Is it wrong to associate non-isotropic flow high with Reynolds-Number and is there a better metric? IT is often stated the flow with high Re is not isotropic, meaning there is no uniform or dominant direction of the flow. But this seems wrong to me - -while there's certainly cases where no dominant direction of flow can be discerned in highly turbulent situations, there's for example the flow through pipes or along fast moving object where there's clearly a strong anisotropy. Even an eddy in a stirred coffee cup has an easily discernible direction of flow locally.
The Reynolds number as such tells me the relation between inertial and viscous forces - is there a number or metric that tells me how non-isotropic a flow is?
 A: All flows (high Re flows or not) are non-isotropic. Flow is a response to a non-equilibrium and occurs because of a gradient of some scalar quantity which has a preferred direction (because a  gradient is a vector). So by that note, does one need a number of any sort to quantify it? 
From a more deeper perspective, non-equilibrium flows themselves may be associated with some global entropy-like metric that enables the study of pattern formation in nature, that could be applicable a wide category of flows from convection rolls in the atmosphere to crystal formation in solids.  But it is not clear if one exists---a debate on the nature of time and the existence of the arrow of time in thermodynamics  But that is not the purpose of this question.
The OP raises some questions about the isotropic nature at the Kolmogorov scale: 
Local isotropy in high Reynolds number flow is Kolmogorov's hypothesis. At the scale that local isotropy prevails---the Kolmogorov scale---kinetic energy is dissipated by viscosity into thermal energy. In essence the momentum in the fluid packet is equivalent to random motion of its molecules, and effectively there is no bulk convective flow. Furthermore the flow is statistically isotropic. All the kinetic energy in a turbulent flow is in its large scale where the flow is non-isotropic.
