Can we differentiate flows with identical Reynolds numbers but with different turbulence intensities?

The Reynolds number is given by

$$mathrm{Re} = frac{v_{rms} L}{nu}$$

Now imagine we fix $L$, $nu$ and $v_{rms}$ – so the Reynolds number is constant. Imagine two different flows:

$$(1): bar{v} = 10, v_{rms}=1$$
$$(2): bar{v} = 20, v_{rms}=1$$

So we have a flow with 10% turbulence intensity and a flow with 5% turbulence intensity. Both these flows have the same Reynolds number, but a different mean flow velocity. Can we differentiate these two flows considering that we do not know $bar{v}$? In other words, a hypothetical situation in which we can only measure the fluctuations $v_{fluc}$.