''DC ±^ AB 



^ A B 



Z' ^DC ± " AB \ 

 \ AB + '^^zl 



'' AB ' DC [V 



(29) 



sin a =— / 1 ± 



, cos a 



1 + — 



(30) 



(7 s 



(c) If - cos a > 1 and h-tt ^ a S 2 77, the equations 



'^ AB 



~ cos a — 1 



CD 



+ ^ sin a + 1 



must hold, where the upper sign is valid for Qq"' T ^""^ '^'" ■nn' + aQ , 

 the lower sign valid for aQ>77/4 and a>2""' + a or aQ> 77 '4 

 and a arbitrary. The period again is given by equation 29, substituting 

 '■'dc ^^ ''CD ' the angle is determined by 



-(l.^),cos.=g(u^) 



(31) 



Doppler Shifts for an Infinite Number of Modes of an 

 Internal Wave with a Period r 



So far one internal wave with the period t and phase velocity c has 

 been considered. A case will now be considered where there is again only one 

 period rn but the wave is composed of different modes as is the case for all 

 real internal waves. 



Case 1 : If the process is observed at the anchor station, we record the 

 fluctuations 



N r 



F(z, t) 



11 = 1 



A W, J (s) cos — t + B^W (z)sin — l 

 '0 '0 



(32) 



15 



