TM No. 377 



Thus, the vertical gradient in the correlation coefficient is proportional to the 

 vertical gradient of the eddy scale with depth. Figure V-26 shows the correlation 

 coefficients plotted as a function of depth. The arrows indicate the depth of the 

 upper and lower velocity sensor and the distance of separation (h = 2m). For the 

 particular wave conditions existing at the time, the correlation between and 5 meters 

 is quite constant at about 0.7. At depths below 5 meters, the coefficient drops off 

 rapidly (and apparently quite linearly) to a value of 0.l6 at a depth of 10 meters. 

 The spatial correlation for a 2-meter separation indicates that eddy motions asso- 

 ciated with the waves vanish at about 12 meters. 



Comparison of Kinetic and Potential Wave Energy - Specific examples have been 

 given of the decrease of the variance of wave motion with depth. The generality of 

 the results from BBELS-5, 7 and Ik are indicated in figures V-27 and V-28, in which 

 the variances of the horizontal and vertical velocity components taken from each 

 BBELS observation (i.e., BBELS 5 and 7-l6; all listed in table IV- 3) are plotted as 

 a function of depth. The numbers represent the numerical values of the wind speed 

 (in m sec-1) observed at the time of each measurement. The wind speed values were 

 used in an attempt to relate the variance distribution to wind intensity. Further 

 discussion of this aspect is given later. 



Referring to. the horizontal variance OJ 1 ' in figure V-27, the general tendency 

 is for the variance to decrease with depth; but there is much scatter and even a 

 few spurious values. The primed sevens (7*) represent the data from BBELS-7. As 

 was indicated previously, the BBELS-7 data were obtained without the back guy; 

 hence, it was felt that this particular set of measurements would be potentially 

 biased (by waves tending to move the meter and bias the horizontal response). 

 And indeed, this group of observations does tend toward lower values than are 

 indicated by the majority of the remaining points. 



A more well-defined relationship is shown in figure V-28, where the vertical 

 variances are plotted against depth. The circled values are from BBELS -11; where, 

 within one hour, a sudden wind speed increase and direction shift occurred. These 

 values should therefore not be judged on the same basis as the other points. This 

 is because the new waves generated by a sudden shift of wind are not produced 

 instantaneously but require time to build up. Thus, at a given instant, the wave 

 structure is not necessarily commensurate with the intensity of the wind field 

 (see Pierson, Neumann and James, 1955). The other values, in general, were 

 obtained in fully developed seas under fairly constant wind conditions. 



The numerical' values of wind speed were used on the plot to see if the 

 higher wind speeds produced higher variances for a given depth. This is not too 

 well shown in the Qu 2 - plot (figure V-27), probably because not enough (reliable) 

 data points were available. The vertical variances (figure V-28) better exhibit 

 this relationship, particularly at depths between and 2.5 meters. Thus, for a 

 given depth, the wind speeds tend to increase as one moves up the ordinate (i.e., 

 with increasing variance magnitude). At depths beyond 5 meters, however, the 

 relationship becomes uncertain. 



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