  When matter orbits around a central mass obliquely with respect to the mass's
spin axis, the Lense-Thirring effect causes it to precess at a rate declining
sharply with radius. Ever since the work of Bardeen & Petterson (1975), it has
been expected that when a fluid fills an orbiting disk, the orbital angular
momentum at small radii should then align with the mass's spin. Nearly all
previous work has studied this alignment under the assumption that a
phenomenological "viscosity" isotropically degrades fluid shears in accretion
disks, even though it is now understood that internal stress in flat disks is
due to anisotropic MHD turbulence. In this paper we report a pair of matched
simulations, one in MHD and one in pure (non-viscous) HD in order to clarify
the specific mechanisms of alignment. As in the previous work, we find that
disk warps induce radial flows that mix angular momentum of different
orientation; however, we also show that the speeds of these flows are
generically transonic and are only very weakly influenced by internal stresses
other than pressure. In particular, MHD turbulence does not act in a manner
consistent with an isotropic viscosity. When MHD effects are present, the disk
aligns, first at small radii and then at large; alignment is only partial in
the HD case. We identify the specific angular momentum transport mechanisms
causing alignment and show how MHD effects permit them to operate more
efficiently. Lastly, we relate the speed at which an alignment front propagates
outward (in the MHD case) to the rate at which Lense-Thirring torques deliver
angular momentum at smaller radii.
