GENERATION OF WAVES BY 

 TURBULENT WIND 



Klaus F. Hasselmann 



Institut fur Schiffbau der Universitdt Hamburg 



Hamburg, Germany 



and 



Institute of Geophysics and Planetary Physics 



University of California, San Diego 



La Jolla, California 



ABSTRACT 



Interactions between random gravity waves and the turbulent atmosphere 

 boundary layer can be treated by an extension of wave-wave interaction 

 theory. The energy transfer resulting from various interaction combi- 

 nations can be characterized by transfer diagrams corresponding to the 

 Feynman diagrams of wave-wave interactions. The complete set of 

 lowest order transfer diagrams is shown to include Miles' and Phillips' 

 theories of wave generation and a further set of wave-turbulence inter- 

 actions which have not been considered previously. The predicted wave 

 growth for the various interactions is compared with existing measure- 

 ments. But a conclusive answer to the question of wave generation 

 must await nnore detailed experiments correlating wave nneasurements 

 with turbulence measurements in the atmosphere boundary layer. 



INTRODUCTION 



The fundamental papers of Miles (1) and Phillips (2) marked an important 

 advance in our understanding of the basic processes by which waves can be gen- 

 erated by wind. It has been widely hoped that the growth of waves could be largely 

 accounted for by a superposition of these two processes. However, it is known 

 that although the theories describe independent aspects of the wave-atmosphere 

 interaction, they are not entirely complementary; there remain interactions which 

 are included in neither theory. Miles considers the coupling of the wave field 

 with the mean atmospheric boundary -layer flow, but ignores the wave -turbulence 

 interactions. These are similarly neglected in Phillips' treatment, which is 

 concerned only with the external excitation of the waves by the undisturbed turbu- 

 lent field. 



Apart from the general theoretical interest, a complete theory of wave- 

 atmosphere interactions has now become particularly desirable through the field 



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