Correlations and Scales

Estimates for Taylor Microscales

From Equation (3) it follows that

,

(11)

where the Kolmogorov time scale is given by

.

(12)

This means that the Taylor microscale is not a characteristic length of the dissipation eddies. It, however, provides a useful artificial length scale for estimating the velocity gradients of the small eddies when macroscopic velocity scale is used for the velocity of the eddies. That is, Equations (1) and (11) imply that

.

(13)

Other useful estimates are

, , .

(14)

Also

, , .,

(15)

and

.

(16)