For incompressible flows, the Reynolds number is the only control parameters, so that you need to match the Reynolds number.

For compressible flows, besides the Reynolds number, you will also need to consider the Mach number.

Based on the intergral scale.

Hi Wang

Thanks for your answer. To keep things simple, I would like to just focus on incompressible flows. We know that critical reynolds number for channel flow based on integral length scale is around 4000. While the critical reynolds number for homogeneous isotropic turbulence based on integral length scale is much smaller (around 400). So, matching just the reynolds number based on integral length scale might not be enough.

Hi, 

Using the following notations, l is an integral scale, say the mixing length; while L is the local length scale.

Since, in turbulent flows, the largest eddies tend to have sizes comparable to the width of the flow. Consequently, l is usually of the same order as the L. But this may not always the case and this may be the reason leads to the conflict.

Taylor length scale is an intermediate length scale between the integral scale and the Kolmogorov length scale, which may not be a proper scale in characterizing the flow behaviors.

You should read the attachment where you find some arguments how to proceed.

Article Universal equations and constants of turbulent motion