374 



The Representation of Oceanic Movements and Kinematics 



rrrTTTTTrr. 

 Fig. 162c. Formation of eddies behind a sharp edge and their growth. 



4. Divergence of the Current Field and the Continuity Equation 



The current field for a horizontal movement can give information about the place 

 where vertical water movements must occur within the field. Since, on the one hand, 

 in an incompressible medium, divergent and convergent stream lines must be asso- 

 ciated with vertical displacements and on the other hand for parallel stream lines, 

 velocity changes will lead to water accumulations (piling up of water; "Wasser- 

 stauungen") which will also cause vertical movements. Quantitative relationships can 

 be derived from the following considerations. 



If A A' and BB' in Fig, 163 denote two adjacent stream lines, ds and ds' are elements 

 of these, c and c' are two lines of equal velocity in the current field and 8n as well 

 as 8n' are the parts of these lines between the stream lines, then it is possible to calcu- 

 late the amount of water flowing through the small area ABA'B' — ds 8n in unit 

 time. This outflow per unit area is termed the divergence of the current field and is 

 indicated by div c. It is a measure of the divergence and convergence of the stream 

 lines and also of the velocity. One therefore obtains 



div c = 



1 



dsSn 



[c'B„' - an] = I + I, f = ^ I (^ ««). (XII.I) 



If the velocity along the stream lines is constant (c — const.) and the small angle be- 

 tween the tangents to the two adjacent stream lines is denoted by 5a then the curve 

 divergence is given by 



c dSn 8a 



div c = ^ -^ = c Y-' 

 on OS on 



(XII.2) 



