which could be compared with experiment. However, the actual comparison here has 

 been made with k R uv under the additional assumption that F 1 ~ F, ^ k-c% since 



the high wave number end borders on the region of local isotropy. Then 



h R uv ~ fc x -' (25) 



A', 



which does not look particularly successful in Figure 1 1 . The abscissa there is fre- 

 quency rather than wave number. 



By a considerably more sophisticated approach, Tchen [18] arrived essentially 

 at 



for "small 



ay 



t\ ~ &i 5 (26) 



du 



The Gradient Transport Postulate 



It is a familiar fact that the validity of any simple gradient transport description 

 requires the transfer mechanism to have a characteristic length much smaller than the 

 gross dimensions of the field. With a random "free path" type of mechanism, for 

 example, the transfer rate Q of some property ijj(x) may often be expanded in a 

 power series in the "mean free path" /: 



/ 



1 I # \ \ 2 / / dty 



Q(*i)~- ■ + — ) ( 27 >* 



2 \ dx h x 3 1 \ dx s )\ 



Provided \b' and ty"' are properly behaved, (27) reduces to simple gradient 

 transport when 



V 6 - 



I « \l 6 — , (28) 



a characteristic length of the gross field. 



In Figures 1, 2, 3, 4 we were reminded of the well-known fact that shear 

 turbulence has structure comparable with the shear zone width. Furthermore, it turns 

 out that if we apply (27) to heat diffusion measurements in isotropic turbulence, 

 where the Lagrangian integral scale serves in place of a free path, the second term 

 is about 30% of the first. 



Of course, (27) indicates only constant coefficients, and it seems reasonable to 

 see whether 



Q(x) » Af(x) + W'(x) (29) 



can be represented as gradient transport with coefficient dependent on .t**, i.e. we 

 define D(x) such that 



Q(x) = D(xW{x) = A+'(x) + W\x). (30) 



* The even powers vanish if we choose x t at the center of the mean free path, and 



/ / 



consider particles traveling only between (xi ) and Oi -\ ). 



^'^■This mathematical trick is not intended to include inhomogeneous flows, in which 

 the transport mechanism actually does vary from place to place. 



387 



