Hasselmann 







^. n 



9F(k) r. , , . dF(k) 



-J^ 'j[T4(k.i')F(i'hT,(!i.k')F(k)]dk- -^ - TfFfk) 



iiv) (r) 



Fig. Z - Lowest order transfer dia- 

 grams and transfer expressions for 

 wave -atmosphere interactions: (i) 

 Miles, (ii) nonlinear interaction with 

 mean wind, (iii) Phillips, (iv) wave- 

 turbulence scattering processes, and 

 (v) wave -turbulence parametric proc- 

 ess. The components g, t, and p* 

 represent gravity- wave, turbulent- 

 velocity and turbulent-pressure com- 

 ponents, respectively. 



diagram (ii), and wave -turbulence interactions, diagrams (iv) and (v). The trans- 

 fer expressions derived from the transfer rule are also shown. Only the depend- 

 ence on the wave spectrum is given explicitly. The transfer functions Tj, , T, 

 depend on the coupling coefficients, and in the case of diagrams (iii), (iv), and (v), 

 on the atmospheric turbulence spectra. The expressions are given in full in 

 Ref. 4. 



THE PRESSURE SPECTRA 



Figure 3 shows schematically a two-dimensional kj-w section of the three- 

 dimensional surface pressure spectra Fp(k,aj) associated with the various 

 transfer processes. The scattering processes (iii) and (iv) of Fig. 2 correspond 

 to three-dimensional pressure distributions, whereas the parametric processes 

 (i), (ii), and (v) yield two-dimensional distributions concentrated on the gravity- 

 wave dispersion surfaces oo - ±cr(k) = ± (gk tanh kH)^^^. Only the pressure fluc- 

 tuations in resonance with free gravity waves, i.e., on the dispersion surface, 

 transfer energy to the wave field. 



The three-dimensional turbulent pressure distribution is concentrated 

 about the "convection surface" w+ k,u„ = 0, where u„ is the mean 



1 m ' m 



590 



