Currents in a Strait 519 



In addition, it is necessary to make an assumption about the dependence of the 

 friction on the current velocity. For a shallow current it is possitble to put R equal 

 to Kpu^ dyn/cm^ (see equation X.9). However, for each horizontal branch 



and the friction per unit mass of this branch is 



The total friction is therefore given by 



/c(2m)2 



and the equation (XVI. 8) thus gives an equation for the determination of the mean 

 velocity in one water body 



6 Kl p 



If the dimensions of the strait are known, w can be calculated. Only the value of the 

 Taylor frictional constant requires a little further comment. For a smooth channel 

 K has been found experimentally to be 0-0025. It cannot be expected that the value of 

 K will be as small as this because of the irregular configuration of the sea bottom and 

 sides of an actual sea strait. In rivers, for example, k may be as much as 10 times this 

 value or about 0-03. Considerably higher values of the boundary friction are there- 

 fore to be expected due to the roughness of the bottom in a somewhat wider strait. 

 A proof of this is the frequently observed sharp decrease in velocity in the layer next 

 to the bottom. 



Choosing mean values for the dimension of a sea strait, for example, / = 50 km, 

 h = 100 m and the difference in density/!/) = 10 x 10"^, according to Table 140, then 

 putting K = 0-03 the equation gives w = 28 cm/sec which accords with the average 

 velocities found by observation. In the Danish sounds (Belts) the velocity of the current 

 is about 10 cm/sec, in the Dardanelles about 25 cm/sec, in the Bosphorus 30 cm/sec, 

 in the Strait of Gibraltar 30-35 cm/sec and in the Strait of Bab el Mandeb about 

 40 cm/sec. The calculated value fits thus very well in this series of observed values. 



For a detailed theory of currents in sea straits it is necessary in the treatment of the 

 stationary state to return to the antitriptic equations of motion in which the gradient 

 force and all the frictional forces are always in equihbrium (Defant, 1930). A suitable 

 model is a rectangular channel, depth h^ and length L, connecting two seas with differ- 

 ent thermo-haline structures. Both water types are homogeneous (upper water density 

 Pi, thickness in the middle of the channel h^ ; lower water density pa^ thickness in the 

 middle of the channel h^ — fh over a plane bottom). The co-ordinate origin is placed 

 in the middle of the channel at sea level with the positive r-axis directed upwards. 

 The upper current flows in the direction of the negative .v-axis (see Fig. 239) and the 

 physical sea level must therefore also slope downwards in this direction (pure slope 

 current). The static pressure in the upper layer [z from l,^ to — {h^ — Q] will be 



