Turbulence 



Variation in isotherm depth may be a turbulence phenome- 

 non. 15 This supposition is based on evidence that energy is 

 transferred from one spectrum component to another through 

 its transfer from large to small turbulent eddies. In larger 

 eddies, energy is received from an external driving force; in the 

 smallest eddies the same energy is transformed into heat. But 

 a subrange of eddy motion, which participates neither in energy 

 loss nor gain, passes the energy of large eddies to small eddies 

 where it is finally transformed. Within such a subrange, the 

 spectrum function must theoretically have the form: 21 



E fc) = Be 3/2 k- 5/S 



where (k) - the wave number 



E(k) = the power spectrum function 



e = the rate of conversion of turbulent 



energy to heat 

 B = a constant 



If a constant value of e is assumed to lie in this subrange, the 

 spectrum E(k) plotted as a function of k on a log-log scale must 

 have a slope of -5/3. A curve of this slope (in the appropriate 

 units of fig. 35) has been superimposed on the power spectrum 

 results of the 19° isotherm depths of section Q (fig. 15). 



This was done by using the following substitution to change 

 the units of the plot from wave number to frequency: k = f/c , 

 where c is the ship's speed. Then the above equation may be 

 rewritten as 



i*W -*«"£)" / 



5/3 



5/3 



And assuming B, e, and c are constants; the frequency spectrum 

 would have the form 



E(f)= Mf " 5/3 



where M is a constant in the inertial subrange. 



The Kolmogorov spectrum deals with three dimensions 

 whereas the above data have been measured in only one dimen- 

 sion. The vertical stability of the ocean and reduced horizontal 

 stability indicate anisotropic turbulence. However, if horizontal 



65 



