TM No. 377 



Figures V-.ll and V-12 (upper graphs) show histogram sorts of serial 055 

 (BBELS-11, 2m V) and serial 038 (BBELS-11, ^m II ) for a 2 cm sec" - sorting 

 interval. The same bi-modal character occurs, with an apparent minimum at 

 velocity values below about 5 cm sec"-'-. Because of the coarseness of the l/2 

 0^, interval, the lower curves in figures V-ll and V-12 do not show a bi-modal shape. 

 However, a gross distortion appears in the distribution, as compared to the Gaussian. 



The explanation for the distortion of the velocity sample distribution seems 

 obvious. It was noted earlier that the ducted cylinders of the wave meters (used in 

 the OMDUM III or LIMDUM I configurations) have a threshold velocity of about 7-8 cm 

 sec" 1 . Thus, there are times (evident in figure III-9) when the wave motion does 

 not exceed the threshold velocity. Since the impellers do not rotate, no signal is 

 provided. The interpolation program fills in this information gap with linearly 

 interpolated velocities. If the wave motion, after having fallen below the detectable 

 velocity, again rises above it (in the same sense or direction); then the interpo- 

 lation program provides a supply of linearly interpolated velocity values between 

 the two points where the wave meter stopped and resumed sensing motion. Thus, a 

 disproportionately large number of near-threshold velocity values are produced in 

 the data. These interpolated velocities are produced in place of the actual lower 

 velocities, which are undetectable. Note that when there is a zero crossover 

 (change of sense), the interpolation process probably gives a much less distorted 

 velocity distribution. This is because, in passing through zero, the velocity 

 values are constantly changing to the next actual velocity value (see figure III-2). 



A velocity null followed by motion in the same sense can therefore cause 

 trouble. At greater depths, where the motions are slower, this effect is amplified 

 (see figures V-ll and V-12). Statistically, the null velocity situation would occur 

 with equal probability upward (+w) or downward (-w). The histogram produced would 

 therefore show a bi-modal distribution, with peaks at or near the threshold 

 velocities. By increasing the range of the sorting interval (e.g., from 2 cm sec" 

 to 5 cm sec"l), the distribution would, perhaps, appear more Gaussian. The question 

 arises as to how closely one should attempt to resolve the data in order to judge 

 the data distribution. The sorting interval can always be resolved (for a finite 

 sample) so that only one (or less) data point falls in each interval. This, of 

 course, produces a meaningless distribution. 



The null velocity situation, however, does not seem to be the whole story. 

 For one thing, the maxima that occur in serial 057 (0.5 m depth) are centered well 

 above the threshold velocity of 7-8 cm sec -1 . Also, in the interpolated velocity 

 traces in figures V-2 through V-k, the regions of variation from positive to 

 negative velocities (or vice versa) seem small compared with the time spent at the 

 large velocity magnitudes. 



The hypothesis that the waves should be Gaussian is based on the assumption 

 that the free surface function If can be represented (as an approximation) by a 

 quasi-infinite number of independent Fourier components, having a quasi-infinite 

 number of wave heights and frequencies. In reality, however, the ocean is not 

 random to the extent that one cannot distinguish relatively organized systems 

 of waves (either wind-generated waves or swell) among much clutter. 



10U 



