Similarly,for the case of turbulence being convected at vector Mach number M, the in- 
stantaneous sound pressure, by using Equation [2], is 
‘on ° 2 
4 2 2 
sf rT; Tj 3(1-M )T;; ‘ 3(1-M*) T;; 
DM ore irr emma Te EE ET an EL Te 
4n (p-M-F)2 | c2(r-M-F) ~~ oc (r-M- 7)? (r—-M-7)3 
= 2 
27M, 2T,, 3(1-M*) T,, 
_ — SS —— ee 
r-M-7 | c(r-M-7)? (r—-M-7)3 
Te (1-M?) T. ) I. 
ij ij ij 
- 5, | ———_ + ———*|+ ,,| ———| fan [88] 
c(r—-M-F)? (r—M -7)3 (r—-M-F)? 
where now T;; = T;, (7, t-r/c). By again neglecting terms involving an odd number of time 
derivatives, the mean-square sound pressure becomes 
= 1 1 tl lm 
YES \) oT ES agen T;; es 
16 72 c* (r—-M-F)2 (r—M-7) 
2 
Eo || SOLSTE YG Gs OLS) OL nie 12 (1— M7) 7; 25 7) May 
SH oye SE ES | (Ca can EY 55 0) 
(r—M-7)? (r—M-7)4 (r—M-F)? (r—M-7)? 
16 7; 7, M; M,, 47,7, MM, 86 
1 5 at FN UO es NE TC Teae TRE TLS 
(r—M-7)2 (r—M-7)? (7 — M-F) 
a ; 2,3 
4 9(1 - M*) Ooh un ie 6(1- M~) 85; iat : 
DS |, ee eee +(1-M") 8;, 8), 
(r—M-7)* (r—M-7)4 (7 -M-F)? 
23 M 2 23 M 2 92 
36 (1 - M*) 77M, 36(1-M*) 7; 7, i Mn 12(1-M-) rt MM, 
(r-M-7)° (r—-M-7)? (7 —M-F)2 
2 
2 2 
12(1 - M*) Simi M, 94(1-M )r, M, M) M s 
$+ - —_—_ - 41 - M*) 8, MM 
are = J ™m 
r—M-r r—M-r 
+4M,M, MM) 1; Tin ( o7 27” [89] 
30 
