SEAWAY 



87 



motions and for swell forecasting. The resolution power 

 of the instrumentation used in their measurement and of 

 their spectral analj^sis is not sufficient to descrilie small 

 wavelets by which the sinface of the larger waves is 

 covered. These spectra, therefore, appear to he of 

 doubtful value in problems of energy transfer from wind 

 to waves. This transfer appears to be primarily de- 

 pendent on the small sharp-crested waves. Projects on 

 the measurement and analysis of these small waves are 

 therefore recommended as a prerequisite to imderstand- 

 ing the wa\'e growth under wind action. 



How small is "small" in this comiection is not known 

 now, and it is probable that it is defined not by absolute 

 value but in relation to the total spectrum energy. It 

 appears to the author, howe\'er, that waves in the gra\'ity 

 range are involved here, and one should not artntrarily 

 identify "small" waves with capillary waves. 



A study of properties of the high-frccjuencj' end of the 

 wave spectrum by Phillips (1958) can be mentioned as 

 an example. The prospective investigator should be 

 warned that the facet \-elocity of small waves depends 

 not on their properties alone, but on the whole wave 

 spectrum. Longuet-Higgins' (1956, 1957) papers can be 

 used for defining the facet \'elocity in any spectrum. 

 It also should be remembered that the very high-fre- 

 quency ends of all of the spectra listed in Section 6 

 represent an extrapolation of the empirical data, and 

 are therefore not relial)le. Pending actual measurement 

 of very high-frequency components of moderate and 

 high seas, it is suggested that hypothetical spectra be 

 used in theoretical studies. These would be composed of 

 the spectra listed in Section 6 with the high-frequency 

 ends replaced by Phillips' (1958) formulation. As sub- 

 projects under the foregoing, the following can be 

 listed : 



(a) Measurements of the very high-frequency end of 

 the spectra by auxiliary instrumentation at the time the 

 usual wave measurements are made. In particular, the 

 small wavelets can be measured with I'espect to a fairly 

 large buoy riding on larger sea wa\'es which in turn are 

 recorded b}' accelerometers. 



(b) ^'erification of Phillips' (1958) formulation by ap- 

 plication to Cox and Munk's, Section 4..", and Schooley's 

 (1958) wave slope spectra. 



(c) Carrying out preliminary work on the wind-energy 

 transfer to waves using spectra as indicated in project 

 (14-6) but with a hypothetical spectrum possessing 

 Phillips' high-freiiuency extension. 



34 Transformation of Small Waves into Large Ones. 

 In the development of waves under the action of the 

 wind there appears to exist a perpetual change from 

 small waves to large ones. Sverdrup and Mimk and 

 Neumann (prespectrum) have shown that waves must 

 grow in length in abs(_irl)ing the wind energy since they 

 cannot grow indefinitely in height. The detail mecha- 

 nism by which the small waves are transformed into large 

 ones is, however, not known. Efforts to formulate and 

 to demonstrate a suitable theory arc recommended. 



The energy transfer from wind appears to depend on 



the action of small waves. In comparison with these, 

 the long waves of moderate sharpness and approximately 

 trochoidal form have \'ery small abilit.y to absorb wind 

 energy. The theory of large-wave growth must ap- 

 parently depend on understanding the processes by 

 which the wind energy absorbed by small sharp-crested 

 waves is transformed into the energy finally appearing in 

 large waves. 



The reverse problem also has been observed in towing 

 tanks. Sometimes an apparently i-egular wave train, 

 after running through a certain distance, is transformed 

 into an irregular wave pattern containing components of 

 much higher freciuency than the original waves. 



35 Manuals of Applied Mathematical Statistics. The 

 introduction of spectral tlescriptions of waves and ship 

 motions brings about the need for knowledge of mathe- 

 matical statistics. It can hardly be expected that prac- 

 tical oceanographers, ships' officers, and naval architects 

 will have the time and preparation foi- a profound study 

 of this subject. It is recommended, therefore, that 

 short and simple texts on the relevant aspects of mathe- 

 matical statistics be prepared. The text should have 

 direct practical use as an objective, and should avoid 

 theoretical discussions beyond those immediately needed 

 for understanding the practical ])rocedures. Tho.se en- 

 gaged in research refjuiring a deeper theoretical insight 

 would be directed to the many existing textbooks and 

 articles on a higher mathematical level. The notation 

 and expressions familiar to oceanographers and naval 

 architects should be used as far as possible, and the un- 

 familiar terminology of the specialized statistical texts 

 should be avoided. The text should preferably be ar- 

 ranged in a graded form, starting with the simplest pos- 

 sible use of mathematical statistics in oceanographers' 

 and naval architects' pi'oblcms, and progressing to the 

 more elaborate ones. 



36 Provision of Recording and Analyzing Facilities. 

 The practical application of the spectral C(jncepts of the 

 sea surface reciuires widespread use of suitable recording 

 and analyzing equipment. Heretofore, the work in this 

 field has been carried out only on a pilot-research basis, 

 making use of the few a\-ailable computing centers and 

 often resorting to tedious manual measurements of 

 various records. Significant progress in practical utiliza- 

 tion of the modern irregular-sea concepts depends to a 

 large extent on widespread availability of suitable re- 

 cording and analyzing equipment. The need for .ship- 

 borne equipment has already been mentioned under 

 project (26). Suitable e(iuipment also must be made 

 available to experimenters in wind flumes, towing tanks, 

 and oceanographic institutions. It is often impractical 

 to develop the necessary instrumentation at each in- 

 dividual establishment because of the lack of specialized 

 knowledge and because of the cost involved. There is 

 also the danger that heterogeneity of the methods and of 

 the forms of reported results will hinder progress. It is, 

 therefore, recommended that steps to develop and make 

 available suitable instrumentation be taken by the 

 proper professional organizations singly or jointly. If 



