  Accretion onto Classical T Tauri stars is thought to take place through the
action of magnetospheric processes, with gas in the inner disk being channeled
onto the star's surface by the stellar magnetic field lines. Young stars are
known to accrete material in a time-variable manner and the source of this
variability remains an open problem, particularly on the shortest (~ day)
timescales. Using one-dimensional time-dependent numerical simulations that
follow the field line geometry, we find that for plausibly realistic young
stars, steady-state transonic accretion occurs naturally in the absence of any
other source of variability. However, we show that if the density in the inner
disk varies smoothly in time with ~ day long time-scales (e.g., due to
turbulence) this complication can lead to the development of shocks in the
accretion column. These shocks propagate along the accretion column and
ultimately hit the star, leading to rapid, large amplitude changes in the
accretion rate. We argue that when these shocks hit the star the observed
time-dependence will be a rapid increase in accretion luminosity followed by a
slower decline and could be an explanation for some of the short period
variability observed in accreting young stars. Our one-dimensional approach
bridges previous analytic work to more complicated, multi-dimensional
simulations, and observations.
