  In magnetized plasma situations where magnetic fields intersect massive
conducting boundaries, "line-tied" boundary conditions are often used,
analytically and in numerical simulations. For ideal MHD plasmas, these
conditions are arrived at given the relatively long time scales for magnetic
fields penetrating resistively into good conductors. Under line-tied boundary
conditions, numerical simulations often exhibit what could be construed as
numerical "noise" emanating from the boundaries. We show here that this "noise"
is real. By combining numerical and analytical methods, we highlight the
existence of boundary layers near the conductors and confirm the appearance of
short wavelength structures riding on long wavelength features. We conclude
that for numerical fidelity the boundary layers need to be resolved. Boundary
layer widths scale as the square root of the plasma \b{eta}.
