TM No. 377 



whereby momentum may be transferred from the wind through the surface waves. 

 Any energy and momentum within the wave must have been transmitted through 

 the wave surface by an actual frictional drag and/or a pressure effect. 

 Assume that the wind momentum is transferred by an eddy process in which the 

 eddies are the waves themselves. As the wind blows horizontally across the 

 waves, it produces a tractive stress on the tops of the waves and, perhaps 

 also, a pressure force upon the upwind side of the waves. Both of these 

 mechanisms could sensibly accelerate the particles when they are moving at the 

 top of their orbits; i.e., when the u component is positive and maximum. Thus, 

 a bias is placed within the horizontally oscillatory component of the SBM, a 

 bias which is of the frequency of the waves themselves. At a fixed point in 

 the water column, momentum transfer of this sort would appear as a direct coupling 

 effect, occurring at the dominant wave frequency. 



The three sets of data were analyzed, using the Tukey spectral estimate 

 program, on the M.I.T. IBM 7090 computer. The results are listed in appendix C. 

 The processing techniques used were identical to those used for the wave data 

 (discussed in chapter III). Table V-4 gives a short summary of the pertinent 

 statistics. 



The variances Ou* , UZj*~ of the RBM are about !5 cm2 sec -2 , whereas the 

 unbiased and biased sinusoidal models have variances of the order of 50 cm 2 sec -2 . 

 The mean values are not listed; however, u and w did not exceed 0.5 cm sec - l for 

 any of the models. The covariances Cf> uw (0) for the RBM and SBM are -3.70 and 

 -2.6 cm 2 sec" 2 , respectively; the SUM displays an expected vanishing covariance. 

 The correlation coefficient r for the RBM (-0.24) is relatively large compared to 

 that for the SBM (-0.03). 



The spectral analysis of the hypothetical wave data serves a twofold 

 purpose. It permits specific examination of the covariance properties of the 

 biased data. More important, however, one can examine the cross properties of 

 the statistical quantities derived from the "controlled data". One of the 

 difficulties in interpretation of statistics such as auto-spectra and cross- 

 spectra is that much of the actual data processing is hidden amidst the long 

 series approximation formulas (see chapter III). It is therefore instructive to 

 examine the relative magnitudes of the effects which different types of data have 

 upon the derived statistics. 



The spectral data for the three wave models are listed in appendix C. The 

 auto- covariance functions ^ u Ct*) and <$>u>C T ) are plotted in figure V-47 for all 

 three models. The RBM (upper traces) displays no obvious periodicity, oscillating 

 rather chaotically about the abscissa. The SUM and SBM auto-covariances give 

 almost identical oscillating curves with a period of about 2.1 seconds. The 

 pattern of 3fc*£"*J and 4lrflTl is similar to a cosine curve (an even function), 

 having a maximum value at T = 0. At this point, the auto-covariance defines 

 the variances of u and w. 



146 



