order to study the scattering of particles, the consideration of their trajectoric\ \hould be w I y I Iliiniinating.
T h l b introduclion i n turhulence diffusion thcorj of the Lagrangian point of
view was made in G. 1. Taylor’s (1921) famous papcr, “Diffusion by continuous movements.” He considers what could be called a ‘’ linear homogeneous turbulent flow”:
-
G-0,
E = O ,
w = o
u‘(x, y, z, I ) = u’(t),
u’(x, y. 2, I ) = w’(x, y, 2, t ) = 0
using for the mean f a time average, he supposes
(6.1)
u p ( / ) * = U;
independent of time
and introduces the correlation coefficient of the turbulent velocity
(6.2)
-
u’(t)u’(r + 11) = U i R ( h )
the independence of the time t ofu’($u(m is a definition of the homogeneity of turbulence, (6. I ) being then a particular CBSC of (6.2). Now considering
the displacement of a particle, starting from the origin at time r = 0:
X(I) = \‘u’(s) A,
y(r) = z(1) = 0
’ 0
the main result of G. 1. Taylor is the formula
t
I
x(ljr = u; 5 ~ ( $ 9 , - s,) ds, ds,
0 0
(6.3)
One can compute the dispersion of the particles if one knows the correlation
of the turbulent velocity u’(r); from (6.3) he obtains this remarkable asymptotic expression:
(6.4)
icy = At for t large
Froin this formula G. 1. Taylor deduces a result that has been the foundation
of one of the most popular experimental methods of tneasuring y* in atmospheric diffusion. Let us assume that in the neighborhood of a chimney
(Fig. I):
(a) U = const.
ti = W = 0
(c) w’(t) satisfies (6.2)
(b) U’ = t j = 0
A particle of smoke emitted by the chimney at the time to will have
trajectory