Currents in a Strait 



521 



considered : adhesion to the bottom u^ = 0, ghding du^jQz = and average frictional 

 influence r](8u2ldz) = Kp^ ul. If the roughness of the sea bottom is shght the factor k 

 is of the same magnitude as k^ ; for a rough bottom it has been found in hydrauhcs 

 to be about 10 times greater. 



Solutions of equation (XVI. 11) can be given for all three cases. For the extreme 

 cases of adhering (haften) and gliding (gleiten) and with uniform atmospheric pressure 

 (I = 0) one obtains 



Slope of the physical sea level : 



2^ 



2v 



Slope of the boundary layer: /g = 7- 



Velocity of the upper layer : 

 Velocity of the lower layer : 



aiz^ - hi) + M{z + /?i). 



.(XVI. 13) 



adhering : 

 gliding 

 where 



u., = A(z + h^(z + fh) with A = 



m 



(i-) 



U2 = A [(z2 - hi) + Ih^iz + h,)] with A = 



4[\ 



l-^A 



Pi . 



and m = 4a 



3M 



Because A is always negative, the slope of the internal boundary surface will always 

 be opposite to that of the sea surface ; however, because of the density difference 

 (pa — Pi) in the denominator it is always considerably larger. The slope of the boundary 

 surface found by observation is a function of the water interchange between the two 

 seas. The currents in the two water bodies always flow in opposite directions. The 

 current profile in both water bodies is of a parabolic form. In the upper current the 

 maximum occurs at the sea surface; if the wind is in the direction of the upper current 

 it will decrease rapidly with depth, but if the wind is against the upper current the 

 decrease will be small. The upper water in this case will be piled up against the current. 

 If there is a very strong wind at the surface against the upper current, the current 

 maximum may be somewhat below the sea surface. All these theoretical conclusions 

 are in complete agreement with observation. In the lower current the velocity maximum 

 will adjust in variable depth below the boundary surface according to the variable 

 friction at the sea bottom. If there is adhesion it will appear in the middle part of the 

 lower layer, if there is gliding at the bottom it will occur at the bottom itself and for 

 moderate friction it will be situated between the discontinuity surface and sea bottom. 



Numerical values corresponding roughly to those for the Bosphorus may be taken 

 as an example: length of the strait = 30 km, depth = 70 m; upper layer p^ = 1-013 

 down to 40 m; lower layer p^ = 1-027, p2 — pi= 14 x 10"^; slope of the physical 

 sea level 6 cm in 30 km, -qj p = 250 cm^/sec, which is about the same as the frictional 

 coefficients for tidal currents; wind = 5 m/sec along the strait. For the slope of the 

 boundary surface (metres in 30 km) the equation gives the values contained in Table 

 142. 



