532 



Internal Waves 



were observed beside wave-like variations with a long period (see Kalle, 

 1942, p. 383; 1953, p. 145). At first they were believed to be caused by the 

 turbulence of the currents. But there exist frequently cases where the oscil- 

 lations are entirely of a regular wave-like nature. These are doubtless stability 

 oscillations. Figures 220 and 221 present two cases of such regular oscil- 



FlG. 221. Stability oscillations in Arkona basin (Baltic) with a period of 2-3 min. Simul- 

 taneous temperature registrations at three different places around the ship, 30 July 1944. 



lations on two different stations in the Baltic. Neumann (1946, p. 282) 

 on the basis of the Baltic observations, tested thoroughly the theoretical 

 results concerning the cellular waves in stratified media with reference to the 

 shape and period of the waves as a function of the stability of the stratification. 

 Figure 222 shows a fairly good agreement between the observed and the 

 theoretically computed periods. The form of the cell is generally rectangular 

 and its horizontal dimension amounts to about 2\ the vertical one. More 

 research will uncover further details about these interesting phenomena, which 

 are certainly connected with turbulence. 



(j8) Progressive internal waves of longer periods. An exhaustive theory of 

 internal progressive waves in water masses, in which the density is a con- 

 tinuous function of depth, was developed by Fjelstad (1935). He also gave 

 a practical method to compute all possible internal waves for any given dis- 

 tribution of density. 



The mathematical basis of the theory is the same as for the cellular waves. 

 Particularly, the same equations (XVI. 24), (XVI. 25) are valid. In the case 

 of a progressive harmonical wave with a period T = 2nja and with a velocity 

 c = afx £ and v\ can be assumed to be proportional to e i{at ~ kx) and finally 

 the differential equation for the vertical displacement will be 



dz 



dr] 



Qo^z)--*\g — 



1 dg 



-7- +o 2 Qo)v 

 dz! a 1 \ g dz ) 







The following boundary conditions have to be added: 



For the bottom z = , 

 For the free surface Z = h , 



V =0, 



dr) 

 dz 



-zgV =0- 



(XVI. 30) 



(XVI. 31) 



