  We consider torsional oscillations of magnetars. This problem features rich
dynamics due to the strong interaction between the normal modes of a magnetar's
crust and a continuum of Magneto-Hydro-Dynamic (MHD) modes in its fluid core.
We study the dynamics using a simple model of a magnetar possessing a uniform
magnetic field and a thin spherical crust. Firstly, we show that global
torsional modes only exist when one introduces unphysically large dissipative
terms into the equations of motion; thus global modes are not helpful for
understanding the magnetar Quasi-Periodic Oscillations (QPOs). Secondly, we
solve the initial-value problem by simulating the sudden release of an
initially strained crust and monitoring the subsequent crustal motion. We find
that the crustal torsional modes quickly exchange their energy with the MHD
continuum in the core, and decay by several orders of magnitude over the course
of about 10 oscillation periods. After the initial rapid decay, the crustal
motion is stabilized and several time-varying QPOs are observed. The dynamical
spectrum of the simulated crustal motion is in qualitative agreement with that
of the x-ray light-curve in the tail of a giant magnetar flare. The asymptotic
frequencies of some of the QPOs are associated with the special spectral
points--the turning points or edges--of the MHD continuum, and are not related
to those of the crust. The observed steady low-frequency QPO at 18 Hz is almost
certainly associated with the lowest frequency of the MHD continuum, or its
first overtone. We also find that drifting QPOs get amplified when they come
near the frequencies of the crustal modes. This explains why some of the
observed QPOs have frequencies close to the expected crustal frequencies, and
why these QPOs are highly variable with time.
