530 



Internal Waves 



It represents an internal standing cellular wave, where the horizontal wave 

 length is l x = 2n/x, the vertical one X z = 2n/e. Figure 219 shows schematically 

 such an internal oscillation. One recognizes the division of the entire space 

 into "cells" of equal shape. The period of oscillation T = 2nja becomes 



2tz 



vlft 



1 + 



£ 2 +l/4//' 



= 2ti 



= 2n 





+ 



r 2 A 



\671~Qq 



\(Ex x y 



\6tf 



(XVI. 27) 



If the vertical density gradient is denoted r where r = —dg /dz = q /H, and 

 if we remember that r/g = E is the stability of the stratification (see vol. I) 



Fig. 219. Presentation of a cellular standing internal wave when the density increases 



continuously. 



we can derive the two other equations in (XVI. 27). It will be seen that 

 the period of the cellular oscillations is dependent upon the stability of 

 the stratification and upon the horizontal and vertical dimensions of the 

 cells of oscillation. 



Of particular interest is the case where e = 0, which is identical to l z = oo. 

 This means that in all z the phase of the oscillation is the same. Then equa- 

 tion (XVI. 27) gives a nearly constant period of oscillation for horizontal wave 

 lengths l x , which are small compared to AnH 



T = 2n 



0o 



Vfr 



(XVI. 28) 



thus independent of X x . For regular surface waves on a homogeneous water 

 layer T = y2nljg and is thus dependent of the wave length (see 11.11). 

 Therefore, there is a considerable difference in the behaviour of internal 

 waves. 



If we superpose on a wave (XVI. 26), another one of the same type but 



