86 



THEORY OF SEAKEEPING 



and must be of the type permitting mass analj^sis with 

 the minimum of labor. The \'arialMHty of sea conditions 

 indicates that simphcity of data collecting and analyzing 

 far outweighs the desire for extreme accuracy. In par- 

 ticular, the wave-energy distribution can be measured in 

 ordy a few discrete directions. Gelci, Casal6, and Vassal 

 expressed the mean directional spectrum by only two 

 bands, Section 8.72. 



29 Pending the collection of a sufficient amount of 

 new wave measurements, the Material Used for Spec- 

 trum Formulation in the Past Should be Re-examined. 

 In particular the following two projects can be suggested: 



(a) The shape of Neumann's, Section 6.2, spectrum 

 was obtained by intuiti\'e analysis f)f a few wave records 

 (see legend in Fig. 36). A formal spectral analysis of 

 these records is recommended. In particular, this would 

 help to clarify the evaluation of the constant C in 

 Neumann's spectrum formulation, Section 6.23. 



(6) Darbyshire's (1955), Section 6.11, wave data 

 represent the only large collection of open-ocean instru- 

 mental wa\'e measiuements a\ailable to date. Re- 

 examination of this material is recommended with par- 

 ticular regard to (i) verifying wind velocity over relevant 

 fetches by re-examining meteorological conditions; (ii) 

 including the necessary (theoretical) corrections of 

 Tucker's gage indications, particularly for high-frecjuency 

 waves; (iii) making independent spectral analyses, and 

 (iv) experimenting with replacement of Darbyshire's 

 empirical formula by alternate, possibly more sophisti- 

 cated, formulations. In particular it is desired to bring 

 out more clearly the effects of fetch length and of wind 

 duration. Also, it is desirable to establish the spectrum 

 form for a sea in the development stage, following the 

 example of Gelci, Casale, and Vassal (Sections 6.3 and 

 6.4; Fig. 45). 



30 The collection and analysis of open-ocean data 

 suggested in project 22) probably will take considerable 

 time. Meantime appreciable progress can be made by 

 Spectral Analysis of Observations in Restricted Water 

 Areas of various sizes and at \'arious wind velocities, 

 project 14). A particular oljjective of this analysis 

 would be to find out if the constant defining the spectrum 

 area is truly a constant or whether it depends on other 

 fact(jrs, particularly on "wave age" (i.e., the ratio of 

 predominating wave celerity to wind velocity), verifying 

 the conjecture made by the author in the fourth para- 

 graph of Section 6.23. 



31 Development of Descriptive Wave Spectra, Sec- 

 tion 6.6 The dcwlopmcnt of a compact description of a 

 sea surface is recommended. This should be suitable for 

 ship-motion analysis or prediction. It appears that a 

 three-parameter definition indicative of the wave height, 

 wave period, and sea irregularity can be useful. Such 

 a definition was given by \'oznessen.sky and Firsoff's 

 spectrum. Section 6.6. Additional work connected with 

 it may consist of 



(a) Evaluation of the three parameters for certain 

 spectra of measured waves at sea, such as, for instance, 

 Walden and Farmer's, Section 6.53(5). Attention 



should be called to the fact that the spectrum in this 

 case describes an observed sea which is usually generated 

 by many separate causes. This spectrum therefore is 

 basically different from the spectra based on wind veloc- 

 ity and a specified simple fetch and duration. In 

 particular, the descriptive spectrum must have flexibility 

 in specifying the dominant wave period. 



{b) Preparation of a photographic album of various 

 spectrally analyzed .sea conditions for guidance in visual 

 sea observations.^' The photographs can be labeled 

 and classified by the three ^'oznes.sensky and Firsoff 

 parameters. 



(c) Establishing relationships among the actual spec- 

 trum of waves, the ^'oznessensky and Firsoff three-pa- 

 rameter spectrum, simple measurements of wave heights 

 and periods on a wave record, and the visually observed 

 significant wave height and period. This can be ac- 

 complished by theoretical considerations based on 

 mathematical statistics, in conjunction with the spectral 

 evaluation of wave records (in subprojects a and b). 

 The primary objective of this project is to enlarge the 

 collection of wave data reducible to spectral presenta- 

 tion, which is needed in the prediction of ship motions. 



(d) A special study to bring out the physical signifi- 

 cance of the sea irregularity parameter a in Voznessen- 

 sky and Firsoff's formulation. There is some evidence 

 that in a "young sea" (large U/c) both the scalar spec- 

 trum and the directional energy distribution are broader 

 than in the case of a fully developed sea. This observa- 

 tion apparently permits the grouping of period irregular- 

 ity and of short-crestedness under one parameter. The 

 foregoing is a conjecture, however, and the subject must 

 be investigated. 



32 Synoptic Wave Data. Collection of ocean-wave 

 data on a .synoptic basis is needed and is sure to come 

 with time. A compact (and at the same time significant) 

 method of reporting the wa\'e data must be developed. 

 To describe a complete spectrum a large number of 

 ordinates must be reported. Any number of discrete 

 ordinates will create uncertainty because the spectral 

 form resulting from a computational procedure is usually 

 irregular. Furthermore classifying a large number of 

 reported spectra presents a problem. It does not ap- 

 pear to the author that it will be practical to report the 

 complete spectra. The spectrum forms most often ob- 

 served may be reported with sufficient accuracy by the 

 three Voznessensky and Firsoff parameters which also 

 provide a simple means of wave classification. The less 

 fieciuent two-maxima spectra can be approximated by 

 superposition of two simple spectra; i.e., by a total of six 

 numbers. This demonstrates a possible approach. 

 A broad study of the problem is recommended. 



33 Spectra of Very High-Frequency Wave Com- 

 ponents. The spectra discussed in Section 6 are macro- 

 scopic descriptions of sea waves. They give information 

 on waves sufficientlv long to be significant for ship 



" This idea of a photographir album was advanced at the 

 August 6 and 7, 1958 meeting of the .Seakeeping Characteristics 

 Panel of SNAME. 



