Internal Waves 



539 



increases continuously in the upper layers. It was to be expected that there 

 existed a close connection between vertical displacement of the water-masses 

 and corresponding variations of the velocity, perhaps also in the direction 

 of the current. In most cases it could be verified by current observations. 

 The combined analysis of current and serial observations provides the foun- 

 dations for the testing of the theory of the internal waves. 



First of all reference is made to the observations which Fjelstad (1938, 

 p. 49) carried out in Herdlefjord, Norway, to prove his theory. The waves 

 can be expected to be of the simple Kelvin type, because of the narrowness 

 of the fjord. The simultaneous hourly observations of temperature, salinity 

 and currents lasted 88 h. The amplitudes and phases of the vertical dis- 

 placement as well as amplitudes, phase and direction of the current were 

 computed by harmonical analysis (see Table 89). There u represents the 

 velocity of the current in the direction of progress of the wave, v the com- 

 ponent normal to it, and t the direction of the major axis of the current 

 ellipse relative to the east direction. The smallness of v proves that the internal 

 wave corresponded actually approximately to the Kelvin type. The first four 

 internal waves were computed from the mean vertical density distribution 

 to test the theory. Their velocities of propagation are 62-7, 33-4, 23-4 and 

 174 cm/sec. The amplitudes and phases of these four waves can be computed 



Table 89. Internal waves in Herdlefjord (Norway), summer 1934 

 Station 1 : 88 h observations (according to J. E. Fjeldstad) 



Depth 

 (m) 



Current 



In the direc- 

 tion of 

 the wave 

 it (cm/sec) 



Normal to 

 the direction 

 of the wave 



v (cm/sec) 



Computed 



Phase 



T in ; u cm/sec 



8-5 

 10-5 

 5-9 

 3-4 

 10 

 1-3 



0-2 

 01 

 0-5 

 0-8 

 01 

 0-9 



244° 



239 



246 



249 



213 



113 



12-5 



9-4 

 6-7 

 2-6 

 11 

 1-4 



231 c 

 233 

 230 

 226 



227 

 46 



by the method of the least squares, if it is assumed that the observed dis- 

 placements are mainly caused by these four waves. The assumption is well 

 taken as the table shows. Moreover, the theory provides also the possibility 

 of computing the corresponding currents. But the regular tidal current which 

 belongs to the zero order wave was not included in these theoretical values. The 

 comparison with the observed currents shows an excellent agreement, which 



