Chapter XV 



Ocean Currents in a Non-homogeneous 



Ocean 



1. Introduction 



If all the external forces that may act on the sea are excluded, ocean currents can still 

 be produced by internal forces. Differences in the mass structure will represent an 

 internal system of forces that will act until the resultant mass displacements lead to the 

 establishment of a mass distribution corresponding to that of a static equilibrium. 

 It is customary to denote ocean currents generated by such internal forces as "con- 

 vection currents" although they have nothing to do with oceanic convection pheno- 

 mena. In order to avoid this unsuitable notation it seems to be advisable to call them 

 "density currents", since they depend solely on the three-dimensional difference in 

 the density field. Treatment of these density currents involves greater difficulties than 

 that of drift and gradient currents, in particular, since the external forces (wind and 

 atmospheric pressure) can be regarded as independent from the currents themselves, 

 while the density currents and the density differences producing them influence each 

 other. Furthermore, the density anomalies, being internal forces, are distributed three- 

 dimensionally in space, while wind and atmospheric pressure at the sea surface act 

 only in two dimensions. 



The beginnings of a theory of density currents goes back to Mohn (1885, 1887) 

 whose work can without doubt be described as "the beginning of a new era in physical 

 oceanography" (Helland-Hansen and Nansen, 1909, Vol. II. 2, p. 390). However, 

 this theory, the aim of which was rather wide-spanned, was incapable of influencing 

 the further development of theoretical oceanography, since it was running far ahead of 

 the development of oceanography, which at that time made its progress mainly along 

 geographical lines and because the defects in it were difficult to eliminate. It was soon 

 forgotten (Thorade, 1925). The foundation for a firmly founded theory of density 

 currents was provided by the application of the Bjerknes theorems of vortex formation 

 and circulation acceleration to oceanographic problems. Thereby it was necessary to 

 leave aside classical hydrodynamics, dealing only with homogeneous media, and to 

 make use of physical hydrodynamics where the media had a full physical reality. 

 Some of the results were later derived directly from the hydrodynamic equations of 

 motion. These derivations are, in part, clearer and more comprehensible, and it 

 therefore seems advisable to discuss the simpler problems first. 



2. Relationships Between Current and Density Fields in a Horizontal plane. The law 



of Parallel Fields 



A general relationship between density and current fields can be derived quite 

 simply (Defant, 1931). In general, the vertical component of the velocity, that is, 



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