378 The Representation of Oceanic Movements and Kinematics 



which has been used by Okada, 1935; Thorade, 1935, in a graphical procedure for the investigation 

 of currents. Integrating it from z = to a depth z = h and replacing in a first approximation the in- 

 tegral on the left-hand side by the mean value of the individual quantities (indicated by a bar over the 

 symbol) then the following expression results 



-•--[(a -(!).]■ 



ds -ds A. 



Taking the x-axis in the direction tangential to an isoline so that dsjdx = then, since dsjdy is in- 

 versely proportional to the distance D between two isohnes, the current component v perpendicular 

 to the isoline will be given by 



Z=^[(ll-(i)o]- 



The expression in brackets on the right-hand side can be determined from observations and the velo- 

 city component can therefore be obtained. Lines of equal silicate content will in the same way give a 

 second velocity component across these lines and finally afford an estimate of the total mean velocity, 

 provided A is known by other means. Accurate determination of the isolines is, however, an essential 

 presumption in the use of this method. 



For a homogeneous sea with a homogeneous current structure the relationship 

 (XII. 10) {u and v independent of r) takes the simple form 



di (du dv\ 



It can also be readily derived from the continuity equation. It can be used to judge 

 the accuracy with which the vertical mass transport can be deduced from the distribu- 

 tion of the current flow vector. Thereby it shows immediately that for its evaluation 

 the deeper the sea the more accurately the horizontal distribution of u and v must be 

 known. The use of this relationship is thus hmited to shallow shelf seas. Here, par- 

 ticularly in representations of tidal currents, it allows the corresponding vertical 

 tide to be deduced (Defant, 1925). If c is the velocity of the tidal current 



C = Cq cos {at + e), 

 ^ = ^0 sin (at + e), 

 then using (XII. 1) the relation (XII. 16) can be given the form 



8i h 8 



Insertion of values for c and ^ gives the equation 



which is independent of the time. Now the following cases may occur (see Fig. 1 63) 

 (1) Parallel stream Unes 



8n = const, and ^0 = ■ ^-. 



a OS 



Assuming Co = 100 cm, for the distance 8s between two stations 50 km and for 

 h = 50 m, then one obtains for the semidiurnal tide (or = Itt 112-3 h) the necessary 



