Generation of Waves by Turbulent Wind 



9^n f 



dk^dk^dk^ 



(n.1.2 ,^-2,1) 



(i) 



dt J '•* 



F„F^F^dk„clk. 



(li) 



Fig, 1 - Examples of transfer dia- 

 grams and transfer expression for 

 (i) a third- order scattering process 

 and (ii) a third-order parametric 

 process, a and b represent arbi- 

 trary field components; Wj, Wj, and 

 w represent wave components; T^^, 

 T are transfer functions; and the 

 indices n, n refer to the wave com- 

 ponents Wj, Wj. 



It is important to note that the transfer diagrams reflect only the structure 

 of the transfer expressions. They are normally not directly related to the basic 

 component- interactions responsible for the energy transfer. Thus although all 

 transfer expressions are due entirely to resonant interactions, the resonant in- 

 teraction conditions of Eqs. (5) and (6) occur only in the scattering, not the 

 parametric transfer diagrams. The structure of the interaction analysis can be 

 summarized independently in terms of interaction diagrams (6). (However, for 

 conservative wave-wave interactions, the interaction and transfer diagrams are 

 very simply interrelated (8).) 



APPLICATION TO WAVE-ATMOSPHERE INTERACTIONS 



The complete set of lowest-order transfer diagrams in the case of wave- 

 atmosphere interactions are shown in Fig. 2. The linear interaction with the 

 mean boundary -layer flow according to Miles appears as the degenerate pa- 

 rametric diagram (i). Phillips' external excitation by the atmospheric turbu- 

 lence field is represented by the diagrams (iii). (If the external field is ex- 

 pressed in terms of the turbulent pressure p* instead of the turbulent velocity 

 components t, these reduce to a single linear diagram.) The remaining proc- 

 esses represent a nonlinear interaction with the mean boundary- layer flow, 



589 



