SEAWAY 



55 



I = Mittelwert 



kn 



Bft. 



7 24 Beob. 



4-Skn 

 2 Bft 

 4247 Beob. 

 I 



L 



1-3 kn 

 1 Bf + 

 1254 Beob. 



7-10 kn 

 3 Bft 

 8629 Beob. 



1-15 kn 

 4 Bft 

 3,519 Beob. 



22- 27 kn 



6 Bft 

 11,920 Beob. 



/-'^^ 



41-47 kn 



9 Bft 

 974 Beob. 



20 



10 







46-55kn 

 10 Bft 

 42G Beob. 



IT-TI H-n J. 



SS-S3 kn 



II Bft 



III Beob. 



.■^nJ^Lfln n 



15m 



Wellenhbhe - 



15m 



Fig. 62 Waves at different wind speeds. Frequency distribu- 

 tion of ten weather-ships' observations in Atlantic Ocean 

 (from Roll, 195 5) 



queucy co of this \va\'t' 



„. ^. In the case of an irregular .sea it 



appears to bear a relationship to the mean \va\'e fre- 

 quency. 



The spectrum obtained from e(|uation (lOo) l.)y a 

 Fourier transform (.see Section 8) is 



E(c. 



2E (oj- -I- a'- + li') 

 — "-rr. -. - 



TV (oj — a 



n + 4«^ 



(lO-t) 



The parameters a and (3 were e\'aluated on the basis of 

 analyses of numerous records made in 1951-1952 in the 

 Barrents Sea using a \va\'e-measuring buoy. Individual 

 records contained on the a\'erage 400 waves. The 

 parameters were found to be functions Jo 3i\% wave height. 

 They are shown in I''ig. fi(i plotted aganjis average wave 

 height. 



Voznessensky and Firsoff have thus defined a sea 

 spectrum in terms of the parameters E, li, and a. These 

 parameters correspond to the spectrum characteristics 

 most important in defining ship motions; namely, wave 

 height, frequency at the maximum of the spectral 



density cia-\e, and degree of sea irregularity respectively. 

 The spectrum was deri\'ed on the basis of instrumentally 

 measured and analyzed waves l)ut the definitions can bo 

 useful in connection with visual observations or (pref- 

 erably) visual inspection of wave records. The mean 



apparent period T of the Ava\-es can Ije estimated either 

 by visual observations or by inspection of wave records. 

 A small amount of additional research may estalilish the 

 (juantitative connection between the oliserved frequen- 

 cies and the parameter i3. Likewise, a measure of the sea 

 irregularity can be de\'ised on the basis of which the pa- 

 rameter a can be e\'aluated. Thus a three-parameter de- 

 scription fif an ol)ser\-ed sea .spectrum can be developed 

 for use by ships' personnel, particularly aboai'd weather 

 ships. 



The al)o\'e remarks should not be construed as recom- 

 mending visual observations. It is highly desirable that 

 ship-borne wave recorders be used on all weather shijis. 

 It is also desirable that shipboard anah'zing eciuipment be 

 prf)vided. However, with Voznessensky and Firsoff's 

 method there is a possibilit.y that, after a small amount 

 of additional research, results of visual wave observa- 

 tions, of visual examination of wave records, and of 

 spectral analysis of wave records can be presented in the 

 same spectral form. The method pro\ides therefore the 

 possibility of collecting spectral sea data on a broader 

 scale than heretofore. 



7 Statistics of Directly Observable Sea Waves 



Three stages are discernible in the observation and 

 study of sea waves, the first, A'isual observation with a 

 stop watch as the only instrument, the second, instru- 

 mental recording of wave ele\'ations, and the third, the 

 de\-elopment of spectral analysis technif|ues. 41ie con- 

 cept of a wave spectrum and the formulations of various 

 spectra were discussed in Section (i. Methods of evaluat- 

 ing spectra from wave records and \-arious mathematical 

 problems arising in this process will l)e discussed in Sec- 

 tion 8. The present .section will be concerned with the 

 handling of data obtained in the first two stages prior to 

 the emergence of the third. The older methods are by no 

 means superseded by the spectral techniques; all are be- 

 ing currently u.sed for different purposes. 



The great bulk of past wave data has been obtainetl by 

 visual observation. Instrumental recordings until re- 

 cently were obtained from pressure recorders located at 

 appreciable depth near shore. The only in.strumental 

 wave recordings in the open sea a\-ailalile at present are 

 those of Darbyshire (1956) and of Walden and Farmer 

 (1957). The same form of simple statistical analysis has 

 been used for the \'isual observations as for the instru- 

 mental recordings. Fig. 61 shows a section of a long 

 record of irregular sea waves. The record is clearly not 

 sinusoidal, but one can nevertheless speak of the time in- 

 tervals between successive crests as "apparent periods," 

 designated as T in order to distinguish them from the 

 true period T of a sinu.soidal wa\'e. Likewise, the A'erti- 

 cal distance from a trough to the neighboring peak is 



