The Representation of Oceanic Movements and Kinematics 



371 



Fig. 159. Stream lines around a cylindrical obstacle (island). 



of the obstacle where r — a^jr vanishes. The stream hnes of the potential flow are 

 given in Fig. 159. 



(2) Choosing F = (fl/2)z2 then 



= (a/2)(jc2 - j2) and W = axy. 



The jc-axis and the >'-axis are stream lines (^ = 0) and one obtains in that way the flow 

 towards a straight and vertical coast at which the flow divides into two branches (see 

 Fig. 155 (b)). 



(3) The function F = Az'^ leads to current cards for bays or around projecting land 

 masses where as a first approximation the boundaries can be taken as straight. Intro- 

 ducing again polar co-ordinates we obtain 



= ylr" cos ncf) and 'F = Ar"^ sin n^. 



Parts of the curves V = can be taken as solid boundaries ; this leads to sin «^ = 

 or to the lines ^ = and ^ = Trfn. Putting n = 77/a, then ^ = and <j> — a,2a, . . . 

 can be taken one after the other as the sohd boundary. This gives the irrotational flow 

 (vorticity free) between or off two straight coasts which meet each other at an angle a. 

 Fig. 160 shows some cases which are of interest. 



The configuration of coast lines and outer boundaries of ocean basins are con- 

 siderably more complex than in the simple cases which are susceptible to mathematical 

 analysis. The simple character of currents that carry water masses from a distance into 

 coastal areas will be disturbed and changed by the coast lines. An important role is 



^=180° a--'^5° a--90° 



^=270° 



Fig. 160. Stream lines off a coast as shown on the picture (triangular shape). 



