UNCLASSIFIED TM Wo. 377 



The auto-spectra provide the best illustration of the depth attenuation of 

 wave motions. Figure V-21A shows the composite auto-spectra ^uj f° r four depths 

 (series A) as a function of frequency (mcps). The time of the start of each 

 observation is given next to the depth value. This family of four curves clearly 

 demonstrates the attenuation of the wave motion with depth. The curve for zero 

 meters (wave trough level) shows a strong peak at about 250 mcps (h sec), which 

 is undoubtedly associated with the wind waves. This is followed by a sharp 

 attenuation to about 1000 mcps (l sec). Beyond this point the energy tends to 

 flatten out and fluctuate up to the Nyquist frequency (2500 mcps). 



The characteristic curves form a family showing strong but unequal attenua- 

 tion at all frequencies. There is a distinct "reddening" with depth of the 

 dominant peak of each curve; e.g., the peak shifts from 250 mcps (h sec) at the 

 surface to about 150 mcps (6.6 sec) at a depth of k meters. This illustrates the 

 "low pass filter" effect mentioned earlier in this chapter. 



Irregularities in the spectral curve occur in the higher frequency range 

 (beyond 750 mcps), particularly at the 4-meter depth. These fluctuations of the 

 spectral density at high frequencies are less meaningful than at lower frequencies, 

 and could be caused by "noise" inherent in the spectrum computations and highly 

 magnified in the logarithmic presentation. 



Figure V-21B shows the spectra of the horizontal component u for series A of 

 BBELS-5. There is a striking difference between the two functions $u, and ^u, . 

 The (3^ function indicates a marked decrease of energy below 1000 mcps (compared 

 t° $\*j )• Again, however, there is strong attenuation at all frequencies, 

 except below 200 mcps at depths of 2.0, 1.0, -iacd '0.0 meters. The strongest 

 decrease in spectral density occurs between 0.0 and 1.0 meter, and between 2.0 and 

 4.0 meters. The 0.0 meter curve clearly displays two peaks - at 100 mcps (10 sec), 

 and at about 400 mcps (2.5 sec). The other three curves indicate the same low 

 frequency peak at 100 mcps, but the secondary peak (strongly attenuated) is 

 evident only at 1.0 meter depth. 



Figure V-22A shows the vertical velocity spectra for series B taken between 

 1305 and 1333. The 4.0 meter curve from series A is repeated, since (for 

 convenience) it is considered timewise to be the end of series A and the beginning 

 of series B. Here again is a clear indication that the spectral energy at all 

 frequencies shows a strong attenuation with depth. 



Comparison of figure V-21A with V-22A indicates strong similarities between 

 the spectral functions at any given depth. Specifically, the curves for 0.0 m I 

 and 0.0 m II show remarkable similarity, with the major peak at 250 mcps (4 sec) 

 and similarly located minor peaks at 1100 mcps and 2000 mcps. 



The curves for the function ^y, of series B (figure V-22B) again show peak 

 values that are much smaller than those for the corresponding vertical velocity 

 spectra <^tu . The 0.0 m II curve displays a double peak (similar to that of the 

 0.0 m I curve in series A), one peak occurring at 200 mcps and one at 350 mcps. 

 Also, there is a similar sharp decrease in energy, at the higher frequencies, 



114 



