TM No. 377 



Figure V-2U is a plot of the variances (Jj l (obtained for eight pairs of 

 measurements) as a function of depth. The broken lines connect the variances of 

 the simultaneously measured pairs. The wind speed was about 9-10 m sec -1 from 

 the SSW during this sampling period (from 1^12 to l6l8). 



These values show a similarity to the plots from BBELS-5 and 7 in figure 

 V-20, which is indicative again of an exponential decrease in the variance of 

 wave motion components with depth. 



Figure V-25 depicts the superposition of some of the various auto-spectra 

 from BBELS-1^. The uppermost curve (0.0 m) shows two peaks: a major one at 

 about 250 mcps (k sec), and a lesser one at 50 mcps (20 sec). The curves for the 

 deeper observations show a strong decrease in energy. Note the "reddening" of the 

 250 mcps peak at the surface to 150 mcps (6.6 sec) at a depth of 9 meters. Above 

 100 mcps each curve, in the order of ascending depths, consistently falls to the 

 right of the preceding one, and thus shows a progressively larger energy content 

 proportional to the area under the respective curves. 



Note in table IV- 3 the linear correlation coefficient r between the two w 

 values. This number is, in a sense, a spatial correlation coefficient for W]_ and 

 W2 at a fixed vertical distance apart, and is defined for this case in chapter III. 

 If one considers the fluctuations at two points Z]_ and Z 2 in the field of wave 

 motion, the correlation between W]_ and w2 will, in general, vary with the magnitude 

 of the distance Z2 - g l = h. One would expect the correlation to diminish as h 

 increases. This suggests a method of defining a length that may be associated with 

 an eddy size. If r (h) is the correlation coefficient between the fluctuations at 

 points separated by a distance h, a length L can be defined by the relation 



L = \ Htfdh i ( v - 10 ) 



provided, of course, the integral converges. For a real turbulent regime this 

 will be the case for h greater than some finite length; i.e., beyond some length 

 the spatial correlation r, for all practical purposes, vanishes. The length L, 

 called the "scale of turbulence" (see Sutton, 1953, or Hinze, 1959), represents 

 the average size of eddies or the length scale of the fluctuation, but without any 

 strict definition of the model of an eddy. 



For the experiments made with the LIMDUM I system, the separation is fixed; 

 and the correlation coefficient is measured as a function of the depth. From 

 equation (V-10), it follows that: 



H-jVwj h . 



(v-11) 



117 



