Turning now to the question about the eddies that benefit most from the energy transfer across the wave number . According to the equation

(25.1)

Energy transfer depends on the ability of the strain rate to align the smaller eddies so that and become different. The general tendency of eddies is to move towards a state where , and are equal in the absence of a strain rate. This tendency is called "return to isotropy". The lack of isotropy that is generated by the strain rate depends on the time scale for "return to isotropy" relative to the time scale of the straining motion. Since the strain rate has the dimension of (time) ^-1, the time scale of “return to isotropy” could be roughly taken as for the eddies of wave number . In other words is of the order of time for eddies of size to return to isotropy once the strain rate is removed. As we have seen above smaller eddies have larger s( ) and thus will return to isotropy faster.

Denoting to be the combined strain rate of all eddies with wave numbers below , the time scale of the applied strain rate is of order 1/ . If is large compared to s( ), the anisotropy is large. If is small compared to s( ) , the relatively rapid return to isotropy prevents the creation of a large anisotropy. This leads to the formulation that anisotropy is proportional to /s( ) . The energy transferred from all larger eddies to an eddy of wave number is

(25.2)

This follows from Eq. ( 25.1) if we note that can be written as E( ) and the total applied strain rate is modified by the anisotropy factor /s( ).