SEAWAY 



41 



120 

 110 

 100 

 90 

 80 

 70 



I- 



' 60 

 SO 

 40 

 30 

 ZO 

 10 

 



0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 O.IZ 0.Z4 0.26 

 u I I I I ■ I I I \ I I I 



28.0 20.0 16.014.012.0 10.0 9.0 8.0 7.0 6.0 



T 



5.0 



4,0 



120 

 110 

 100 

 90 

 80 

 70 



J 



50 

 40 

 30 

 20 

 10 



004 006 0.08 010 012 0.14 0.16 0.18 0.20 0.22 0.24 0.26 

 f'l/T 



28.0 20.0 15.0140 12.0 10.0 9.0 8.0 70 6.0 



T 



5.0 



4.0 



Fig. 42 Duration graph co-cumulative spectra for wind speeds Fig. 43 Fetch graph co-cumulative spectra for wind speeds 

 from 20 to 36 knots as a function of duration (from Neumann, from 20 to 36 knots as a function of fetch (from Neumann, 



1953) 1953) 



the form; this evidently influenced the fitting of the 

 Hiiio curve in Fig. 40. 



The form of the spectrum can lie characterized broatUy 

 by the total range of periods T, by the value of T at the 

 freciuency of maximinn energy, usually designated 

 Tmox, and by the mean -v'alue of T. In principle, all 

 values of period T or of fre(|uency / are possible. How- 

 ever, examination of Fig. 38 shows that abo\'e and below 

 a certain range of freciuency, /, the energies contained in 

 waves are negligiljly small. Thus, at a 30-knot wind 

 the significant range is between / = 0.048 and/ = 0.240, 

 or between periods of T = 21 and 4 sec, respeeti\-ely. 

 The frequency ranges at different wind speeds are shown 

 in Table 9. 



The mean value of the frecjuency pro\'ides a con^•enient 

 method of checking the form of the spectrum. In terms 

 of the theoretical spectrum it is given bj'-' 



T = 27 



i: 



dE{oj) 



■JO -I 



(85) 



Here the symbol T is used to designate the mean \'alue 

 of "apparent" periods. This period also can be evalu- 

 ated by direct obserwation of periods in a seaway. Fig. 

 41 shows the period distributions obser\'ed by Neumann 

 (l!)o4) over six ranges of wind velocity. The ;i\-erage 

 periods calculated from the spectra, T, and resulting 



from the observed data, f\, are shown by \'ertical lines. 

 A reasonable agreement is demonstrated. No such 

 agreement is established as yet for the spectrum area E] 

 i.e., for the significant wa\'e height corresponding to a 

 gi\-en wind, and practically all ol)ser\'ers indicate wave 

 heights somewhat lower than Neumann's, jjarticularly 

 at higher wind s])eeds. 



6.22 Co-cumulativs energy spectrum and seaway 

 devefopment for a limited fetch or wind duration. Since 

 the wave height is proportional to the square root of the 

 spectrum area E, plots were made of the value of 2/pg 

 times the integral, e(|uation (78), versus frer|uency /.• 

 such curves are called co-cumulatire spectra, al.)bre\'iated 

 as CCS curves. Figs. 42 and 43 are reproduced here as 



^' Neumann (l'J.^3) attributes this formula to Dr. \V. J. Pier.'ion, 

 Jr. 



