Internal Waves 535 



where the wave velocity is 



1 a 



c =- 

 e 



I'V- 4 ™ 2 -'^) 



A necessary condition for the existence of this wave is 



m~ir 2 



that is at least a' 2 > 4co 2 . The wave velocity without rotation is in this case 

 c = 1/e, therefore we can write 



For c = 200, as before, m = 1 and 2co = 1-3 x 10 -4 (60° latitude), it follows 

 b > 102 km. Consequently internal waves of such a form may probably 

 occur also in the open ocean. They correspond to the Poincare-waves at 

 the ocean surface mentioned above (p. 208). 



The vertical distribution of t], which characterizes the internal wave, will 

 result from integration of the differential equation (XVI. 30). rj{z) can be 

 ascertained by a comparatively simple numerical integration, when the vertical 

 density distribution is given, as shown by Fjelstad. With sufficient accuracy 

 we can write 



Q dz dz 



and as a 2 /g (magnitude in the case of tide waves 10 -n ) is always very small 

 compared with 0, the equation (XVI. 30) will be simplified to 



U. 77 % 



^r-- 2 s<M = o. (XVI. 36) 



Furthermore, the boundary condition for the free surface can be replaced 

 by the more simple one r\ = 0. Thereby the wave of zero order is being lost, 

 whose velocity is c = a/x = \(gli) and which is the regular tide wave. But 

 we want to disregard this "external" wave. The boundary conditions are 

 therefore w = r\ = for z = and z = h. Stormer's (1907) method of 

 integration can be applied in simplified form to this differential equation. 

 It gives the vertical distribution of r\ with a relatively small amount of com- 

 putational work, if approximate values of the parameter x 2 /a 2 are known 

 as Fjeldstad has shown. For more details reference is made to the original 

 publication. As an example we can take station 115 of the "Michael Sars" 

 where the depth to the bottom is 580 m (Helland-Hansen, 1930). 



Figure 223 shows its density distribution a t as well as Fjeldstad's computed 

 vertical displacements n and horizontal velocities u for the internal waves 



