The Representation of Oceanic Movements and Kinematics 



375 



Fig. 163. Divergence of the current field. 



The divergence is positive if the stream lines move apart and negative if they contract. 

 If the stream lines are parallel {hi = const.) then 



div c — 



8c 

 Ts 



(XII.3) 



The divergence here is a consequence of the change in velocity in the direction of the 

 stream lines; a decrease indicates pihng up ("Stauung") and an increase indicates a 

 suction of the water masses. 



For a given current field the divergence field can be calculated numerically or gra- 

 phically and can be represented on charts; special methods for this have been given 

 by Bjerknes and co-workers (1912, 1913). 



The general continuity equation (X. 22) can be written in the form 



dp 

 dt 



+ p div c = 



for an incompressible water mass this gives 



div c = 0. 



(XII.4) 



(XII.5) 



If allowances are made for changes in density due to changes in temperature and 

 salinity, then equation (X. 21) applies and for stationary conditions one obtains: 



dpu 8pv 8pw 



8x 8y 8z 



div c = 0. 



(XII.6) 



The total horizontal water transport ("current amount") in a water column from the 

 surface (z = 0) to the bottom of the sea (z = h) is then 



A/ = pc dz 

 Jo 



and its components along the x- and j^-axes are given by 



(XII.7) 



M, 



pu dz and My = 



pv dz 



(XII.8) 



