Module 5 :
Lecture 17 : More on Scaling Relations


It is to be mentioned that the Taylor microscale is not a fundamental length scale since it involves the use of the integral velocity scale in its estimate of dissipation. Actually dissipation occurs at the other end of energy spectrum from the integral scale where is relevant. Thus the Taylor microscale is a ‘mixed' scale combining large scale and small scale quantities.

However, it plays a meaningful role in estimating

 

The following relationships are found to be useful



(17.3)
(17.4)

The Taylor microscale Reynolds number is

 

This Reynolds number can be interpreted as the ratio of the large-eddy time scale, and the time-scale of the strain rate fluctuations.