478 Ocean Currents in a Non-homogeneous Ocean 



current does not turn with depth, or the current directions at all depths will lie in 

 one and the same vertical plane. Since for frictionless motion the current follows the 

 isobars and these coincide with the stream lines, D will be identical with equation 

 pCV.2). Except at special disturbance locations (discontinuity surfaces, discontinuity 

 layers and fronts) the stream Hnes therefore will also coincide with the isolines at all 

 depths. 



If turbulent friction should also be taken into account, it is necessary to go back to 

 the general equations of motion and elimination of p leads to the equation 



P^e.^a^s,^,^ (XV.4) 



dx cy By ex j oz^ 



For a simple potential flowzJ = and the condition of parallehsm of stream lines and 

 density lines still applies. If, however, a vortical motion has to be dealt with, this 

 parallelism will be lost. 



The angle at which they intersect will depend on the turbulence and on the water depth. It can be 

 shown that now 



tan y = -^r— , 



where I, = dvjdx — duldy denotes the vertical vorticity component. If the co-ordinate system is placed 

 in the direction of the average current, then f = 0. At the sea surface assuming a linear pressure 

 gradient (Ap = 0) and a decrease of velocity with depth u = \a z^ (sea bottom z = 0) as well as a 

 depth of water h, is obtained 



tan y = j— . 

 fpir 



For fflp = 200 cnr/sec and/= 10-^ sec-i (at about 45° N.) 



tany=(^) 



if the depth of water H is measured in metres. For a large water depth y will be almost zero; if the 

 water is shallow (shelf seas) it may reach values of 10-20°. 



Summarizing, it may be stated that for steady frictionless currents in a non-homogen- 

 eous sea the isolines of the different oceanographic factors and the stream lines must 

 coincide, but in the presence of strong turbulence especially in shallow seas this 

 parallelism is lost. 



Attempts have very often been made in oceanography to deduce the current field 

 from the distribution of the temperature and the salinity and other factors. In general, 

 such deductions are permissible and the method gives results corresponding reasonably 

 with reality, but deductions from isoline charts should not be taken as more than 

 indications of the rough course of the currents. However, exactly at the point where the 

 current field is of particular interest (near discontinuity surfaces and fronts) the method 

 fails completely (Castens, 1931). 



These arguments are connected with the "law of parallel fields" (Helland-H.\nsen 

 and Ekman, Ekman, 1923). Comparison of the distribution of the oceanographic 

 factors at different depths shows the striking phenomenon that the isolines at any 

 particular depth are parallel to each other, and moreover that they are parallel also 



