496 



Tides of the Oceans 



7. Theoretical Considerations on the Semi-diurnal Tides in the Oceans Especially 

 on Those of the Atlantic Oceans 



It would be interesting to compare maps of the co-tidal lines of the oceans 

 based on the observations with theoretical maps of the tides. However, it 

 has not been possible hitherto to derive for the oceans tide maps based on 

 an exclusively theoretical mathematical consideration. The complicated con- 

 figuration of the oceans, the co-oscillation of the water-masses with adjacent 

 seas, the Coriolis force and friction are a few of many factors influencing 

 the tides. We refer to Chapter XI. 2-7 for methods which have been developed 



Table 84. Ratio of minor to major axis of tidal current ellipses 

 of semi-diurnal tide as a function of the latitude 



in order to obtain at least a first approximation. Proudman and Doodson 

 (1936, 1938) have given the solution for an ocean of constant depth bounded 

 by two meridians 180° apart, i.e. bounded by a complete meridian (p. 286). 

 The application of these results to the actual oceans can, of course, only be 

 made with reservations. However, it is to be expected that the methods of 

 Proudman and Doodson will be developed in a not too distant future to such 

 an extent that it will be possible to compute the theoretical tide, also for more 

 complicated ocean basins where the boundaries are portions of meridians and 

 circles of latitudes. 



In order to obtain footholds regarding the form of the zonal oscillations 

 one may subdivide the ocean in a number of west-east oriented channels 

 bounded at both ends by the continents and apply the improved canal theory 

 of Airy (p. 290). One then obtains the number of nodal lines and their 

 position which are changed into amphidromies under the influence of the 

 Coriolis Force. Furthermore in order to obtain ideas about the meridional oscilla- 

 tions of the ocean, we may consider them as co-oscillating with the Antarctic 

 belt with which all oceans communicate. These canals being considered by 

 themselves and independently from the neighbouring canals the computations 

 should naturally be used with great caution and be regarded merely as very 

 rough evaluations of possible co-oscillating systems. Prufer has made such 

 computations for the Indian Ocean, and Dietrich for all three oceans. The 

 forced M 2 tide of the Atlantic Ocean shows a node in its west-east direction 

 between North and South America in the west and Europe and Africa in the 



