FIG. H. yi;2 tidal currents in MODE 

 area between Eleuthera and Bermuda. 

 The arrow toward °G refers to the 

 current vector (scale below) when the 

 Moon passes over the Greenwich merid- 

 ian; 30 °G, 60 °G refers to other 



Greenwich epochs. The upjjer ellipse 

 refers to a computer model by Parke 

 and Hendershott, the lower ellipse is 

 based on deep-sea tide measurement.s. 



Finally, there is the possibility of incoherent phase 

 modulation by internal tides along the entire path. This 

 is then analogous to the incoherent modulation by inter- 

 nal waves in general. Internal tides have typically one- 

 third the amplitude of the internal waves (Table V), and 

 so contribute 10% to ((^j). If this were the only contri- 

 bution, then because of the periodic input at tidal fre- 

 quencies cOj,, the multipath spectra would be concen- 

 trated at tOj., 2a)j., Sojj., . . . , and the local energy densitv 

 would be high. In the presence of internal waves there 

 is interaction with all frequencies, but some remnant of 

 the tidal line spectrum can be expected to remain. The 

 problem needs further consideration. 



ACKNOWLEDGMENTS 



John Clark and his associates have furnished the 

 acoustic records on which this analysis is based. 

 Flicki Dormer and Betty Ma have carried out the data 

 reduction. Disctissions with Ted Birdsall have been 

 most helpful. 



APPENDIX A. 



Equation (10) can be written 



where s = h/oj i » 1 . Hence 



r" 



(0f) = i/|) j u}dw~in^vl 



•'i.s ._ 



and 





--O.OZe'^'" 



ior n = noe'''\ «o = 5. 2x10"^ sec"^ 1-^ = 3. 2x 10"^ sec"^. 



APPENDIX B. 



In some oceanic models we may have a relation 



(4''h=m')if > (9') 



with a coefficient/ replacing the 3 which appears in 

 Eq. (9). In this case the following changes need to be 

 made in the results of Sees, n and HI: 



i/7rV<l , 



<(A0)2) = (^/3)/-i '' + (n'/8)r' '' (i,f '' - 1)-' 



o = (77/3) + (7778) (tt/"^ -I)-' . 



For example, if /= 9, a = \. 19 and c = n/la = 1. 32 in 

 Eq. (40'). 



(26') 

 (27') 

 (28') 

 (29') 

 (30') 

 (33') 

 (34') 



rfoj 





APPENDIX C. 



The mean-square vertical displacement is given by 



r" / 2 2 ^1/2 



(j2) = i£2£Zio f ^-°(a) -a..,) 



where 



^=Z(/+J^)-' = 0.468 . 

 The relative contribution 



'■'dw 

 equals 



I -(■/372;r) = 0.39, from oJu to 2oJu 

 = 1, fromcitio to "o , 



whereas the j contributions are 



0.214, 0.164, 1, forj = l, j = 2,T. ■ 



Similarly, 



246 



