TM Wo. 377 



Most obvious is the fact that there is information in the spectrum range up to 

 1000 mcps (and possibly higher) which is apparently filtered in the CERC spectrum 

 analysis procedure. 



As noted in chapter IV, two CERC wave records were obtained and processed 

 digitally, producing the spectra WS-15 and WS-16 in appendix B. These spectra 

 appear quite similar to the wave motion spectra, mainly because of the increase 

 in frequency range up to 2500 mcps. 



An 0MDUM III record (BBELS-lU, serial 106, 3-0 m i) made on 8 June 1965 at 

 1^57-1501 was compared to the wave staff record WS-15 made at l600-l6lO. The 

 auto-spectra are shown in figure V-19, where ^>*j (cm^ sec~l) and ^-^ (cm^ sec) 

 are plotted on the same ordinate scale. The spectra up to 500 mcps (2-second 

 period) are very similar. The <$ w appears to decrease much faster than the g^ 

 function from 500 to 1200 mcps. Since the 0MDUM III w(t) record was made at a 

 depth of 3.0 meters, the accompanying attenuation of high frequencies with depth 

 is undoubtedly reflected in the spectrum. Beyond this, C^ seems to whiten and 

 remain constant. The peaks at 250 mcps (U sec) stand out, and even the small peak 

 at 50 mcps is comparable in the two spectra. Since two different quantities are 

 being compared, not much can be concluded regarding the relative slopes of the 

 two spectral densities. 



True similarities between the auto-spectra of free surface wave records and 

 wave particle motion records could best be identified if a record of w(t) made 

 very near the surface were available for comparison. This is because of the 

 strong damping of the high frequency surface motions with depth. The wave staff 

 can detect high frequency motions (the limiting frequency being the natural 

 response of the wave staff detector and recorder) which are completely "raw" and 

 unfiltered; whereas the wave meter lying beneath the free surface detects motions 

 which are subjected to a "low pass" filter that increases exponentially with depth. 

 Unfortunately, no near-surface w(t) records were made near the time of the WS-15 

 and WS-16 records. However, the long period, low frequency motions do appear 

 similarly represented by each spectrum in figure V-19, which indicates a certain 

 similarity between wave particle motions and free surface motions. 



Vertical Distribution of Wave Energ; 



The classical theory of surface wave motion predicts that the amplitude, 

 velocity, and acceleration of particles in surface waves all decrease rapidly 

 with depth. The decrease of motion is exponential in nature. This is demon- 

 strated by equations (il-^) through (11-12), which apply for the cases of short 

 and intermediate waves . 



The experiences of divers and submariners attests to this attenuation of 

 surface wave motion with depth. There is, however, little quantitative evidence. 

 An excellent discussion of this matter is presented by Wiegal (196U). In con- 

 sidering the engineering aspects of wave forces on submerged objects, Wiegal 

 presents studies and data regarding the attenuation of wave pressure forces 

 determined both in the laboratory and in situ. 



112 



