220
1'. J . S I '1.1 I V A \
CK,. 4. Fxperimental values of& when all experimental data is used. Solid line given by
Eq. f 11).
that r is in the inertial sobrange and (I) depends only on r and c, then
(,) = uI:l'Jr- 2;3
(12)
(13)
where a is a universal constant. With the estimate for E given in Eq. (4), then
(0' 2 a($)'/'r'- 2'3
which by comparison with Eq. (1 I ) suggest that a is approximately 2. The
comparison is quite favourable between Eqs. (13) and (1 l), however it is
unlikely that an inertial subrange structure would be present with a value of
R = 620 and Eq. ( I 1) appears to describe the experimental data over even
the largest length scales measured.
4. TIME SCALES
One would like an estimate of the average persistence time ofa particular
valw of r' along the trajectory. Starting with a value of r' in [r' - 0.028.
r' + 0.0281 one can construct a "mean history" in terms of r' values a
particlc encounters following this particular range of initial values. A normalizcd exprcssion of such a mean history is
(14)
~ ( t ;
r i ) = [?(l) - ~]/[7loj - A]
whcre r', refers to the initial value on [Pi - 0.028, r; + 0.0281 at f ' = 0 and A
is the average value of r' for all realizations recorded: A = 0.097. The ovcr-