204 [TS]-relationship and Connection with Mixing Processes and Large Water Masses 



observation can also thereby be replaced by an approximate, rather more correct 

 value. Only in this way is it possible to perform an objective and satisfactory "inter- 

 polation" of oceanographic values in order to fill gaps (missing data) in the observa- 

 tional material. 



3. The [r5'] -curve and the Mixing of Water Masses 



If two homogeneous water masses are mixed in any given proportion, the mixture 

 will have a definite [rSJ-curve. Each of the two homogeneous water masses is 

 characterized by the two points, 1 {s^, §i) and 2 {s2, i dz), in the co-ordinate system, 

 proceeds in the ordinary way; if two masses are mixed in the ratio nti : Wg then the 

 mixing final temperature and salinity of the mixture will be given by 



-& = 



mi + /«2 



s = 



m^Si + AWa^a 



m^ 



nu 



An example is presented in Fig. 94 where a homogeneous water mass U (10°, 35%o) 

 from 100 m to 500 m depth is situated above a second mass Z (5°, 34-5%o) which extends 

 down to a depth of 900 m (Defant and WiJST, 1930). These two homogeneous water 

 masses are represented in the [7'5']-diagram by the two points U and Z. The boundary 

 surface at 500 m depth, which is initially a sharp physical discontinuity surface, 

 gradually disappears due to mixing. Different stages of this destruction of the dis- 

 continuity is shown on the left-hand side of Fig. 94 (Defant, 1929). It is obvious that, 

 whatever the ratio of mixing of the two water masses may be, the mixture will be 

 represented on the diagram only by points lying between U and Z. However, the 

 graphical construction shows that all points of the mixture must be situated on the 

 straight line from U to Z and that only the depth changes on this line according to the 

 intensity of mixing. This is readily shown theoretically (Defant, 1935). It can also 

 be demonstrated that the distance of any point along the straight line from the two 

 end-points (representing the two original water types) is inversely proportional to the 

 ratio of mixing, the result of which is the mixed water type at the point in question. 

 It is thus simple to determine from the position of a point relative to the end-points 

 U and Z in Fig. 94 to what degree (in percentage) the final mixed water mass under 

 consideration is composed of each of the original water types. 



The case where three water types are mixed is illustrated in Fig. 95. The three types 

 are: 



The thermal boundary surface at 500 m disappears in the same way as in the pre- 

 vious case. The salinity boundary surface does the same up to the time when the inter- 

 mediate water mass Z becomes involved in its total height in the mixing process and in 

 that way is slowly destroyed at its core. An advanced stage of this is shown in the 



