Pierson 



1 °° 



i(^,0) = 277 "^ Z] [^n(^) c°s n0 + b„(aj) sin n^] . (2) 



n= 1 



It then follows that 



r S(a;, ^) d5 = S(aj) (3) 



and that 



7 



J 



f(aj, 0) d0 = 1 . (4) 



An attempt to describe S(co,0) correctly therefore implies that S(aj) is correct. 

 If spectra estimated from a time history at a point are not correctly described 

 then surely directional spectra estimated from more complete data will not be 

 correctly described. 



The Frequency Spectrum 



The book, Ocean Wave Spectra , describes a wide variety of proposed forms 

 for S(aj) as reviewed and summarized at the Easton Conference on Waves held 

 in 1961. Based on an application of a theory given by Kitaigorodskii (1961), and 

 by means of the results of Moskowitz (1964), Pierson and Moskowitz (1964) have 

 proposed a new form for S(co). It is given by Eq. (5). 



2 -/S(^ya>)^ (5) 



S(-) = ^ e 



where a = 8.10x10"^, /? = 0.74 and co^ = g/u. Here u is the wind speed meas- 

 ured at 19.5 meters above the sea surface. The anemometer that measured u 

 was at this elevation on the ship. 



This spectrum has many features that agree with other proposed spectra 

 and an analysis of the effect of the variation of wind with height has reconciled 

 many of the apparent discrepancies pointed out so strongly at the Easton con- 

 ference. 



[I might add parenthetically that the spectrum proposed by my colleague, 

 Dr. Neumann, is remarkably close to this one for winds near 30 knots. It is, 

 however, seriously off for higher winds, and any design considerations based on 

 the spectrum due to Neumann for high winds should be re-evaluated (see Pierson, 

 1964).] 



As the group to which this paper is addressed does not consist of those 

 working on the problem of forecasting ocean waves, it is important to remark 

 that the above spectral form represents the writer's opinion as to the best pres- 

 ently available description of the frequency spectrum of a fully developed wind 



428 



