380 The Representation of Oceanic Movements and Kinematics 



If the mean salinities are known these relationships give the Knudsen relations in the 

 form 



z' z — s s s' z — s _ 



/' = / - -, ,; u = i J u = i- -_-, ;. (XII.19) 



z z — s z z z — s 



If the upper current is known at one point and the distribution of salinity is known 

 at two, these relations allow an evaluation of the mean water transports at different 

 cross-sections in the strait; if no current amount is known they give at least the inflow 

 and outflow conditions which in itself is valuable. 



If section A is taken so far inland within the river mouth that only fresh water is 

 present {s = 0, as well as z and u = 0), then it is the mean water amount carried by 

 the river seawards per second and from (XII. 19) 



/' = / -A — ^ and u' = / -j^ — ;. (XII.20) 



A longitudinal section given by F. L. Ekman for the Gotaelf showed s = 18,2' = 22%o 

 so that /' = 5-5 7 and u = 4-5 / that is /' \u' = \\ : 9. The thickness of the upper cur- 

 rent was 3 m, that of the lower current was 9 m and thus in one second there was a 

 flow of 1 1 volume units per unit area seawards in the upper current compared with a 

 flow of 3 units upstream in the lower current. 



Another example given by Knudsen refers to the Baltic. Cross-section B\ cross- 

 section through the outlets of the Baltic (the Oresund and a section from Gedser to 

 Darsserort) ; cross-section A : the entire surface of the Baltic and sections through 

 all the river mouths. Here / in (XII. 21) was the entire amount of water entering the 

 Baltic per sec due to precipitation, evaporation and run off by rivers. From the salinity 

 distribution is obtained s' = 8-7 and z' = 17-4%o from which it follows that /' = 2/ 

 and u' = i. Thus the upper current carries twice as much water out through all the 

 outlets of the Baltic as is carried into the Baltic by the lower current and the amount 

 of water flowing in with the lower current is equal to the actual inflow from other 

 sources (precipitation, evaporation and river water). Since /' = / + u' only half the 

 outflow is derived from fresh-water gain, the other half is balanced by the inflow in 

 the lower current from the sea. 



In a third example Knudsen placed the cross-section A through the Oresund and the Kadet-channel 

 and cross-section B through the Kattegat from Fomas to the Skalle Riff. K\A,s= 8-7 and z = 17-4%o; 

 however, at B, s' = 20 and z' = 33%o. With these values the relationships XII, 20 give /' = 1-27/, 

 u' = 0-77 / so that /' : u' = 1-65. 



The amount of water flowing out through the Kattegat section is about 5/4 times greater than that 

 flowing in from the actual Baltic Sea through the Oresund and the Kadet-channel, that is, it is about 

 2-5 times larger than the total gain of the Baltic in fresh water. It is also found that the amount of 

 salt water flowing in into the Kattegat from the south is about 1-5 times larger than the amount of 

 salt water flowing in into the Baltic. This amount of water is the same as half the entire inflow into 

 the Baltic and indeed penetrates into the western part of the Baltic but mixes with the upper current 

 and is carried out again. 



A further example is given by the oceanographic conditions in the Bosporus. At a 

 cross-section at the south-west end salinity measurements (September-October 1917 

 and May 1918; Moller, 1928) gave . = 37-65 and s = 17-47%o with the boundary 

 surface at a depth of 23 m ; however, a cross-section at the north-east end gave z' = 

 35-79 and .y' = 17-23%,,, the boundary surface depth being 44 m. From (XII. 19) 



