W
t
b -
z
a
t
*
v)
2
W
0
-
-
-8 -6 -4 - 2
0
2
4
6
X DISPLACEMENT
1
1
1
1
1
1
1
'
FIG. 9. Sample of particlc displacement probability distribution (at tinir 2.6)
Mechanisms to allow extremely rapid acceleration of particles in short times
after release apparently were not present. While this in part may be due to
the nature of the simulation, one might also speculate that the absence of
vortex stretching in the two-dimensional field implies the absence of
mechanisms for rapid particle acceleration. It should be noted that at longer
limes the displacement distribution did approach a Gaussian form.
Figure 10 is a comparison of the Lagrangian autocorrelation with its estimate from the Corrsin equation using the computed rather than the Gaussian probability distribution. it can be seen that the correspondence is quite
good. Unfortunately. statistical noise in determination of the probability
2
1.0
0
u
0 . 8
IJ
w
a
0.6
a
0
0
0 . 4
0
b4
= 0 . 2
0 . 0
5
w - 0 . 2
P - 0 . 4
2
4
(3
4
-I - 0 . 6
0
2
4
6
8 10 12 14 16
T I M E
f;ici.
10. ( 'onilwisoti ol 1,;igr;ingiiin nulocorrclation and Corrsin liypothcsis rstim:itc
(Joftsil ciir\c) ituitip directly dcterniined prohiihiltty distrihution.