and in fact 



A. S. Iberall 

 D^J, - , 



3"o= 



(v) We are left with the three momentum equations 



rl 7) 7^ 



— + V, , . — - + W^ , ^ — 1 U, , , = , X momentum 



d d d , 

 U, , . — + V, , . — + W, , . V , , . = , y momentum 



3 B B , 



U . , . — + V, , , — + W, , , W^ , , = g , z momentum 



(1) Bx (1) 3y (1) 3z / (i> 



to satisfy throughout the core. At present we do not have a satisfactory program 

 for this end game. (The end game probably requires determination of a spectral 

 density function by means of an integral equation, summed over states a>^ < u < 

 ccq, ±a, odd and even, of Fourier or Laplace form.) However, we can illustrate 

 very crudely that our amplitude fimctions do possess a valid order of magnitude. 



Laufer shows that the rms fluctuations in the cross-channel and lateral di- 

 rection are essentially equal and not greatly different (by about a factor of 2 or 

 3) from the axial rms fluctuation. We will disregard this fact and imagine that 

 the first two momentum equations are satisfied identically by each traveling 

 wave system, namely, by letting both u and v approach zero. Specifically, we 

 will consider that both 



a2(5 = (1-CT) \S , 

 & = (l-a)S, 



are true and that the excitation e is small. Thus there only remains the z 

 momentum 



-— = W —- = 2 



Dr (1) Bz ^ 



(what is essential is that both w and x not vanish, i.e., that neither Q nor ® 

 vanish. The lesser magnitude of X compared to g momentum suggests that the 

 better condition may be Q = (1 - a ) ®.) 



Further we will imagine that there is only one frequency component ^g, 

 corresponding to the high-frequency eddy size. 



Imagine now the standing wave system given by 



732 



