336 



THEORY OF SEAKEEPING 



10 12 14 IG 18 20 22 24 2G 28 

 Wind Speed; U In m/sec 



Fig. 7 Minimum fetch needed for development of three main 

 wave stages. At l3* = 1.3 5 the seaway is practically fully de- 

 veloped (from Neumann, 1952b) 



CaseBJorlS < 1/3 



W 



13' 



P 9 

 Case B for 1/3 < /^ < /3„,* 



g 



(\w) - sm 



rf/3 



d.x 



""' n^u^ ^::"^z'^ m 



(59) 



(60) 



p g C2m - Bm 



Quoting from Xeumami (1-19526, page 265): "Just 

 as the (juantity C'((3) was designated the 'effecti\'e fric- 

 tion factor' or 'resistance factor' for the wind friction on 

 the sea surface, so the dimensionless quantity B(fi) is 

 named the 'effective dissipation factor' for the turbulent 

 wave motion. The difference between the two repre- 

 sents the 'effective energy factor' for the whipping-up 

 of the wave motion." 



9 Final Results 



For the remaining part of the discussion the reader is 

 referred to the original paper, Neumann (1-19525). 

 Suffice it to say here that by numerical integration the 



8 10 12 14 IG 18 20 

 Wind speed U in m/sec 



22 24 2G 28 



Fig. 8 Minimum wind duration (in hours) needed for de- 

 velopment of three main wave stages (from Neumann, 

 1952*) 



fetch and the dvuation are obtained as functions of /3 = 

 c/U. The minimum fetch and duration required for the 

 full development of the three "equivalent" wave com- 

 ponents are shown in Figs. 7 and 8. Here |8,„ corresponds 

 to the celerity of the wave of the most frequently occur- 

 ring period. 



Citing an example from Neumann (1-19526, page 

 270): "At a wind speed of 5 m/.sec a .sea space (fetch) 

 about 14 km long (in the wind direction) and a duration 

 of wind action of 2.25 hr is sufficient for the full develop- 

 ment f)f a complex seaway. At a wind speed of 10 m/sec, 

 it is already 106 km and 8.6 hr. These minimum values 

 rise rapidly with increasing wind strength. In a storm 

 with wind velocity of 20 m/sec the fetch must be at least 

 1050 km or 600 sea miles long, and the wind must last 

 35.6 hr in order to build a fully developed seaway. At 

 24 m/.sec it would be 1800 km or 1000 sea miles and 51.8 

 hr. Observations of storm .seas, which could be applied 

 to verification of these results are very scarce and are 

 very difficult to establish. We find the orders of magni- 

 tude of the computed minimmn \'alues to be completely 

 in agreement with findings of experienced wave ob- 

 servers. So V. Cornish (.see H. Thorade, 1942) estimates 

 the minimum fetch needed for the full development of 

 storm waves at 600 to 1000 sea miles." 



The conditions of seaway at all stages of development 

 are shown in Figs. 1-22 to 25. Here nondimensional 

 ratios are introduced : 



fi = ^igx/V) 



13 = Figt/D 



gH/U^- = Hgx/m 



gH/U^- = fifty U) 



