These forced, non-propagating comoonents can act as the com- 

 ponent c in Fig. 6 coupling the free incident wave i 

 to the scattered free wave s . For the lowest order 

 interaction with a quadratic harmonic, the Bragg condition 

 is accordingly given by ([20a] [^2]) 



^ilSi + ajki + o^k^ = kg 



The net coupling is cubic in the wave amplitudes, the 

 scattered wave s being generated by a quadratic inter- 

 action between the free incident wave i and the forced 

 wave c , which itself is produced by a quadratic 

 interaction between two free waves 1 and 2. For a contin- 

 uous spectrum, the summation over all possible interactions 

 of this kind yields an energy transfer rate given by a 

 Boltzmann Integral over combinations of cubic products of 

 the spectral densities at the four wavenumbers occurring in 

 each scattering process ([20a]). The structure of the 

 integral is rather complex, and it has not been possible to 

 find a simple explanation for the particular form of the 

 nonlinear transfer rates computed for the different cases 

 shown, for example, in Figs. 5 and 7. The H theorem, which 

 states generally that wave-wave scattering changes the 

 spectrum irreversibly in the direction towards a uniform 



25-19 



