UNCLASSIFIED TM No. 377 



It is of interest to examine (as Kinsman did) the amplitude distribution of 

 wave velocity components measured with the wave meters. The relationship of the 

 probability distribution of wave velocity components may indicate some interesting 

 assymetric or nonlinear characteristics of the wave motions. Further, it Is well 

 to determine the approximate distributions of the wave meter data, since strong 

 deviations from Gaussian (e.g., extremely lopsided distributions) would tend to 

 detract from the physical meaning of the variance and its associated spectra. 



Before looking at the velocity sample distribution, let us examine a free 

 surface distribution from a record of v\ (t) made with the CERC wave staff (discussed 

 in chapter IV ) mounted on BBELS. The record was made on 9 June 1965 from 0000 to 

 0006 hours. During this period the wind velocity was 7 m sec"- 1 - from the SSW. A 

 copy of the original analog record was obtained and digitized at 0.2- second 

 intervals using the NUWS Telerecordex film reader . For the sample, N = 1805, the 

 mean <p = 375 cm, and the variance O^n 2 = 5l6 cm.2, giving a standard deviation 

 O^l =22.7 cm. 



The histogram sort of values of fl at 1 cm increments Is shown in the upper 

 plot of figure V-7» The ordinate is proportional to the number of values N or 

 percent of population of "y which occurred within each height interval designated 

 on the abscissa. The general pattern of the distribution appears roughly symmetrical 

 about the mean. A closer look indicates, however, that the upper side (above 375 cm) 

 falls below the Gaussian, whereas the lower side (below 375 cm) may fall above it. 



The best way to examine the distribution is to follow a procedure used by 

 Kinsman (i960). This analysis entails a l/2 0<fy frequency sort of the data. 

 Figure V-7 (lower plot) shows the percentage of population within l/2 O^ intervals. 

 The solid curve is the classical Gaussian distribution curve. The broken line 

 connecting the circles serves only to suggest the actual on distribution. The 

 experimental curve is similar to the Gaussian, although the curve tends to fall 

 below the Gaussian on the lower side and is skewed toward higher values near the 

 peak. 



In figure V-8 the frequency distribution of the wave heights is expressed as 

 a cumulative percent ordinate versus the excursion from the zero (mean 'n ) wave 

 height in units of standard deviation Oy . The straight line entered is the 

 Gaussian. From these plots it would appear that this wave record, like those of 

 Kinsman (i960), is substantially Gaussian except for skewing toward the extreme 

 values. 



Turning now to some velocity data distributions; figure V-9 (upper plot) 

 shows a frequency sort of the vertical velocity values w from serial 057 (BBELS -11, 

 C5 m X)« For this sample N = 2088 and Ow = 3^.6 cm sec -1 . The distribution 

 appears to be bi-modal, with the peaks occurring symmetrically at about ± 15-20 cm 

 sec - -'-. The lower plot in figure V-9 compares the overall distribution with the 

 Gaussian. The experimental curve (broken lines) seems to be somewhat over-populated 

 at the ± 0-1 GZi values. This effect may be caused by the peaks in the actual data 

 histogram (upper plot). Figure V-10 is the cumulative frequency plot of the w 

 velocity distribution shown in figure V-9. The behavior closely follows the 

 Gaussian (straight line) except for higher positive velocity values. 



103 



