steady parabolic velocity for the advection term in a passive scalar equation
 

Hello everybody

Without solving the momentum and continuity equation how can I define a parabolic velocity in the advection term of a passive scalar in openfoam?

I know how to create a parabolic boundary condition but I'm not quit sure how to set a parabolic velocity profile that is not changing in all times and through the domain.

My domain is just a 2D channel (a rectangle) and I'm not solving the momentum and the continuity equations and just want to have that profile in the domain for all times.

All ideas and pointers are welcome. Thank you.