The Three-dimensional Temperature Distribution and its Variation in Time 103 



Thereby, it was assumed that a small particle of water passing through the unit sur- 

 face is not immediately mixed completely with the surrounding water but is mixed in 

 the proportion 1 : n. For the velocity in a turbulent flow, n would be equal to zero 

 and the exchange coefficient A for the property s (eddy conductivity and eddy diff"us- 

 ivity) would then be less than the eddy viscosity coefficient -q. Determinations of A 

 and T] also verify this. Table 41 gives list of such determinations measured in currents 

 in different parts of the oceans. 



It can be seen that -q is of the order of 100-200 or more while A is of the order of 

 5^0, on the average about 20 g cm^^ sec^^ The ratio -qjA is of the order 5-20. 

 Taking an average value of about 10, then Afrj = l-2n, n = 0-45, that means that the 

 small quanta of water in random movement are mixed with the surrounding water 

 only to the extent of about 45% of their mass and accordingly the temperature and 

 salinity, for example, tend towards the values of their surroundings at this rate. This 

 value is not unreasonable considering the difficulty of mixing water of different densi- 

 ties and the constant tendency for water masses of different densities to separate 

 again. 



The exchange equation applied to the pair heat-temperature has the same form as 

 that for the molecular thermal conductivity (p. 50), except that the thermal conduc- 

 tivity coefficient a = {^lcj,p) is replaced by the quantity CpA (specific heat x exchange 

 coefficient). The exchange coefficient A is of course not constant and will vary from 

 layer to layer. Taking a mean value of about 20 g cm-^ sec~^, then since Cj, is 

 approximately equal to 1, Cj,A will be about 15,000 times greater than a. The molecular 

 thermal conductivity is thus of no importance compared with the eddy conductivity 

 (dynamical convection). The thermal conductivity equation for turbulent heat trans- 

 port is therefore 



d^_A 8^& 



Tt~'^ a?' 



where A is assumed to be independent of the depth. If this is not the case the equation 



is 



8^ _l 8 / 8^ 

 Tt^'p 8z y-^ 



Temperature changes at the surface will be transmitted much more rapidly by turbu- 

 lent thermal conductivity down to the deep-ocean layers. For the process of molecular 

 heat conductivity surface disturbances were shown to require a half-value time of 

 some miUions of years (see Table 40), however, for conductivity it would take only 

 some hundreds of years according to Table 42. Indeed, in the upper layers surface 

 changes will penetrate downwards by turbulent action remarkably rapidly; only a few 

 days are required to spread completely through the layer down to 50 m. Periodic 

 changes will of course reach deeper. For values for A of 20 and 100 gcm~^ sec~^ 

 the amplitude of a diurnal variation will decrease to 1/100 of its value at the surface 

 in 34 and 75 m, respectively. For the annual variation the corresponding values are 

 644, 1440 m, respectively. This corresponds better with the values given by tem- 

 perature observations. 



