434 General Theory of Ocean Currents in a Homogeneous Sea 



the vortex formation is repeated periodically corresponding to these bottom waves. 

 Figure 186a shows this case for the Northern Hemisphere ; there is a current curvature 

 cum sole above the ridges and contra solem above the troughs. If the sea surface has an 

 overall slope so that already at a larger distance from the ridge a current at right angles 

 to the ridge is produced then a current field will be formed similar to that shown in 



(a) 



(b) 



Fig. 186. Stream line pattern: (a) for currents crossing a wave-form bottom configuration; 

 (b) for the crossing of a single bottom ridge (Northern Hemisphere, according to V. Bjerknes 



and co-workers). 



Fig. 1 86^. The stream lines approach the ridge directly at right angles and pass over 

 it bending cum sole on the forefront side and contra solem in its rear and then finally 

 return to their original direction. This latter curvature in the rear can, however, only 

 occur if there is a convergence on the lee side which is stronger than the divergence on 

 the forefront side. 



Recently, Gortler (1941) has gone into this problem more carefully taking into 

 consideration the frictional effects also. The mathematical formulation is different as 

 compared with the previous one and shows an improvement in so far as it leads to 

 simpler basic equations which are more likely to be solved quantitatively. The results 

 otherwise agree with those obtained previously. Gortler dealt mainly with a case 

 similar to that above. The bottom ridge was assumed to have a vertical profile 

 ^ = Po{l + cos (2ttII)x} with|jc| < y and h = outside this region. A horizontal 

 projection of the stream lines of the main current is shown in Fig. 187 in the same way 

 as in Fig. 185, but here friction has been considered. For an insight into the frictional 

 effect the dimensionless quantity hrlH is decisive where hr depends on the frictional 

 depth and H is the depth of the sea. This quantity usually appears in the expression 

 G = (Rll)l(hrlH), where R = [///gives the radius of inertia associated with the 

 current velocity U (equation XIII.26), with which the flow approaches the obstacle. 

 The different curves in Fig. 1 87 show for a fixed value of Rjl the effect on the course of 

 the stream lines of the disturbance in the equilibrium between gradient and Coriolis 

 force above the ridge due to the generation of a "secondary" current. When C is 3 



