244
A. LEONARD
I
I
Fic;. 3. Two possible interpolations of k ( r ) between known asymptotic forms.
inertial subrange asymptote. Unpublished calculations based on turbulence
as given by Burgers'equation (Burgers, 1940, or see Burgers, 1948) ("Burgerlence") suggest that &) will approach its asymptotic form more quickly as
shown by curve B.
Furthermore, turbulence measurements in an atmospheric boundary
layer (McConnell, 1973) and an air jet (Clay, 1973) have shown that the
inertial subrange behavior of k(r) given by (4.15) persists.down to about a
Kolmogorov length q whereas curve A assumes a lower bound on the linear
range of k ( r ) at = 5q.
Nevertheless, as a tentative lower bound to the amount of energy loss
attributable to eRS we will use curve A for E(r). With the filter
(4.17)
(4.9) gives
G(() = [A- 1(6/n)1'2]3 exp( -6 15 12/A2),
(4.18)
€19 = -#q3GA2
plus a negligible contribution from the asymptotic form ofJ(r).
(4.19)
( ( i % 1 / & ~ ~ ) ~ ) = (iiliil a3iil/;tx:)
We relate I;;;' to skewness by noting that
and therefore
(4.20)
ERS = -~((C%~~/~X~)')A~
= gs( ( & , / ~ X , ) ~ } ~ ' ~ A ~ ,