TKANSPORT MOIJEL LIMIT A l IONS IN TURBULENCE
37
I
I n i t i a l
C on d 1 t I on
(a11 3 cases )
t
D i f f u s i o n
E q.
t ‘ t l
i
z
I
I
I
I
W a v e
E q
I
I
I
t * t l
T e l e g r a p h
I
E q
t
FIG. 2. Qualitative traits of the mean concentration profiles gtven by the solutions of
Eqs. (35). (37), and (39)--dl with a Dirac function at the origin a0 initial condition.
Clearly Eqs. (44) and (45) are the two asymptotic forms of Eq. (46).
Before leaving this discussion, it may be helpful to identify a sense in
which turbulent diffusion may be considered “wavelike” for small enough
time intervals after a fluid point has been “tagged” at a prescribed space
position. There may be two or three rationalizations for the adjective
wavelike. One which has been mentioned from time to time is rather like the
following :
No contaminant dispersing from a point source by turbulence is observed
to reach infinite distance in infinitesimal time. But the (parabolic) diffusion
cquation requires that behavior of its solutions; therefore, turbulent transport cannot be parabolic. The apparentiy bounded shapes of smoke plumes
in atniospheric turbulence are the observational justification. The statement
is corrcct. but is literally correct for molecular diffusion as well; the energy of