80 



THEORY OF SEAKEEPING 



For a fully arisen sea 



fiT) = 209 T' if r < 0.315C/ 



'f{T) = 209 r^exp [-329(7'/L^ -0.315) = ] 



if T > 0.315 U (150) 



where the component wave period, T. is in seconds, and 

 the grovuid wind velocity' U is in knots. The spectral 

 density E{T, d) is in ergs per cm= per sec. 



8.73 Present work. There are, at present, two known 

 attempts to provide further information on the direc- 

 tional-wave spectrum. The Woods Hole Oceanographic 

 Institution is using Barber's method 1, that of a rotating- 

 line array, affixed to a tower in Buzzards Bay. The ob- 

 ject is to learn more of the characteristics of the direc- 

 tional operator. In addition similar measurements az-e 

 planned for a fixed tower offshore in relatively deep 

 water. Here, open-.sea wa\'es are available, and in addi- 

 tion to measuring the direction of wave propagation, it 

 is hoped to learn something of the scaling properties be- 

 tween small and large waves in order to determine 

 whether sheltered waterways, generating relati\'ely small 

 seas, are natural test facilities for ship models. 



At the Scripps Institution of Oceanography, swell 

 waves are measured at two points near the California 

 coast. The swell spectra result from waves tra^'eling 

 several thousand miles from the generating areas in the 

 South Pacific. Additional detectors are planned for in- 

 stallation along the route of wave propagation to study 

 further the angular decomposition of waves and their dis- 

 persive characteristics as well. Trade-wand effects on 

 wave attenuation are of special interest in this work. 



8.74 Summary of directional spectrum. Only three 

 estimates of the directional distribution of open sea 

 waves are available to date : 



1 Arthur's (1949) derivation and measurements, in- 

 terpreted bj^ St. Denis and Pierson as the cos-S law. 



2 Gelci, Cazale, and "S'assal's (1957) evaluation from 

 swell observations. The rough estimate of the direc- 

 tional energy distribution is given by equation (149). 



3 SWOP project's (Chase, et al, 1957); a directional 

 function is gi-\'en by equation (146). 



Gelci, Cazale, and A'a.ssars evaluation appears to be 

 the only one based on statistics of many observations 

 over a period of se\'eral years. Since it is based on 

 swells arriving from a distance, it can be expected to be 

 deficient in high-frequency components. 



There is no reason to expect a uniform directional 

 spread of wave energies in different conditions at sea. 

 Eckart (see Section 4.1) indicates that directional spread 

 depends on the observer's position in the generating area. 

 Project SWOP indicated a broader .spread for high fre- 

 quencies and a narrower one for low frequencies. On 

 this basis a plausible hypothesis can be made that a 

 "j^oung sea" with large ratio of wind speed to wave 

 celerity, U/c, will have a broad directional spread and 

 that as U/c ratio decreases, the directional spread will 

 become narrow. 



9 Research Suggestions 



It is hoped that ideas for further research will stem 

 primarily from exposition of the shortcomings of the 

 existing knowledge which were emphasized throughout 

 the pre\ious text. Generally speaking, two parallel 

 directions of research must be pursued: 



(a) Development of semi-empirical methods. 



(6) A long-range development of rational methods. 



A large amount of ob.servations of natural phenomena 

 and simulative experimentation is needed to form the 

 basis for the first, and to give orientation to the second, 

 as well as to provide the data for verification of theo- 

 retical methods. 



The description of a sea surface by a spectrum has been 

 the most valuable practical achievement of the last 

 decade. Through its use great steps have been made in 

 understanding a ship's behavior in the natural (always 

 irregular) seaway. The discussion of energy Isalance in 

 Section 3, and the work of ]Munk, Section 4.4, and Phil- 

 lips, Section 4.2, have also indicated that a spectral con- 

 cept of the seaway is necessary in de\-eloping a rational 

 theory of wave growth. 



In discussing spectra a distinction should be made be- 

 tween 



A Spectra defining waves as a function of meteorologi- 

 cal conditions. 



B Spectra defining the sea state at a given time and 

 place, regardless of its causes. 



Descriptive spectra B are needed because an observer 

 on board a ship rarelj' has the information to determme 

 spectra A. Usually, rather tedious work is required of a 

 meteorologist before the wa^■es can be forecast and there 

 is considerable uncertainty in this process. Although 

 spectra A are needed for forecasting waves, they are not 

 suitable for describing an observed seaway because a sea 

 state is .seldom defined by the simple wind conditions as- 

 smned in deriving these spectra. 



9.1 Development of Semi-Empirical Methods. At the 

 time of this writing there are four spectra formulations of 

 Tvpe A based on independent observations. The}' dif- 

 fer widely both in the indicated rate of wa\-e gi'owth and 

 in the ultimate spectrum of fully arisen sea. Each spec- 

 trum is an empirical evaluation of the observed data 

 available to the particular researchers. Often extrap- 

 olation is resorted to, to eke out insufficient data. The 

 demonstrated discrepancies between the different spec- 

 tra ai'e evidence that a large amount of additional ob- 

 servations is needed. 



The magnitude of the discrepancies, however, make it 

 improbable that a uniA'ersally valid spectrum formula- 

 tion can be arrived at hy the purely data-fitting tech- 

 nic|ue which has been used heretofore. The ^'arious con- 

 ditions under which the wave data were measured must 

 be given more consideration, and, inasmuch as possible, 

 (juantitatively appraised. The three separate param- 

 eters used now, wind velocity', fetch, and duration, do 

 not appear to be adecjuate for une(iui\'ocal spectrum 

 definition. A search must be made for other possible 



