™ No. 31^-2 



When examining the depth variation of a particular velocity component^ 

 say, ¥' , one finds that the variance ¥*^ decreases in an exponential manner. 

 Note that the area under the spectrirai cjurve of ^ (f ) versus frequency is 

 equal to the A/ariance of the particalar component caused, by fluctuations 

 occurring bet-ween the frequency ranges studied. 



Thus f 



W^ - ( ^ §11 (f) d f (5) 



I 



The turbulent kinetic energy ma.y be defined by the relation: 



Eg:. 1/2 /-(U'^ + ¥«2) . (6) 



Thus, the spectra of the velocity components are in fact true energy 

 density spectra, since the area 'under the spectral curve for a particular 

 velocity component must be equivalent to the turbulent energy contribution 

 of the component of velocity. 



The covariance spectra (bottom curves) display a negative peak which 

 occurs at the spectral band of the -waves. The auto-covariance function at 

 zero lag for the 1-meter depth was -23,3 cm^ sec~^ and the linear correlation 

 coefficient was -0.17. For the if-meter depth the covariance function was 

 -lU.l cm^ sec"2 and the correlation coefficient was - 0.30. As with the 

 Narragansett Bay measurements j, these covarlanees seem extremely large in 

 terms of the usual empirical estimate cf stresses of the order of 1 dyne cm-2. 



Based on the hypothetical wave model data, it appears that if the stresses 

 in the s'urface regime are about 1 dyne cm'2, then only very small velocity 

 correlations of about -O.O5 are required to produce a Reynolds stress of 

 this value. Probably the ducted meter system will be unable to detect such 

 small correlations because of the ms^sking effect of relatively large scale 

 perturbations caused by the interaction of the meter with the flow around it. 



However, the results so far available indicate strong negative correlations 

 peaking at the periods of 3-6 seconds. It is difficult to imagine that the 

 meter system, properly mounted in the wave regime, wo'uld artificially produce 

 correlations at these relatively low frequencies. 



Wo qu3,ntitative conclusions can be 'HBde yet regarding the momentum flux 

 mecb-anisms . However, there is no prior justification for discounting the 

 values of cova,rlance functions obtained from them since there are no previous 



direct meas'urements cf stress to refer to . 



