Wu 



(4), Ap and Bh/3t cannot be also of the same sign everywhere. Suppose, as 

 a qualitative picture, that 3h/Bx and Bh/Bt are everywhere opposite in sign, 

 then a propagating wave toward the tail is clearly indicated (see Fig. 1). 



f5>o 



Ap>0 



at ^ 



Ap< 



ih > o 



Fig. 1 - Wave propagating toward the tail 



To investigate further the qualitative features of such periodic waving mo- 

 tions, it suffices to consider the case of simple harmonic form (7), since for 

 arbitrary time dependence all linear effects, such as the pressure, lift, and 

 moment, can be obtained by the Fourier synthesis and as for the quadratic ef- 

 fects such as T, P, and w, it can be seen that in their time averages, the com- 

 ponents with different multiple frequencies are not coupled. In fact, consider 

 two functions: 



(x, t) = Re 



E gn('')e^""' 



h(x, t) = Re 



E Ki^)^'""^' 



(10) 



The time average of gh is 



T 



;h = lim - I g(x,t)h(x,t) dt = - Re 



T-»co T v/ 2 



E gn('')h*(x) 



(11) 



1178 



