406 Tides in the Mediterranean and Adjacent Seas 



substitutes for the entire sea a rectangular basin of a length of 600 miles 

 (1000 km), a width of 310 miles (500 km), and a constant depth of 4130 ft 

 (1259 m), so that its natural period becomes exactly equal to that of the 

 Black Sea (see Fig. 172). It would then be easy to reproduce the tides by 

 superposition of the following four oscillations which can be determined 

 theoretically: (1) the east-west oscillation forced by the west-east component 

 of the tidal forces; (2) the north-south oscillation forced by the north-south 

 component of these forces; (3) and (4) north-south and west-east oscillations 

 which are caused by the action of the Coriolis force on the oscillations 

 under (1) and (2) respectively. This theory was first applied to the com- 

 bined M 2 and S 2 tides at the time of the syzygies and gave at the west and 

 east coast the amplitude 4-6 cm, in the centre of the north and south coast 

 11 cm and a distribution of the co-tidal lines as shown in Fig. 172. The 

 establishments of Constanta, Odessa, Sevastopol, Feodosiya and Poti are also 

 entered in the figure; one can see that both the amplitudes and the establish- 

 ments fit very well the theoretical picture. Even the approximate establish- 

 ments and amplitudes of Novorossisk and Tuapse as given by Endros (1932, 

 p. 442) fit well. The distribution of the tidal forces for such a basin is such 

 that the action in the north-south direction always lags in its phase by one- 

 quarter period to the action in the east-west direction, so that the superpo- 

 sition must produce an amphidromy rotating to the right (cum sole). The 

 oscillations caused by the Coriolis force are negligible and are only able to 

 weaken slightly the amphidromy, but not to suppress it. 



Later on, Sterneck has replaced his schematic theory by an "exact" theory, 

 in which he took fully into account the morphological conditions for the 

 computation of each separate oscillations. The assumption of synchronous 

 action of the tide-generating forces was dropped and he took into account 

 the small differences in phase of the force in the various sections of the sea. 

 For the computation of the four components of the oscillation he used the 

 method of step-wise integration. He obtained the amplitude and the phase 

 of the tide (Ma+Sa) for the northern and southern points and the centres 

 of the fourteen cross-sections. The result does not deviate considerably from 

 his schematic theory.* 



A hydrodynamical theory of the tides of the Black Sea which in a more 

 exact way takes into account the effect of the deflecting force of the rotation of 

 the earth should be based on Taylor's theory of the oscillations in a rotating 

 basin (p. 216). Grace (1931) has computed accurately for a basin of uniform 

 depth of similar dimensions as the Black Sea, the oscillations forced by the 

 tide-generating forces and compared his results to those of Sterneck. He finds 

 first of all that for a rectangular basin having approximately the dimensions of 



* The diurnal K t tide, on the contrary, has a counter-clockwise amphidromy; however, its 

 amplitudes are very small (1-6-01 cm). The harmonic constants confirm this result. 



