488 



Ocean Currents in a Non-homogeneous Ocean 



agreement was very satisfactory; later this kind of comparison has often been repeated 

 confirming the results. 



If, instead of as in Fig. 222, the vertical section is placed in the direction of the 

 relative velocity Vq — V^, then there will be no component at right angles to the surface, 

 that is, in (XV. 12) ^o — i^i = as well as £)« — D^ = and the dyn. depths in the cross- 

 section must be the same at C and D. If one of these verticals is kept fixed, then the 

 other will move away at the relative velocity Fq — V^ and for every point along its 

 track always applies Da — Dt, = 0. This implies that: curves of equal dyn. depth, 

 which then give the dyn. topography of an isobaric surface relative to another, represent 

 at the same time stream lines of the relative velocity {velocity of one surface relative to 

 that of the other). 



This theorem is of great importance in the discussion and interpretation of the 

 relative topographies of individual pressure surfaces in the ocean. An example is 

 presented in Fig. 223 which shows the relative topography of the isobaric surface at 

 750 decibars for the same area containing the section shown in Fig. 202. The indication 

 arrows show the direction and the intensity (nautical miles per hour) of the (relative) 

 velocity of the layer at 750 m depth relative to that of the surface. If the water in this 

 depth is motionless, then they represent the sea surface current. The dyn. isobaths 

 are stream lines for the whole system. 



.57°W 56 



'W 56" 



Fig. 223. Dynamic topography of the 750-decibar surface south of the Great Banks of 



Newfoundland according to the observations from 5 to 7 May 1922 (according to Smith). 



The arrows indicate the computed relative current in nautical miles per hour. 



Both applications of the circulation theorem have made use of curves in vertical 

 planes, which contain a large number of solenoids. The theorem may also be applied 

 to horizontal curves, which include little or no solenoids. For curves of this type the 

 first term on the right-hand side of equation (X.54) vanishes and there remains only 

 the term expressing the effect of the Coriolis force. On integration it gives 



-Co=-/(F, 



Fm 2). 



(XV. 13) 



