672 



BARBER AND TUCKER 



[chap. 19 



between the wave steepness HfL {L being the wavelength) and the ratio of 

 wave phase-velocity C to the wind speed V (which they called the "wave 

 age"). Observations supported this, and gave an empirical curve for the 

 relationship which formed the basis for their method of prediction. 



Neumann (1953), developing a method for predicting the frequency spectrum 

 of the waves, had insufficient measured spectra. He therefore worked with the 

 apparent period T between two successive crests passing a fixed point, and the 

 corresponding apparent height H defined as the mean difference in elevation 

 between these crests and the trough in between. He argued that such a wave 

 is due to the fortuitous superposition of all the spectral components with 

 periods near T, and that the largest value of H observed for a given value of 

 T is, therefore, a measure of the spectral density near T. Following Sverdrup 



0.2 



i0.05 



Observations 



Long Branch Wave Records 



May 3, 1948 



May 5, 1948 



[October 6, 1948 

 I October 7, 1948 



«\ xj.,^*, *\5-x\<i !l^x^ 



- .XX..X \ I . ^\\\i' 

 /x Vx ^. '-. %"-. 



J I I I I I I I I L. 



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 I.I 



Fig. 3. Relationship between the wave height H, apparent wave period T and wind speed 

 V in the generating area, measured from wave records. (After Neumann, 1953, Fig. 5.) 



and Munk, he assumed that there would be a unique relationship between the 

 maximum values of HjT^ and T/V (note that for a simple wave train, L = 

 gT^l27T and C = gfT/27r). He plotted measurements from several wave records 

 taken with a surface-height recorder under conditions which should represent 

 a fully-arisen sea (Fig. 3), and found that the highest values were approxi- 

 mately on the curve 



i^/T2 = 0.219 exp[-2.438(f/F)2]. (7) 



Assuming that H^ is proportional to the energy per unit range of periods, this 

 gives a spectral density function 



E'{g) = Apg^TT^a-^ exip {-2g^/(7^V^), 



(8) 



