[TS]-relationship and Connection with Mixing Processes and Large Water Af asses 209 



On the other hand, the chord drawn through Z perpendicular io AO intercepts an arc 

 on the [r5]-curve with a centre angle ha (the depth marks at the end-points of the 

 chord are -\-\h and —\h) and 



Z = R- RCOS ajla) + i RaW. 



Comparison of the two values for Z finally leads to an exchange coefficient 



This equation can be used for the numerical determination of A if the [r5^-curve 

 for a water column has been found by observation for successive times. In Fig. 97 I 



Fig. 96. Calculation of exchange coefficients by the method of Jacobsen. 



denotes the initial distribution which is followed by distribution II after / seconds. 

 It shows the changes that have taken place in the water column during time t. The 

 points are depth marks for the determination of h. The tangent at A cuts the [r^]- 

 curve I at the depth marks h^ and //g; the size of ^ is thus /?! — h^. The equation then 

 allows calculation of the exchange coefficient yi if Ms known. 



The Jacobsen method appUes almost only to oceanic regions which are practically 

 motionless and in which the gradual disappearance of a disturbance in the vertical 

 structure due to vertical mixing can be determined by successive measurements. An 

 application to stationary water displacements is possible using the principle 

 that phenomena occurring one after the other in time can be replaced by others 

 occurring side by side in space. Then the [r^J-diagrams I and II in Fig. 97 represent two 

 successive stations at a distance L in the direction of water displacement. If u is the 

 velocity of this displacement then L = ut and from the above relation one obtains 

 Ajpu =h ^jSL. It can be seen that this method again gives only the ratio Aju. 



