NIJMLRI('A1. SIMULAIION O F IAGHANGIAN QUANTITIES
157
paper did not cxaniine space time Eulerian correlations and their relation to
the Lwgrangian autocorrclation, nor was thcrc any treatment of heavy particles. The primary purpose of this ~ t u d y was to examine both fluid point and
heavy particles in the channel flow with particular emphasis on the effects of
the shear flow region, and in addition to examine the space-time correlation
and its relation to the Lagrangian nutocorrelation, that is. to test the Corrsin
hypothesis.
3.2.1. Purticle Trajecrories. Figure 15 shows the configuration of particles, initially, as viewed from the top of the channel. Particles were released
in pairs and tracked with information for both single- and two-point relative
diffusion and velocities retained. In the case of heavy particles they were
assumed spherical and Stokes drag was employed as a resistance law (see
Kau. 1972). Particles were moved from the initial position by invoking linear
8
.
8
8
8
8
Y
8
8
8
8
8
8
8
8
8
8
0.8 * * , *
i
0
0.8
- 1
- Y
FIG. IS. Position of prticlcs prior to release.
interpolation of the local Eulerian velocity field. Particles leaving the Eulerian field were reintroduced according to the requirements of the cyclic boundary conditions and particles impacting the upper lower walls were reflected
into the flow. Effects of reintroduction were included in computation of
mean-square displacements.
3.2.2. Lugrangian Results. Figure 16 is a typical set of particle trajectories.
Computer motion pictures were generated of this process and the momentum flux to the wall in the case of the fluid points is quite evident from these
motion pictures, In general, single fluid point diffusivities behave as expected, that is, they follow Taylor's diffusion law in the case of diffusion in
the vertical and cross-stream direction. Diffusion in the down-stream direction is affected by shear. Two-point relative diffusion also shows some expected features. in particular, the initial stage where the particles tend to stay
157
paper did not cxaniine space time Eulerian correlations and their relation to
the Lwgrangian autocorrclation, nor was thcrc any treatment of heavy particles. The primary purpose of this ~ t u d y was to examine both fluid point and
heavy particles in the channel flow with particular emphasis on the effects of
the shear flow region, and in addition to examine the space-time correlation
and its relation to the Lagrangian nutocorrelation, that is. to test the Corrsin
hypothesis.
3.2.1. Purticle Trajecrories. Figure 15 shows the configuration of particles, initially, as viewed from the top of the channel. Particles were released
in pairs and tracked with information for both single- and two-point relative
diffusion and velocities retained. In the case of heavy particles they were
assumed spherical and Stokes drag was employed as a resistance law (see
Kau. 1972). Particles were moved from the initial position by invoking linear
8
.
8
8
8
8
Y
8
8
8
8
8
8
8
8
8
8
0.8 * * , *
i
0
0.8
- 1
- Y
FIG. IS. Position of prticlcs prior to release.
interpolation of the local Eulerian velocity field. Particles leaving the Eulerian field were reintroduced according to the requirements of the cyclic boundary conditions and particles impacting the upper lower walls were reflected
into the flow. Effects of reintroduction were included in computation of
mean-square displacements.
3.2.2. Lugrangian Results. Figure 16 is a typical set of particle trajectories.
Computer motion pictures were generated of this process and the momentum flux to the wall in the case of the fluid points is quite evident from these
motion pictures, In general, single fluid point diffusivities behave as expected, that is, they follow Taylor's diffusion law in the case of diffusion in
the vertical and cross-stream direction. Diffusion in the down-stream direction is affected by shear. Two-point relative diffusion also shows some expected features. in particular, the initial stage where the particles tend to stay