The Representation of Oceanic Movements and Kinematics 



379 



Scq = —14 cm/sec = —0-25 nautical miles per hour. This horizontal change in the 

 maximum velocity component is well within the accuracy of measurement. 

 (2) Divergent stream lines for a constant velocity (cq = const.) : 



u 



hCff 8a 

 a 8n' 



For identical a, l,^ and h and taking again the distance between two stream lines, 

 8n = 50 km and Cq as 50 cm/sec one obtains — Sa = 0-284 angle units or about 16 

 degrees of arc. This divergence is usually easily readable from charts of tidal currents. 

 The method thus gives results of sufficient accuracy provided the ocean depth is not 

 too great ; for example, it has been apphed successfully to the evaluation of the tidal 

 conditions of the North Sea (see Vol. II). 



Where the structure of the sea has two or more layers a relationship of the form 

 of (XII. 16) can be derived for each boundary surface between two successive super- 

 imposed layers. These relations fix the time changes in the inclination and position 

 of the boundary surfaces as a function of the divergence of the currents in the indi- 

 vidual layers. 



5. The Knudsen Relations 



The relations for the current amount (XII. 1 1) and for the sahnity amount (XII. 14) 

 allow an insight into the current conditions in more or less exactly limited oceanic 

 regions such as sea straits and river mouths and others. Knudsen (1900) derived some 

 simple laws of this type which are based fundamentally on these relations and just 

 because of their simplicity and clearness lead directly to valuable conclusions about 

 the general current conditions in such areas. 



In straits, river mouths and also in the open ocean lighter (low saline) water often 

 spreads out over heavier (more saline) ; in such cases the currents in the two layers 

 are mostly of opposite direction. In Fig. 1 64 A and B are two vertical cross-sections 



Fig. 164. Water and salt transport through sea straits. 



through such an oceanic region (for instance a strait). If the mean salinities are s 

 and s' at A and B in the upper current and z and z' in the lower current and the 

 current amounts are / and /' in the upper current and u and u' in the lower, then, under 

 steady conditions the constancy of water and salt transport in each current will give 

 the equations 



I = u 



u ; IS = U2 



I s = u z 



