[rdemyan]

I have a system where the injection of energy is essentially in one dimension. I'm not clear on how to calculate the Taylor microscale. As I understand it, there can be isotropic turbulence on a very small scale even if the large-scale eddies are anisotropic.

The Taylor microscale is given by (taken from wikipedia):




where <v'> is the root mean square of the velocity fluctuations. In general, for velocity fluctuations in three dimensions:




The issue is that the rms velocity for the Taylor microscale is based on the large-scale eddy velocity fluctuations (and not the velocity scale of the Taylor microscale itself). As I understand it, isotropy is often assumed on the large scale so that:



So for isotropic turbulence, equation 1 (first equation in this text) yields:



But if, in reality, there is only a fluctuation in one direction for the large scale eddies, how can I calculate the isotropic Taylor microscale?