Homogeneous Isotropic Turbulence 



For turbulent motion to be homogeneous in a medium, it is neces- 

 sary tfet the statistical properties of the velocity fluctuations be 

 identical at all points of the medium. Because the ocean has boundaries, 

 the turbulence could not be homogeneous unless most of the eddies had a 

 size that is small compared to^ say, the depth of the ocean. If, in ad- 

 dition, the ocean were a homogeneous fluid, with no temperature or density 

 gradients, it is possible that these smaller eddies would produce velocity 

 fluctuations which are similar in all directions; ioe. , the turbulence 

 would be isotropic as well as homogeneous. 



The ocean is not a homogeneous liquid. Nevertheless, if the turbu- 

 lent eddies are small enough, the effect of the density gradients in turn 

 might prove to be so small that the existing theory of homogeneous isotropic 

 turbulence can be applied to obtain a useful first approximation of the 

 turbulent motion. 



Instead of trying to determine whether homogeneous isotropic turbu- 

 lence takes place in the ocean, or not, it would be more convenient to 

 assume that it does and then determine whether the associated size of the 

 eddies is consistent with known conditions in the ocean. This could be 

 done if the total energy, E , of the turbulent motion were known together 

 with the ratBj g, , at which heat is produced as a result of the viscous 

 motion. Upper limits for these two quantities were established in the 

 preceding section. 



The theory of homogeneous turbulence (Batchelor, 1953) shows the 

 energy density . E(k,t) , associated with particular eddy sizes at high eddy 



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