Recent Reseavah on Ship Waves 



3o In the interior of the sector, two distinct wave systems 

 will occur, the diverging (|6| > 35°) and transverse 

 ( |e| < 35°) systems. 



^/x=- 



amOcosQ 



'd/^^-fani&''2&' J 



Fig. 1 Plot of y X, from Eq. (9) , as a function of the 

 wave direction 9. 



Finally, if the loci of a given wave crest are plotted, by 

 requiring that the wave phase (7) be constant, while (9) is Satisfied, 

 the familiar Kelvin wave pattern shown in Fig, 2 is obtained. (The 

 phase difference of ir/Z between the two wave systems along the cusp 

 line is not explainable from the above simplified argument, but is a 

 natural consequence of the method of stationary phase. Fig. 2 is 

 reproduced from Lunde [ 1951] ,) 



Divergent Wave Cresl^s 



B«Z8' 



Fig. 2 Wave crests of the Kelvin wave system (from 

 Lunde [ 1951] ) 



The amplitude of the individual elements in the Kelvin wave 

 system will vary, in accordance with the function A(9) or the "free- 

 wave spectrum" of the vessel. Moreover, the Wave amplitude will 

 vary as R for large R, in consequence of the radial spreading 



523 



