32 



THEORY OF SEAKEEPING 



80 



60 



40 _ 



20 



20 



Wave Period (sec) 



Fig. 29 Correlation of period of maximum amplitude 



-with mean gradient wind speed in strongest part of storm 



(from Darbyshire, 1952) 



responding to the maximum \va\-e fompniieiit amplitude 

 (see Fig. 29). Implicit in this choice of characteri.stics 

 is the assumption (cjuoting from Darbyshire, 1952): 

 ". . . that in the de\-elopment of a wave spectrum, the 

 wa\'e compf)nents all grow independently. The em- 

 pirical formulae obtained for the spectral distribution of 

 energy in the storm area imply that waves with periods 

 covering a wide range grow together under the action of 

 the wind ..."-- 



From Figs. 28 and 29 it follows that 



(max r)/T'„ax = 0.33 

 (rformax//)/F„,ea„ = 0.25 



(60) 



The s.ymbol T' is used in (60) in the ntjtation of the 

 present liionograph for gradient wind, which corresponds 

 to undisturbed ^•elocity in aerodynamics. The symbol 



^^ It does not appear reasonable that the waves of longest ]3eriod 

 would occur immediately at the onset of a wind. Neumann 

 assumed that high-frequency waves appear first, and that the 

 spectrum is-ill develop from the high-frequency end. This appears 

 to be confirmed by Ijima's observations (see section 6.4). 



0.4 



0.2 







o.e 



0.4 



0.2 







y- '• ^ /Kr 



(o) For all Periods 



0.14 0.22 0.30 



(b) For each One-Second Period Interval 



- 7 sec •• • 



lOsec . 



0.14 



0.22 0,30 0.14 0.22 



T/V (sec/knots) 



0.30 



Fig. 30 Graphs of Ht T against T ;V (from Darbyshire, 

 1952) 



t'(Was used in the previous sections for the wind velocity 

 at "anemometer" or "mast-head" height. The gra- 

 dient wind velocity T' is in knots throughout Darby- 

 shire's work. 



Having obtained relation.ships (60) Darbyshire writes 

 "these two relations . . . suggest that if Ht is plotted 

 against T/V to give the en\'elope of the wa\'e spectrum, 

 the envelope .should always ha\-e the same shape and an 

 increase in wmA speed should change only the \'ertical 

 .scale of the curve. This implies that the en\'elope can be 

 expressed in the form 



Ht = JiT/V) 



(61) 



where F is the mean wind speed and/(r F) is a function 

 which is maximum at T/V (T sec, 1' knots) = 0.25 and 

 nearly zero when T/V = 0.33. Assuming //^ = V" 

 f(T/V), Hr/T'' = iV/T)"f(T/V) and the values ob- 

 tained Ijy di\'iding 7/j- by some power of the correspond- 

 ing \'alue of T should lie on a curve which is a function 

 T/V . . . ." "The values obtained by letting n = 1 

 gave the most consi.stent results. The.se values of H-p/T 

 are shown plotted in Fig. 30." Despite a very large 

 scatter, Darbyshire fits a curve of the form 



U = Ke^ 



where K = 0.44 



