variations and gradual time variations in the mean values of the turbulent fluctuations. Since 
the operations of differentiating and averaging permute, this assumption is expressed by the 
equation??? 
me ene [g(@)]=0 [15] 
Bi te Ene i 
Therefore, reductions of the following type may be made: 
Ti, es iP, a= [16] 
and 
T;; qT), =0 [17] 
SIMPLIFIED GENERAL EXPRESSIONS FOR THE SOUND FIELD 
By making the above assumptions, Equations [7], [8], [13], and [14] become 
1 "k 
BL Po 3 = [E- 
=e 1 1 7; a —, c2 ; GS 
p- = = /—— | Foo — FF.) dy dy [19] 
16 7202 Aen Ti eae ieee 
jae 1 1 TRULY I"m 7 Pz 
Ba 16 72p,c° J r2 rs ee 
of: 
" T ret) 
= 6G, Se ooves os 2) Ge We | aap ain (ISI) 
i 2 ti \ lm Ue ij “Im | %Y %Y 
F dy dy” [18] 
and 
r? r4 ts i i 
of r.T.t ri? 
RSI gee gs SHES T dy d [21] 
74 74 Pe ij ~lm ij y vy 
