SEAWAY 



59 



liiiiitcil way. 'I'lic liasic pr(il)lt'in is tn dcliiic that particu- 

 lar seaway t'rdin whicli this "sample" record was oh- 

 taiiied. 



This record is only one of many samples which mij^ht 

 have been taken from the population which is that iiar- 

 ticular seaway. Other records of the same length, taken 

 at other times and other places, will in general yield, if 

 long enough, the same information on the state of the sea, 

 pro\'ided the seaway retains its statistical homogeneity 

 throughout the sample space and time; that is, remains 

 stationary. 



The sample record is then seen to he one meml)er of a 

 large family of possililc sample records. It may he 

 thought of as a single function in an ensemble of func- 

 tions. If in addition to being stationary and random 

 (stochastic), the sea surface is CJaus.sian as well (that is, 

 points read at random from the sample record are dis- 

 tributed according to the normal ])rohai)ility law), then 

 the sample record li'ntls itself to c()in]jutati(m of certain 

 statistical quantities. An impi)rtant property of .such 

 ensemble functions is given by the Ergodic theorem, for 

 stationary Gaussian processes, whicli states that time 

 and space analyses yield the same statistical properties as 

 an ensemble analysis. In other words, // the seaumij in 

 stationary and random and, Gaussian then analijds of a 

 long eno'ugh sample record from this sea surface may de- 

 fine {statistically) the seaway for all lime and space where 

 these assumpti(ms apply. This is what is desired in most 

 expositions relating to the seaway. One sacrifices de- 

 terminism for the statistical properties of one member 

 (record) of an ensemble of functions which, if it describes 

 the average statistical properties of that ensemble, is a 

 good description of the parent pojiulation (seaway) from 

 which the original .sam]jle was drawn. 



Ocean waves are obser\-ed to be random in that they 

 are, in general, unpredictable .space and/or time-wise. 

 Analysis of \va\'e elevations chosen at I'andom from many 

 different wave records has shown a high percentage of 

 freciuency di.stributions which conform well to the normal 

 probability (Gaussian) law. This permits the computa- 

 tion of certain statistical quantities which describe the 

 distribution of wave heights in the seaway from which 

 the particular .sample (record) was taken. (See Section 

 8.6). Stationariness is somewhat arbitrary and u.sually 

 is based on the appearance of the record. If the waves 

 are not obviously growing or decaying during the record- 

 ing period, the seaway is considered to be stationary for 

 that interval of time. 



The treatment of wave data is independent of the con- 

 ditions just mentioned. Howe\'er, interpretation of the 

 results depends verj' much on the assumptions that the 

 data are stationary, Gaussian, antl that only a relatively 

 narrow range of wave frecjuencies is involved. Justifi- 

 cation for results of wave analysis is on the u.ser of the re- 

 sults and not on the experimental data or on the meth- 

 ods of analysis. The fact that the complexity of waves 

 forces stati.stical treatment does not, however, relieve 

 one of the responsibility of exercising good judgment in 

 the experimental design of wave analysis. 



The ti)iil most applicable to I'ealization of a probabilis- 

 tic definition of wa\'es is the energy spectrum of the sea 

 •surface. This is essentially an analysis of the' variance, 

 or second moment property of the record of the seaway. 

 Some of the .seaway statistics derivable from such an 

 analysis were given in Section 7; more will lie di.scu.s.sed 

 in this .section. 



At this stage tiien, determinism has been abandoned 

 (at least tempoi'arily) for probaljility methods, antl the 

 key to a statistical tlescription of ocean waves is fomid to 

 be the energy spectrum, because it may yield the kind of 

 information desired of this stationary, random jDrocess. 



As has l>een noted, the cjualifications pertaining to the 

 process ha\-e no hearing on computation of the spectrum 

 but relate only to the .statistics derivable from the spec- 

 trum. In this connection, the applicability of such 

 terms as stationary and Gaussian are somewhat arl )it rary. 

 It is generally agreed that "nearly stationary" and 

 "nearly Gaussian" conditions are acceptable a.s.sump- 

 tions, but the.se again are somewhat arbiti-aiy and will 

 bear further discussion later on. 



Section 6 has already mtroduced the reader to \arious 

 attempts at an analytical formulation of a one-parameter 

 family of spectra that is rejjresentative of the sea surface, 

 under any conditions. Which particular formulation is 

 the best is still open to question. The problem however 

 is being investigated \'igorously by a number of ocean- 

 ographers and although some of these are quite adamant 

 in their particular l)eliefs, at this time, basic differences 

 in their spectrum formulations are not so great that a 

 mutually acceptable and reasonably reliable spectrum 

 may not be realized at some future time. 



The "empirical-theoretical" spectra discussed in Sec- 

 tion (i are u.seful in that they may describe the state of the 

 sea, if once the time-space \-ariation in the wind field is 

 determined. If the point of wave observation and the 

 date and time are specified, then weather maps are con- 

 sulted for resolution of the wind field and by the care- 

 fully documented work of, for example, Pierson, Neu- 

 mann and James (H),'^ the state of the sea may be de- 

 fined. The importance of this work lies in the fact that 

 it enables prediction treatment of partially developed 

 seas, (slowly) changing seas, and swell originating from 

 distant storms. If the spectrum formulation of Pierson, 

 Neumann, and James is unacceptable to an investigator, 

 their work still permits the adaptation of any other 

 spectrum form gi\'en in Section (i. 



The use of weather maps (spaced 6 hr apart) is still 

 somewhat subjective and it is desirable, for the time be- 

 ing, to be able to estimate the energy spectrum of the 

 seaway from wa\'e records or other suitable measure- 

 ments. This is especially true for full-scale seakeeping 

 trials where the results always relate to the state of the 

 sea. A mechanically observed, computer-deri\'ed state 

 of sea is the only accurate description aA-ailable. As such, 

 it is also u.sed in wave research in attempts to \-erify the 



'• Other sea-state determinations have been given liy Braeehn 

 (1952); Bretschneider (1959)(see ref. p. 105); Gelci, C'azal^, and 

 Vas.sal (1957), and Walden (1958). 



