Internal Waves 553 



atmospheric disturbances (passage of a storm region). After the disturbance 

 subsided the system gradually approached a new equilibrium by its free 

 oscillations. 



The internal waves which were observed in the Kattegat with a period 

 of 14-5 h are surely oscillations with the free period of the entire basin. Ac- 

 cording to computations one needs a width of 136 m to obtain a period of 

 the free oscillation which differs only by 1 % from the period of the inertia 

 oscillation which is 14 5 h. The width of the Kattegat is of this order of 

 magnitude. Concerning inertia oscillations in the Baltic, see p. 554. 



3. Internal Waves in Lakes and in Basins 



The reflection of progressive internal waves at the boundary surfaces of 

 enclosed water-masses, changes these waves into standing internal waves. 

 In a basin with an irregular shape, where the density increase is continuous, 

 one can expect an unlimited number of free standing oscillations, because 

 an infinite number of internal waves of different orders may be present and 

 in a horizontal direction the number of nodes may lie between one and 

 infinity. Every internal wave of any order can cause by reflection a standing 

 internal wave. This circumstance makes it likely that there will be always 

 a free-standing internal wave which reacts somehow to an external intermittent 

 disturbance of arbitrary period. Because of the small amount of energy which 

 is necessary to create such internal waves they will occur quite frequently in 

 nature. 



In basins of constant depth and of rectangular cross-section (lake), the 

 periods of oscillation of free-standing waves in the presence of two layers 

 are expressed by (see also Schmidt, 1908, p. 91) 



where h and q are the thickness and density of the lower heavier water-mass, 

 h' and q the corresponding values of the upper lighter layer, / is the length 

 of the basin, and n — 1,2, 3, ... If the basin is not closed in on all sides, 

 but open on one side (bay), then 2/ in (XVI. 43) has to be replaced by 41. 

 During a large part of the year many lakes and bays have well-developed 

 discontinuity layers of density (thermodine) and internal standing oscillations 

 ought to be a frequent phenomenon. Wedderburn (1905, 1907, 1909) 

 proved the existence of such standing internal waves in Scottish lakes and 

 Exner (1908) did the same for Lake Wolfgang in Austria. They found a very 

 satisfactory agreement between the observed and the theoretically computed 

 values of the periods. According to the corresponding conditions in the 

 case of the surface seiches, it is evident that the shape of the basin exercises 

 a great influence upon the period of oscillation. Since the period of the longer 

 standing internal oscillations in somewhat more extended water-masses is fairly 



