Long Waves in Canals and Standing Waves in Closed Basins 201 



west, the period increases to 6-4 h, because the sea becomes shallower and 

 because the "Talweg" becomes longer. Endros reaches a remarkable con- 

 clusion, that there are in the Black Sea three different main directions of 

 oscillation, each having a different period, which coincide at the eastern end, 

 whereas they split up in the western part. 



Opposing this interpretation, Defant (1933, p. 56) remarked that, in view of the enormous 

 extension of the area of the Black Sea, it is perhaps no longer permitted to neglect the deflecting 

 force of the earth's rotation (see p. 217), and that the periods of 6-4 h and 5-5 h might be oscil- 

 lations influenced by the rotation of the earth. He supports his objection by comparing the Black 

 Sea with a circular basin having the same main oscillation. The longest oscillation of such a circular 

 basin (a nodal line at a diameter), neglecting the earth's rotation, is found from the equation 

 °ooi y ' gh = 1-84, in which a = 27ijT and a the radius of the circular boundary and h the depth 

 of the basin. If the basin is rotating with an angular velocity to, a simple oscillating motion is no 

 longer possible (Lamb, 1932), (Goldstein, 1929, p. 213). Instead, two rotating waves develop 

 having their centre in the middle of the basin. One of these waves moves in the same direction as 

 the rotation (positive wave), the other one in the opposite direction (negative wave). Their angular 

 velocity and their period depend on a quantity 



Aura- 



gh 



When (5 = (no rotation), the angular velocities and periods of both waves are equal. Their super 

 position gives the simple standing wave. With rotation, however, their periods and angular velocity 

 become different. If the value of fi becomes sufficiently great, the wave period nears the period of 

 the rotation. 



In small lakes /§ is so small, that the influence of the Coriolis force is almost imperceptible. 

 However, if the lake has dimensions as large as those of the Black Sea, the influence can make 

 itself felt. If we put T = 6 h, then (3 = 0-391, quite different from zero, and we find for the 

 periods of the positive and of the negative waves respectively 5-47 and 6-49 h. The influence of the 

 earth's rotation is very important and, in view of the striking similarity of these periods with those 

 by Endros, it cannot be denied that perhaps there is actually some influence of the earth's rotation 

 on the oscillatory system. 



The Sea of Azov is one of the shallowest basins with large dimensions 

 (length 390 km, mean depth about 10 m). It is a region where very strong 

 winds pile water up to 5 m in the shallow north-eastern Bay of Taganrog. 

 This causes oscillations of large amplitude. Kurtschatoff found 24-5 h for 

 the uni-nodal seiche reaching from the south coast to the Bay of Taganrog. 

 The enormous variation of 2-5 m at the end of the north-eastern bay near 

 Taganrog can be computed from the largest amplitude of 80 cm observed 

 in Temrjuk (at the south-eastern angle). The dimensions of the sea fit this 

 longest oscillation. Furthermore a great number of other seiches have been 

 observed, among which those with a period of 14-8 and 12 8 h stand out. Endros 

 regards the former as the binodal seiche of the entire Sea of Azov, and it 

 is very noticeable at Jeisk. It cannot have, however, the same direction as 

 the principal oscillation, otherwise Jeisk and Temrjuk could not have the 

 same phase. Endros considers the 1 -28 h wave as an oscillation in a curved 

 direction west-north-south-east. Oscillations in this sea are very complicated 



