TM No, 3i|2 



(3)__and (U). Since the data were only approximately sinusoidal, the value 

 of U« W^' for USH (table l) is small but not zero. 



Biased Simple Haraonie Wave Model (BSH) 



The third hypothetical wave model is described as a Biased Simple 

 Harmonic Wave function. This model is identical in every respect with USH 

 except that the U(t) function has been slightly increased at its positive 

 maximum point. This intentional biasing was done for two reasons: (l) to 

 synthesize a desired negative value of U' W* for the BSH model and (2) to 

 bias the BSH model by a simple mechanism, perhaps not -unlike tb^t existing 

 in natural ocean waves . 



This technique seems reasonable since, as stated previously, any energy 

 and momentum within the ira-ve must be ti-ansmitted through the actual wave 

 surface by a frictional drag and/or a form drag of the wind. Thus, the wind 

 blows effectively horizonts-lly across the waves and causes an actual tractive 

 stress on the crests of the waves and probably a pressure force upon the 

 "upwind" side of the waves. Accepting this as fact, it can then be assxjmed 

 that the transfer of momentum downwards in the waves is caused simply by 

 t\:irbulence in the water. The wind momentum is transferred by an eddy process 

 in which the eddies are just the water waves themselves. Both of these forcing 

 mechanisms could produce a sensible acceleration of the particles at the 

 crest, i.e., when the U(t) component is positive and maximum. 



This is the reason for placing within the horizontal oscillatory component 

 of the BSH model a biasing component which is of the frequency of the waves 

 themselves. Hence, at a fixed point in the trater coliomn, a momentijrai transfer 

 of this sort would appear as a direct coupling effect occurring at the 

 dominant wave frequency. 



STA.TISTICA1 CHAMCTERISTICS OF THE HYPOTHETICAl. WAVE MODELS 



The thjree sets of data were analyzed for pertinent statistical parameters 

 using the Tukey spectral estimate program prepared by Convair on the MET IBM 

 7090 Computer. 



The statistical parazieters of the three pieces of ds-ta are listed in 

 table 1. The number cf pieces of data, the period of sampling, and the time 

 spacing are identical for all three sets of data, None of the mean values 

 of the horizontal and vertical velocity components, designated by U' and W*, 

 exceed 0.5 cm sec"-'-. 



The A.'ariances U»2 and W'^ (which are equivalent to the auto-covariance 

 function at zero lag) are about 15.16 cm2 sec'^ for the BR model and between 

 U9 and 55 cm^ sec"^ for the USE and BSH models (figures 2, 3, and k) . Ihe 



