enough to permit normal viscous loss and little further diminution in 

 size takes place. Dissipation by fluid viscosity occurs at lengths 

 characterized by (Batchelor, 1953)1 



/ 3 \t 



where v , the kinematic viscosity, is .015 ( in c.g.s. units) for water. 

 For e = 2x10 ergs, ti = 0»7 cmo The velocities associated with these 

 eddies would be extremely small. 



The Stably Stratified Ocean 



In the previous section it was shown that if turbulent velocities 

 are approximately 1cm sec in homogeneous water, eddy sizes would be 

 almost equal in magnitude to the depth of the ocean. However, if a unit 

 volume of water could be moved isothermally along a vertical eddy from 

 the cold bottom of the ocean, the density difference between it and the 

 surrounding water would necessitate doing work against gravity in the amount 

 of 70,000 ergs in order to reach the surface. Because the kinetic energy 

 at depth is only of the order of an erg, the sizes of the vertical eddies 

 must be several orders of magnitude less than the depth of the ocean. 



The ability of turbulent stresses to move a fluid against gravi- 

 tational forces can be expressed quantitatively by Richardson's number 

 (Proudman 1953): 



where the denominator represents work supplied by large scale motion 

 working against the Reynolds stresses of turbulent motion. In this equation, 



■12- 



