  We study numerically the formation of a vortex lattice inside a rotating
bucket containing superfluid helium, paying attention to an important feature
which is practically unavoidable in all experiments: the microscopic roughness
of the bucket's surface. We model this using the Gross-Pitaevskii for a
weakly-interacting Bose gas, a model which is idealised when applied to
superfluid helium but captures the key physics of the vortex dynamics which we
are interested in. We find that the vortex lattice arises from the interaction
and reconnections of nucleated U-shaped vortex lines, which merge and align
along the axis of rotation. We quantify the effects which the surface roughness
and remanent vortex lines play in this process.
