If the turbulence is being transported in the 2,-direction, the mean-square sound pres- 
sure becomes tr 
3(1-M2)- 
ay 1 ij 1 Crh em Bae ec 3(1- rTP 
: 167204) 72(1-M cos 0)2 |r4 (1-M cos 6)* 7” = 72 (1-M cos 6)? } | r4(1-M cos 6)4 
4(1-M) 5,1) P, A eae 12M(1-M?) 2, 1.7, = 16 M?r, 7, a 
+ OF Lo Dy iis (oer arererarieee nd Ua Bri ep cea ere ee hey Uc 
72(1—M cos 6)? Pee Al 73(1-M cos @) ‘ r*(1-Mcos 6)” i 
2 dl 2,4 
4M rr = 8Mr, — of 9(1-M*) retry 
= T,, 1. Aes Ty a ee 
r2(1—M cos 6)” r(1—¥ cos 6) r*(1—M cos 6)* 4 (1—Mcos 6)* 
2,3 on 
6(1-M*) 6..7,7 386(1-M*) r. 7.37 
ij lim 2 2 5 a7 eb ——_ 
Se ae le) oF; 1m Tj 1B Ver sora a Ta , T)3 
r?(1-M cos 6)? 73(1-M cos 6)3 
2 2? 2 2)? 22 
36 M2(1-M?) rr, 12M7(1-M) 7, 7, 12M(1-M?). r, 
+ ———- T., T,, + ——__ T_T, ¥ + ——_ 7. T’ 
3 413 33 3 *1l 
r*(1-M cos 6)2 ‘ r?(1-M cos 6)? i r(1—M cos 6) : 
24. M3 (1—M?) 7, slates Eee 
SS TES — IE (LSI) Tp TES 2 OI RS TBS (CI I? [90] 
r(1-M cos@) 
For the case of lateral quadrupoles having axes in the #,- and z,-directions and being trans- 
ported in the z,-direction at Mach number M, the mean-square sound pressure is given by 
ar 1 “(¢ 4 sin? 6@cos?¢ Sapa 
2 2 , 
\| a GOS Hn US 
Pp = 
16 72c4 r7(1-M cos 6)® 
2 Petia mere 
ce? |38(1-M?) cos?6@ 6M(1-M?) cosé Eli cece 
ee ti | 7 Ts 
2 2 
r (1-M cos 6) 1-M cos@ 
4 3 2 
c* 19(1-M?) cos?@ 18M(1-M2) cosé : 9M? (1-M?) 
r4 (1—M cos 6)* (1-M cos 6)3 1-M cos 6)2 
T13T;3 dn dn” 
[91] 
Beyond several diameters from a circular jet, cos? may be replaced by its average value; 
namely 44, as before. 
31 
