560 Internal Waves 



These experiments show that in shallow ocean regions (shelf regions) 

 internal periodical displacements might be generated with the same period 

 as the disturbance that caused them. They can occur because of topographi- 

 cal irregularities at the bottom of the ocean or on the edge of the shelf, if 

 ihe boundary layer is at the right depth. The most frequent disturbance will 

 probably be the periodically returning tidal currents, which ought to cause 

 the generation of internal tide waves in shallow waters. But the influence 

 of such internal tide waves ought to be limited as they are dampened very 

 rapidly, so that their amplitudes decrease quickly when the waves spread 

 out in all directions, as was emphasized by Ekman (1931). 



In the open ocean, topographical bottom influences can hardly be ex- 

 pected to be the cause for the generation of internal waves. External in- 

 fluences from the atmosphere are rather the cause; but these will not have 

 a tidal period. The cause for the internal tide waves, which occur frequently 

 over great depths in the free ocean, far from the continents, cannot yet be 

 stated with certainty. One might think of inhomogeneities in the vertical 

 structure of the main currents, on which the regular tidal current is super- 

 posed, which is of the same kind in all depths. But the superposition with 

 the main current causes periodically varying water transport in the super- 

 imposed water layers, which ought to be related to the vertical displacements 

 with tidal periods of the boundary layers. The vertical heterogeneity of the 

 main currents is in general dependent upon the vertical distribution of the 

 thermo-haline properties and the discontinuity layers of density are also in 

 most cases discontinuity layers of the field of motion. This heterogeneity 

 in connection with the periodical tidal currents, might well be one of the 

 causes of the so frequently observed internal waves of tidal period. 



So far, the effect of the earth's rotation on the internal waves was not 

 considered. Because of the earth's rotation the periods of long internal waves 

 are much shorter and their velocities much larger than without taking into 

 account the Coriolis force; therefore, it is to be expected that the resonance 

 conditions for oscillations at internal surfaces of discontinuity are much more 

 favourable than was supposed previously. This was confirmed by investiga- 

 tions by Defant (1950) and Hatjrwitz (1950). The main features may be 

 illustrated by the following model. Let the upper water-mass move with 

 the constant velocity U l , the lower with the constant velocity U 2 , both parallel 

 to the undisturbed discontinuity layer. A tide generating force, 



acting in a horizontal direction on the whole system, will produce tide waves 

 at the surface and on the discontinuity layer. 



The equations of motion and the continuity equation for both water waves 

 give for the water surface and for the discontinuity layer one wave solution 

 with waves of the frequency a and the wave numbers x. The velocity of pro- 



