102 The Three-dimensional Temperature Distribution and its Variation in Time 

 salinity) and j is a function of z only, then at the unit surface as a first approximation 



ds 



s = s, + ^z, 



where Sf is the value in the surface where z = 0. Every small particle of water passing 

 through the surface from below will take with it an amount w„ s^, while those from 

 above will carry an amount m^ s^. The final exchange flux S through the unit surface 

 upwards can be expressed as the difference 



S = I^m^Su — ^tn^Sai 



whereby the summation has to be taken for all the small particles moving upwards 

 and downwards through the surface. Now 



ds J ds 



Su = -^z + 3^ ^w and s^ = Sf + —Za, 



where the values of Zy are all negative and the values of z^ are all positive. This gives 



8s 

 S = {Sm^z^ — i:maZa) ^^ . 



Considering the different signs of z, the quantity in brackets gives a negative sum 

 —Em I z I , where every small mass m of water moving through the surface is now 

 multiplied by the initial absolute distance | z | from the unit surface. This sum de- 

 pends only on the state of turbulence of the flow. Schmidt has called it the 

 "Austausch (exchange) coefficient" t]. It has the dimensions g cm~^ sec~^. The basic 

 equation for the exchange is thus 



The most important exchange quantities involved in oceanographic turbulent trans- 

 fer processes are: heat-temperature, salt-salinity, gas amount-gas content, number of 

 organisms-organism content. The flow momentum-flow speed also follows this law 

 (see later). 



It appears that the assumption that every small quantum of water starts from its 

 initial position with a property s corresponding to the mean vertical distribution at 

 that point does not entirely accord with the actual conditions. Only for the pair 

 flow momentum-velocity does there appear to be a complete and immediate equaliza- 

 tion of the velocity diff'erences. For all other properties a correction must be applied 

 to the above basic equation. Ertel (1942) has attempted to take these circumstances 

 into account, and obtained the equation 



ds ds 



S = -^(X - 2n) -= - A j^. 



