Russian Issue 3 - Harvard University Department of Physics

"Radiation & Risk", 1993, issue 3
chastic model which generates a random process
that has specified statistical features. The
statistical procedure for calculation of diffusion
is based on use of an equation for random pulsations
of the particle turbulent velocity and on
plotting of tracks of thousands of individual particles.
The particle motion in the wind velocity field
is expressed by a sum of the average and turbulent
components that are separated with application
of the definite specific averaging time.
The equation for the particle total velocity in the
direction / On the system of coordinates related
to the average wind direction at the given point)
has the form:
v,=vl+v;.
As a mean wind field one can take results of
a dynamic model or the field built from network
measurements. In the last case, the obtained
field of mean wind is corrected with allowance
for meeting the equations of continuity providing
for conservation of the material mass. At time
scales that exceed the averaging time ail turbulent
diffusion is described by spatial and temporal
variations in the average wind.
At the time scales less than the time for averaging
the diffusion is estimated on the basis of
assumption that the turbulent pulsations have
two components - correlated and pure random.
v;(t + At) = v;(t)P'L+p„
where At - time step;
pt(At) - Lagrangian auto-correlation coefficient
for the Mh velocity component.
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Scientific Articles
The random component is generated is such
a way that it has a Gaussion distribution of
probabilities with a zero average and standard
deviation given by
This condition provides for turbulence energy
conservation from step to step. To calculate
PL (At) an exponential dependence is often used
p'L(At)=exp(-At/ rL).
Movement of the particle at each moment of
time is determined by the velocity fluctuations
that correspond to CT/ and pi!(At) values at the
given point of space, i.e., the model allows including
variation of these parameters into description
of the diffusion.
Thus, success of the statistical model application
depends primarily on utilization of the
most accurate experimental and theoretical estimates
for profiles of the turbulence energy and
velocity timescaies. The best of the up-to-date
values of these variables [14] are used in the
present model. Components of the turbulence
energy and time scales in the unstable atmosphere
boundary layer (ABL) are given by the
following formula:
'•r
"Radiation & Risk", 1993, issue 3 Scientific Articles
^ = [12 + 0,5h/ \l\X\
^-
w.
= 0,96
h
-(1/3
h
for ~ < 0,03,
h
^- =/n/n 0 , 9 6 ^ - M ; 0,763
r 7-\ 0 - 207
= ° ' 7 2 T - i
= 0,37
7? = VL=0,15^-,
for 0,4 < — < 0,96,
h
for 0,96