  Classical phase space flow is inviscid. Here we show that in quantum phase
space Wigner's probability current J can be effectively viscous. This results
in shear suppression in quantum phase space dynamics which enforces Zurek's
limit for the minimum size scale of spotty structures that develop dynamically.
Quantum shear suppression is given by gradients of the quantum terms of J's
vorticity. Used as a new measure of quantum dynamics applied to several
evolving closed conservative 1D bound state systems, we find that shear
suppression explains the saturation at Zurek's scale limit and additionally
singles out special quantum states.
