WIND DISTRIBUTION OVER SEA WAVES 



by 



Ulrich Roll 



This paper appeared originally in the German language, 

 in the German periodical Naturwissenschaften in 1948 (Vol. 

 35, pp. 230-234), under the title "Das Windfeld uber den 

 Meereswellen". It has been translated at the Wave Research 

 Laboratory, Institute of Engineering Research, University 

 of California, by Mr. J. Kukk, and the translated version 

 edited by Messrs. Ovald Sibul and R. L. Wiegel, research 

 personnel at that institution. 



Developments of modern physics have presented to us knowledge of 

 atomic relationships which we could not perceive without special aids. 

 Because of this, an almost paradoxical situation has resulted; we are 

 often better informed about such "hidden" things than about more obvious 

 everyday natural occurrences. For example, we need only to think of our 

 present inability to predict accurately the progression of weather, for 

 even in those branches of the natural sciences for which sufficient 

 mathematical systems of formulas have been developed, as is the case in 

 wave theory, our knowledge of the physical relationships is still very 

 limited. We know, to be sure, that the wind generates the waves, however, 

 we do not yet clearly understand the mechanism of this transfer of energy. 

 There are four conceivable ways in which turbulent wind flow could produce 

 and develop water surface waves, and three of these have become bases for 

 well-developed theories. 



(D* (2) 



Lord Kelvin and v. Helmholtz proceeded from the assumption 



that a compression of stream lines of the wind over the wave crests pro- 

 duced low pressure areas, and the fanning out in the wave troughs pro- 

 duced high pressure areas. The suction and compression forces resulting 

 from this amplify any insignificant disturbances of the water surface to 

 a point where the differences in pressure are equalized by the forces of 

 gravity. The equations for waves developed from these assumptions, even 

 when considering surface tension, are contradictory to experience in re- 

 spect to the required minimum velocity of 670 cm/sec for the generation of 

 the slowest waves, as these waves actually occur at considerably smaller 

 wind velocities. Moreover, the existence of such a limiting wind 

 velocity is debatable. 



(3) 

 Later, Jeffreys considered the wind pressure on the windward side 



of the wave to be important in the development of the wave. He equates 



the work done by the wind pressure on the wave to the energy consumed in 



the water by friction in the wave motion, and obtains expressions for 



wave values in which there still exists an unknown constant, so that a 



verification of the theory is not possible at present 



Jeffreys also investigated the problem of whether the tangential 

 shearing force of the wind on the water surface - which in the case of a 



I 

 * Numbers in parentheses refer to references listed at end of article. 



