50
STAkLEY C'ORRSIN
( b ) 'i
Fit;. 5. Qiialiiaiive sketch to show how correlation of orthogonal displacement components
can cause mean cunveaivc transport ofcontaminant r in L direction perpendicular lo the mean
griltlirni or r. (a) A local r' lield with gradient in arbitrary direction. (b)The same ficld with
Citl.tCSiiln coordiintcs reoricntcxi for simplicity; a iypicul isoprohabiiity contour for correlated
p:irlicle displacement components, w sketched, ykld~ mean transport in the .v3 direction (as
W L ~
iis the .' c , direction J. even though the mean I" gradient has no component along x,. This
iiic:itis that D,, # 0.
This means that the mean shear, turbulence, mean concentration gradient.
and concvntriition Huctuat ion fields should all be approximately homogeneous and stationary. With Eq. (74). the mean conservation equation for P is
(79)
What measurements are needed to establish the nine components of D'! We
huvc only four equutions. so data at a single point will not suffice. We can set
up several cases, or we can evaluate Eqs. (74) or (79) at several locations in a
pctitly nonuniforin case.
I t is important 10 interject the remark that if D is constant, the resulting