TM No. 377 



closely follows the variation in wind speed, which has decreased from 12 m sec 

 at 1800 hours to U.9 m sec at 2^00 hours. Note that at the point of minimum 0.5 

 meter variance (373 cm^ sec~2 at 0kk5) , the wind has freshened to about 9 m sec"l 

 but is from the west. Waves generated by this wind are directly opposed to wa\ r es 

 generated by winds only h hours earlier. The minimum variance is clearly asso- 

 ciated with this wind shift. From 0815 to 11^5 hours on 30 March, the 0.5 meter 

 and 2.0 meter variances begin to increase. Starting at 2^-00 hours, the wind speed 

 steadily increased to 12 m sec - -'- by 1300 hours. 



Thus, there is a plausible correlation between the wind velocity and the 

 statistics of wave motions at BBELS. However, a word of caution regarding the 

 quantitative evaluation of the variances and the amplitudes of the auto-spectral 

 functions. It has been shown that the amplitude of the wave motions falls off 

 exponentially with depth, and that the attenuation is strongest for the higher 

 frequencies. In view of this, relatively small errors (of 10-15 cm) in the depth 

 positioning of the wave meter could produce relatively large errors in the variances 

 and perhaps bias the spectrum. The BBELS tide range is about 90 cm. Therefore, for 

 long time measurements at a "fixed" depth, the wave meter must be adjusted as the 

 tide rises and falls. This was attempted during the BBELS-11 series; however, it 

 was a relatively crude adjustment and some inaccuracy in the Gui "** estimates may 

 have resulted. The maximum depth error is estimated at about 10 cm. This error, 

 according to the variance attenuation curves in figures V-20 and V-2U, is equiva- 

 lent to a 10-15 percent error in the variance. This effect could not be respon- 

 sible for the gross variance changes at a given depth shown in figure V-3^-. Truly, 

 these observations show real energy changes in the wind- wave regime. 



Equilibrium Range of Wave Spectra 



It has been suggested that because of wave energy inter-relationships, the 

 auto-spectra of the free surface elevation c£~ should display, at some specific 

 region of the spectrum, a functional relationship with frequency (see Phillips, 

 1958). This region of the spectrum is termed the "equilibrium range" because 

 wave motions associated with frequencies in the range are saturated; i.e., they 

 can hold no more wind-derived energy, hence there occurs a continuous outflow of 

 spectral energy in this region. It is believed that this saturation occurs 

 because the physical characteristics of the water limit the slope and height 

 (and, therefore, the potential energy) of waves of a particular frequency. 



■ ■ Consider the behavior of the energy spectrum Qy* for relatively high 

 frequencies. The physical parameters governing behavior of the spectrum in the 

 higher frequency ranges and those governing the surface stability must be 

 gravity -g, wind speed v, and some roughness parameter as l57*- to govern the 

 gross form drag of the waves. However, for the limiting stable configuration of 

 the wave profile, the acceleration of a particle at the wave crest is -g. Using 

 the dimensional relationships of Bridgman (1956), let us consider a possible 

 functional relationship of the free surface spectra <^5<» with the frequency. 



By definition (see chapter III): 



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