A. S. Iberall 



vorticity for the main stream whose frequency components are coexistent with 

 the frequency spectrum of turbulence. Whether we can proceed into the main 

 stream may be regarded as conjecture (it is main- stream energy that has been 

 captured to develop and sustain these piece-wise "coherent" elements; the net 

 effect of the capture is that the layer radiates a structure of acoustic eddies 

 back into the main stream. This is suggested as the energy budget at the wall). 



We continue with a tentative scheme along the following crude path: 



In the core, the main terms are likely to be 



U = ja2bj(Je'^''' -j (1-a) >.bj Se'^'" -jd^Se''^'' 



^^jb.x „ib,x „d.x 



W^-aU^Qe ^ + a(l- a) MgSe ' + a D e '^ 



7= - ja(7-l) SgSe^*'''' + crC e^*"^" -(7-1) M^jSe"'^" 



,^ d . X 

 P = - Mq iD e ^ 



where 



bi = (1- J)V^ . b3 = (1-j) 



7 - 1 



il + + q 



d, = /3-l/5R O) +\ S2R2a)2+J^ L /3'*c^^ 



j (1 + ^^+ ql/33a;3 



1 ^ - 1 1 



1 + + q 



SR2 a; +V S^R^ ^2 + ^ 12^^^ 



Strictly speaking, it is necessary that the form of cp be developed over a 

 series of layers so as to match solutions, particularly the rapidly changing 

 velocity solutions, through the transition zone layer by layer. However, we pro- 

 pose to only deal with the very crude two-zone approximation. We can only per- 

 form a very crude match. 



(i) We will assume that the pressure fluctuations are continuous across the 

 transition layer. In particular at small Mach number (so that d^ is definitely 

 quite small), 



P = -cj'^e'^'' ^ -w® = -E 



SO that the core is flooded by a small excitation E. 



730 



