Reynolds number is 



E(k,t) = a e 2/3 k-5/3 



where E(k,t) and e are on a unit weight basis, a =0.3, and ^ = "j^ 

 is a measure of the eddy size. Because most of the energy is concen- 

 trated in the larger eddies, this expression can be integrated over all 

 k > k . to give the total energy without particular concern for the 

 small amount of energy attributed to those smaller eddies having a low 

 Reynolds number. Then this may be written 



E = 0.l4(e X)^/^ . 



-5 -1 -1 

 In deep water, it was shown that e < 2x10 ergs gm sec and 



E < 2" ^^95 gm (for velocities below 1 cm/sec). Substitution shows a 



\ of 3,4x10 cm to be representative of the size of the larger eddies 



if the equality signs hold for e and E . The fact that X turns out 



to be almost equal to the depth of the ocean is completely fortuitous, 



and these calculations do no more than indicate that a homogeneous ocean 



would be continuously well stirred. This conclusion would also hold for 



reasonable reductions in the values of e and E used. Inasmuch as the 



ocean is not well stirred, the theory of homogeneous isotropic turbulence 



is generally inapplicable. If water above the thermocline is treated 



-2 

 similarly, now, with E < ^ and e = 10 , X becomes 675 cm. This 



layer is actually about 10 cm deep and can be considered fairly well 

 stirred by the wind so that the theory may have possible general appli- 

 cation in this case. 



Energy is lost from the larger eddies by transfer to smaller ones. 

 Eventually eddies become small enough for velocity gradients to be large 



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