Poiseuille Profiles at varying viscosity

My aim was to capture the variation in velocity profile for flows at different viscosity values. I’m assuming the normalised shape of the velocity profiles is going to change given different lattice viscosities, and have implemented a code to demonstrate this. However at different viscosity values the normalised velocity profile (U/Umax) are identical for each case.

The velocity magnitudes are higher with a less viscous fluid, but I was expecting the shape of the normalised profiles to vary which does not seem to be the case. I have a feeling this may just be the way fluid flows work but can someone confirm this for me?

Yes, the Poiseuille profile is universal, at least in a laminar regime. At high Reynolds number, and if you break the symmetry inherent to lattice Boltzmann and to the lattice, turbulent structures will appear. But in a laminar, stationary regime, the velocity profile always corresponds to a parabola which is zero on the walls and maximal in the middle.

Thanks for confirming that for me, makes sense, shouldnt of taken me so long to realise…