TM Ro. 377 



wind waves are recorded in the u direction, but no swell is indicated; whereas 

 the w meter indicates both sea and swell. Since the swell frequencies, which 

 generally occur below 200 mcps, do contribute substantially to the total variance 

 (up to 50 percent in cases of high swell conditions), this directionality aspect 

 could contribute strongly to the inequality of the u and w variances. Also, the 

 relative contribution of swell to the variance increases with depth because of the 

 strong attenuation of the higher frequency wave motions. 



Finally, the disproportion of variances could be partly explained by a 

 diminution of Ot£ caused by the u meter not "seeing" certain horizontal wave 

 components that contain substantial energy but are traveling in off- angle directions, 

 Also, the potential biasing effects of wave-induced motion on the suspended wave 

 meter system cannot be ignored. For it appears that the more stable suspension 

 systems, when coupled with a reduction in drag of the wave meters, do allow more 

 accurate measurements. Further discussion of the angular response of the wave 

 meters with respect to swell and wind waves is given later in this chapter. 



Distributions of Wave Velocity Samples - Workers studying surface elevation 

 statistics have considered the question of the probability distribution of the free 

 surface function 'W (t) at some fixed point in the ocean. Their reasoning is that, 

 if the waves observed are formed by many contributions from unrelated forces and 

 at different times, one can assume that the elements of the Fourier components 

 making up the function 17 (t) are statistically independent. Thus, the distribution 

 should be Gaussian or normal. This assumption has been considered by Pierson (1955): 

 and by Pierson, Reumann and James (1955)? among others. 



The Gaussian time probability distribution is written as: 



27T<7^ 2 - 



where, as usual, "U, 1 is the instantaneous deviation from the mean 0^* . This 

 probability distribution is uniquely determined when the mean and variance of a 

 set of data are known. 



Kinsman (1965), inquiring into the distributions of wave data, presents an 

 analysis of 2k capacitance pole wave measurements made several years earlier 

 (Kinsman, i960). Kinsman made plots of the characteristic frequency distributions 

 from free surface records of1? (t) spaced 0.2 second apart. (This spacing was used 

 because the spectra of the records show no appliable energy at frequencies greater 

 than 2500 mcps; i.e., the Ryquist frequency for the 0.2-second sampling rate.) 

 These distributions showed a positive tail raised slightly above the Gaussian, and 

 a negative tail slightly below. Kinsman saw the skewness toward high values as 

 compatible with the observed fact that the surface waves he measured were net 

 symmetrical, but had relatively longer and flatter troughs and sharper and more 

 peaked crests. However, the overall deviation from a Gaussian distribution was 

 very small. 



102 



