Generation of Waves by Turbulent Wind 



wovt -tyrbi/ltnc* 

 icotlrring intfroetlens 



trOYt-mton flow inltroelions, 

 potommlric mravt-turbultnct 

 intrrocOons 



"■turbultne* 



Fig. 3 - Two-dimensional k ^ - a; sec- 

 tion of the three-dimensional surface 

 pressure spectra F (k.w), (The mean 

 wind Uj^ is parallel to the Xj axis.) 



("anemometer") wind speed and kj is the wavenumber component parallel to the 

 wind. The distribution follows from Taylor's hypothesis, according to which the 

 wavenumber and frequency spectra of a turbulence field are approximately 

 related as though the turbulence were a frozen special pattern convected bodily 

 downstream with the mean flow velocity. It follows that the energy transfer due 

 to Phillips' mechanism is appreciable only where the convection surface and 

 dispersion surface intersect, i.e., for gravity waves whose phase velocities in 

 wind direction are approximately equal to the wind speed (2) (see also Ref. 9 for 

 the present interpretation of Phillips' result). 



Linear wave interactions with the mean wind lead to pressure fluctuations 

 of the same wavenumber and frequency as the wave components. Miles' pres- 

 sure spectrum is therefore represented by a two-dimensional distribution on 

 the dispersion surface. 



The parametric processes (ii) and (v) also corresponds to two-dimensional 

 pressure distributions. The process (ii) is due to a cubic wave- wind interaction 

 involving a wave component (k, cr) and a complex conjugate pair of wave compo- 

 nents (k', a'), (-k' , -cr' ). This leads to a pressure fluctuation with the wave- 

 number and frequency of the first wave component. Process (iv) is due to a 

 similar cubic interaction between a wave component (k, a) and a complex con- 

 jugate pair of turbulence components (k', oj'), (-k', -w'), again producing a pres- 

 sure fluctuation of wavenumber k and frequency a-. 



The scattering processes (iv) are associated with quadratic interactions 

 between wave components (k, a) and turbulence components (k', co'). In this 

 case the induced pressure fluctuations can have arbitrary wavenumbers k + k' 

 and frequencies cr+ w', and the spectrum is a three-dimensional continuum. 



591 



