Chapter XIII 



General Theory of Ocean Currents 

 in a Homogeneous Sea 



1. Introduction 



A THEORY covering all the phenomena of ocean currents and taking into account ail 

 the effects of the internal and external forces must essentially be rather complex and 

 would not allow an immediate insight. The theory must thus, as in other fields of 

 natural sciences, take another path as soon as it can be based on well-founded geo- 

 physical principles, and must use simplifying assumptions taking only the effect of 

 one single current-generating factor into account at a time. All these individual 

 current constituents can then be combined to give some picture of all the factors in- 

 volved in the generation and maintenance of the ocean currents. This, of course, is 

 the aim of any theory; because of the complexity of the phenomena involved, little 

 could be deduced from the dynamics of the ocean currents developed in their most 

 general form that would assist in the elucidation of the nature of the oceanic circula- 

 tion. The history of the theory of ocean currents is long and goes back a long way and 

 would require considerable space; a more or less detailed account of the older parts 

 has been given by KrOmmel (1911, pp. 442-449). The first simplification is the ehmi- 

 nation of the internal forces; this is identical with the assumption o^ a. homogeneous sea. 

 In this case only external forces would be able to produce water movements. Ekman 

 (see especially 1927) was the first to develop the problems of the dynamics of the ocean 

 currents of a homogeneous sea in a classically elegant form and went far towards 

 successful solutions for these. There are two immediately apparent problems : 



In a homogeneous sea, movements of the water may arise besides from the effect of 

 the wind on the sea surface also from the pressure of a sea surface slope. This gives 

 rise to a horizontal pressure gradient which is transmitted through the entire water 

 mass down to the bottom. The first main problem is then the calculation of the velo- 

 city components at each level for a given wind force and a given gradient of the sea 

 surface. The hydrodynamic equations of motion provide the basis for this and can be 

 solved, as has been shown by Ekman, if the frictional coefficient is given. The current 

 system produced by the action of these external forces at all points along a vertical 

 was termed by Ekman the ^'elementary current. 



The constituents of the elementary current can be derived without taking the con- 

 tinuity equation into account. Due to differences from place to place in the wind distri- 

 bution or the sea surface slope or due to local differences in the depth of the sea the 

 continuity requirement cannot be satisfied by horizontal movements alone. The di- 

 vergence of the currents caused in this way gives rise to changes in the sea-level which 

 in turn affect again the elementary current (feed-back). The second main problem 



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