36 



THEORY OF SEAKEEPING 



i|)f 



0^20 



0.10 



o.os 



• Old Visual Obs.(Svcrdrup and MunkjISIl) 

 oHeidberg Obs. wi-th"Young"Sea 

 ®He'idberg Obs. wi+h Swell 



0.01 



Fig. 3 5 Ratio of wave heights to square of apparent wave periods H/T-, as observed 

 with different ratios of apparent wave period to wind speed t\ in generating area (visual 

 observations) (from Neumann, 1953) 



pend on the wind velocity. For example, a 6-second 

 component wave train in a wind generated sea at 5 meters 

 per second wind \-elocit.y certainly has a spectral wave 

 height which is much different from that with a 6-second 

 period wave at 10 meters per second. ..." 



Equation (70) expressing the relation AC> = f(T)dT, 

 is the general expression for a spectrum. The practical 

 solution requires evaluation of the unknown function 

 /(T) ^dhT-/dT. It has been demonstrated by Sverdrup 

 and jMunk, and later by Bretschneider and by Neumann 

 that the relationship H/X = f{c/U) shown by Figs. 18 

 and 19 represents probably the most reliable observable 

 characteristic of significant waves at sea. The relation- 

 ship X = f{c), which is well defined for simple waves, is 

 not known sufficiently well for the "apparent" wa\-e 

 lengths, celerities and periods in a complex seaway. 

 Neumann introduces therefore a plot of the relationship 

 H/f^ versus (f/U), shown on Figs. 35 and 36. The 

 symbol ~ (tilde) placed above a letter designates an 

 "apparent" (meaning a directly observed) quantity in a 

 complex seaway. The first figure is based on the visual 

 observations (presumably of significant wave heights) 

 collected by Sverdrup and IMunk (1947) and made by 

 Neumann (1952a). Here H refers to significant waves. 

 The second figure contains all wave heights, as obtained 

 from the records of a wave gage. In this case individual 

 apparent wa\'es were measured on records as sIioami in 

 Fig. 37. Neumann finds that the straight line (on semi- 

 log paper) 



H/f- = 0.219 exp [-2.4.38 (f/Uy] 



(72) 



well represents the envelope of all observed and recorded 

 data, and accepts it as a basis for evaluation of the 

 spectrum form. Here H is in meters and U in meters per 

 second.-'' 



By putting f- proportional to the apparent wave 

 length, X, the function (72) can be made dimensionally 

 correct 



or 



H/X = (const) exp 



H = (const) 7— exp 



1^1 



2-K U 



9_l 

 2-K U 



(73) 



(74) 



The numerically equivalent expression {g/2Tr)- is sub- 

 stituted in the foregoing for the (dimensional) empirical 

 factor 2.438 (with g = 9.81 mps), U in meters per second 

 (mps). 



The assumption is now made that the foregoing rela- 

 tionship derived for the envelope of the obser\ed ap- 

 parent wa\'es applies to the spectral wave components, 

 and therefore 



25 It is rather unfortunate that Neumann has used dimensional 

 ratios so that any derived constant may he presumed a function 

 of an unknown parameter. 



