the therniocline. 



The picture thus presented by the continuous density model 

 is one much more complicated in nature than that of the two-layer 

 system. We are now concerned with an ocean in which the ampli- 

 tudes and phases of ttie Internal wave are continuous functions 

 of depth. 



The most complete tlieoretical treatment of this complicated 

 problem has been given by Pjeldstad (1933). Assuming free waves 

 in a medium in which density varies continuously with depth and 

 neglecting the effect of Triction, Fjeldstad derives the follow- 

 ing second order differential equation 



,2 



d w . ,2 , ^ 



^ + x g.^w = (2I4.) 



with boundary conditions at the bottom (waO, ZiO) 

 and at the surface (w=0, Z=h). 



In this equation, w represents the relative displacement of a 

 water particle from Its equilibrium position. This means that 

 these amplitudes are not unique, but only that they are deter- 

 mined in such a way that the ratio of true amplitudes between 

 any two fixed depths is equal to the ratio of the w's for the 

 same depth. The term c^ is taken as the internal stability of 

 the water column, or 



2 



X. g is an unknovm parameter which depends on the vertical 

 density distribution. 



58 



