Hasselmann 



Since atmospheric turbulence spectra are normally peaked at much lower wave- 

 numbers and frequencies than wave spectra, it may be expected that for most 

 interactions k' << k, w' << a, so that the resultant pressure distribution lies 

 rather close to the dispersion curve. Furthermore, the maximum of the dis- 

 tribution will lie close to the wave spectral maximum. The strongest wave 

 generation may therefore be expected for frequencies close to the wave spectral 

 peak, in accordance with the observed sequential development of the wave spec- 

 trum form high to low frequencies, the waves growing only in a narrow fre- 

 quency band about the momentary wave peak. (However, other explanations of 

 the sequential wave growth have also been suggested.) 



CONCLUSIONS 



The recent field study of Snyder and Cox (3) indicate that both Miles' and 

 Phillips' theories are incapable of explaining the wave growth observed in the 

 ocean, strongly suggesting that one or more of the remaining lowest-order 

 processes, in particular the wave -turbulence interactions, are the principal 

 source of wave energy. However, the question of wave generation must be re- 

 garded as open until further measurements and transfer computations have 

 been made. Although a complete theory of expansible interactions has been 

 developed, the expansions are valid only for weak spacially uniform interac- 

 tions. Strong, local effects, such as flow separation at the wave crests, are 

 therefore not included in the theory. 



REFERENCES 



1. Miles, J.W., J. Fluid Mech. 3:185-204 (1957) 



2. Phillips, O.M., J. Fluid Mech. 2:417-445 (1957) 



3. Snyder, R.L., and Cox, C.S., J. Marine Res. 24:141-178 (1966) 



4. Hasselmann, K., in "Basic Developments in Fluid Mechanics," Vol. II, M. 

 Holt, editor, Academic Press, 1968 



5. Longuet-Higgins, M.S., Cartwright, D.E., and Smith, N.D., pp. 111-136 in 

 "Ocean Wave Spectra, Proceedings of a Conference," Easton, Maryland, 

 1961, Prentice -Hall, 1963 



6. Hasselmann, K., Proc. Roy. Soc. A299:77-100 (1967) 



7. Peierls, R., Ann. Phys. 3:1055-1101 (1929) 



8. Hasselmann, K., Rev. Geophys. 4:1-32 (1966) 



9. Hasselmann, K., Schiffstechnik 1:191-195 (1960) 



592 



