then at z= H/2 we get 



1/2 1™ 



1 



(-1)" l/n sin 077/2 



1/2 7r/16 and 



P' , =1/2 lim > l/«2 sin^ {n7T/2) = 1/2 77^/8 



In this case, the energy with the chain is twice the actual energy. Choosing 



' (-1)" for « S 5 



C 



we get 



for n > 5 



^total = 1/2 



total = 3/2 



NATURE OF FORCED AND FREE INTERNAL TIDES 

 IN THE OCEAN 



It has been shown by A. Defant ' and B. Haurwitz that, for a two=lay- 

 ered ocean, forced internal tidal waves in an unlimited ocean play no role outside 

 of a very narrow band at those geographical latitudes where (yQ = f. The defini- 

 tions of these symbols are: ojg = frequency of the tide - generating force and 

 f = 212 sm<f>. At these latitudes, however, the wavelength goes to infinity. 

 Therefore, it is believed that internal tidal waves are not forced waves. Taking 

 the tide -generating force as 



K'o exp[( (k X + ojQt)] (51^ 



the Defant- Haurwitz theory shows the following unrealistic property: the tide- 

 generating forces on the earth have a wavelength Xq = 277/kq , which is generally 

 larger than the ocean basins. The ocean itself, however, is assumed to be 

 infinite. Therefore, the wavelength Aq should also be infinite and this 

 means that equation 51 should be reduced to Kgexp (ico^t). 



A more realistic model can be obtained in the following way. Assume (1) 

 that the wavelength Ag is larger than any ocean on the earth and not a multiple 

 of the length of the ocean : Ag > 2 L and Ag 7^ 2'!L ; and ( 2 ) that the tide- 

 generating force can be expanded into its Fourier components in regard to the 

 basin. 



21 



