Ocean Currents in a Non-homogeneous Ocean 



511 



by drawing isolines of the quantity g/(sin 4>) instead of the ^-lines, are based on 

 incorrect reasoning because lines obtained in this way are then no longer stream lines ; 

 they will be intersected by the flow and thus lose their meaning. It is therefore better 

 to retain the g-lines (Thorade, 1937 b). Volume transport charts over more extended 

 oceanic areas have not yet been prepared, although the complete dynamical evaluation 

 of the observational data for such an undertaking would be available. 



{b) Water Transport in Coastal Currents 



Werenskiold (1935, 1937) has presented a very convenient method for the calcula- 

 tion of the volume transport in coastal currents, for which, in a cross-section at right 

 angles to the coast, a lighter water is spreading out in a wedge-form on top of a heavier 

 slowly moving and almost homogeneous water. Figure 235 shows a vertical section across 

 a current between two stations A and B. The .v-axis is placed in the sea surface in the 



Fig. 235. To the computation of the water transport in a coastal current (according to 



Werenskjold). 



direction A-^ B and the water depth is denoted by z. In the section there are drawn 

 two isopycnals p and p -[- ^p and two plumb-lines x and x -f ^.v. The boundary 

 surface of the wedge-shaped top layer forms the isopycnal pi reaching the surface at 

 C. The top-layer has a depth z^ at point x, however, the depth Z^ at the station A. 

 At an arbitrary point M on one of the plumb-lines (density p) the component of the 

 velocity of the density current at right angles to the section will given by the equation 

 (VII.8): 



Vi = 



fp. 



i dp- 



Thereby j is the slope of the isopycnal which is dependent on .y and z. Denoting 

 Sl fPm by b, then one obtains from the relation above 



Tp 



-bj 



dz 

 dx' 



(XV.25) 



where the derivative dzjdx has to be taken along an isopycnal, that is, for a constant 

 p. The volume transport at a plumb-line can then be obtained by integration from 

 to r^. By partial integration one obtains 



S - Vi dz 



Vi- 



Zd 



zdVi. 



