396 



General Theory of Ocean Currents in a Homogeneous Sea 



that the diffusion coefficient i^ is a function of the neighbour-distance / and is given 

 by the equation 



F{1)=^ 



(/i - kf 

 2t ' 



(XIII.24) 



where /q is the distance between the elements which are at the same distance in the 

 turbulent current at time / = 0, while / is the distance at time /. F can be determined 

 from experimental series-measurements from the values for / and this allows a de- 

 cision as to whether the Fick or the Richardson concept of the internal nature of the 

 turbulence fits the observed data; since according to the Fickian theory F must be 

 independent on / (see also, Ichve, 1950). All the observations made (Richardson, 

 1926; Witting, 1933; Stommel, 1949; Hanzawa, 1953; Inoue, 1952) show that F 

 is in fact strongly dependent on / and that there exists a definite relationship between 



them of the special form 



F(l) = f/4/3. (XIII.25) 



Figure 167a shows a summary of observed data and it is easily seen that the assump 

 tion of a 4/3 power seems to be fully justified. 



10"' 10 10^ 10^ lO" 10^ 10^ 10^ 10^ 



Fig. 167a. The relation /^(/) = e/*'^ according to observations (logarithmic scale): points, 



values of Richardson from the atmosphere; crosses, values of Stommel (Blaimore, Bermuda 



and Woods Hole); triangles, values of Hanzawa. 



Equation (XIII.25) which has been found inductively has been given a sound theor- 

 etical basis by closer study of the rate of the energy decrease due to turbulent mixing 

 of the large-scale motion. This method of investigation was first introduced by Kol- 

 MOGOROFF (1941) and after some intermediate work Weiszacker (1948) and Heisen- 

 BERG (1948) have brought this statistical theory of turbulence to a certain degree of 



