Ando
, and
M.
Maeda
, “
Experiments on particle dispersion in a turbulent mixing layer
,”
Int. J. Multiphase Flow
18
,
181
(
1992
).
10.
F.
Wen
,
N.
Kamalu
,
J. N.
Chung
,
C. T.
Crowe
, and
T. R.
Troutt
, “
Particle dispersion by vortex structures in plane mixing layers
,”
J. Fluids Eng.
114
,
657
(
1992
).
11.
J. E.
Martin
and
E.
Meiburg
, “
The accumulation and dispersion of heavy particles in forced two-dimensional mixing layer. I. The fundamental and subharmonic cases
,”
Phys. Fluids
6
,
1116
(
1994
).
12.
N.
Raju
and
E.
Meiburg
, “
The accumulation and dispersion of heavy particles in forced two-dimensional mixing layer. Part 2: The effect of gravity
,”
Phys. Fluids
7
,
1241
(
1995
).
13.
C. T.
Crowe
,
J. N.
Chung
, and
T. R.
Troutt
, “
Particle mixing in free shear flows
,”
Prog. Energy Combust. Sci.
14
,
171
(
1988
).
14.
C. T. Crowe, J. N. Chung, and T. R. Troutt, “Particle dispersion by organized turbulent structures,” in Particulate Two-Phase Flow, edited by M. C. Roco (Butterworth-Heinemann, Boston, 1993), p. 627.
15.
C. T.
Crowe
,
J. N.
Chung
, and
T. R.
Troutt
, “
Numerical models for two-phase turbulent flows
,”
Annu. Rev. Fluid Mech.
28
,
11
(
1996
).
16.
L.-P.
Wang
, “
Dispersion of particles injected nonuniformly in a mixing layer
,”
Phys. Fluids A
4
,
1599
(
1992
).
17.
M. R.
Maxey
, “
The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields
,”
J. Fluid Mech.
174
,
441
(
1987
).
18.
L.-P. Wang and M. R. Maxey, “Kinematical descriptions for mixing in stratified or homogeneous shear flows,” in Mixing in Geophysical Flows—Effects of Body Forces in Turbulent Flows, edited by J. M. Redondo and O. Metais, Universitat Politecnica de Catalunya, Barcelona, December 1992 (Kluwer, Dordrecht, 1993).
19.
J. T.
Stuart
, “
On finite amplitude oscillations in laminar mixing layers
,”
J. Fluid Mech.
29
,
417
(
1967
).
20.
E.
Meiburg
and
P. K.
Newton
, “
Particle dynamics and mixing in a viscosity decaying shear layer
,”
J. Fluid Mech.
227
,
211
(
1991
).
21.
M. R.
Maxey
and
J. J.
Riley
, “
Equation of motion for a small rigid sphere in a nonuniform flow
,”
Phys. Fluids
26
,
883
(
1983
).
22.
J.
Kim
and
P.
Moin
, “
Application of a fractional-step method to incompressible Navier–Stokes equations
,”
J. Comput. Phys.
59
,
308
(
1985
).
23.
J. B.
Perot
An analysis of the fractional step method
,”
J. Comput. Phys.
108
,
51
(
1993
).
24.
X.
Wu
,
K. D.
Squires
, and
Q.
Wang
, “
On extension of the fractional step method to general curvilinear coordinate systems
,”
Numer. Heat Transfer, Part B
27
,
175
(
1994
).
25.
G. P.
Williams
, “
Numerical integration of the three-dimensional Navier–Stokes equations for incompressible flow
,”
J. Fluid Mech.
37
,
727
(
1969
).
26.
A.
Michalke
, “
On the inviscid instability of the hyperbolic-tangent velocity profile
,”
J. Fluid Mech.
19
,
543
(
1964
).
27.
Q.
Wang
,
K. D.
Squires
, and
X.
Wu
, “
Lagrangian statistics in turbulent channel flow
,”
Atmos. Environ.
29
,
2417
(
1994
).
28.
S. K.
Aggarwal
, “
Relationship between Stokes number and intrinsic frequencies in particle-laded flows
,”
AIAA J.
32
,
1323
(
1994
).
29.
J. E.
Marcu
and
E.
Meiburg
, “
Three-dimensional features of particles dispersion in a nominally plane mixing layer
,”
Phys. Fluids
8
,
2266
(
1996
).
30.
X.-L. Tong and L.-P. Wang, “Direct simulations of particle transport in two and three dimensional mixing layer,” in ASME Gas–Solid Flows, ASME Fluids Engineering Division Summer Meeting, Vancouver, British Columbia, 1997.
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