  We present results from direct numerical simulations (DNS) of oscillatory
pipe flow at several dimensionless frequencies Wo = {6.5, 13, 26} and one fixed
shear Reynolds number Re_{\tau} = 1440. Starting from a fully-developed
turbulent velocity field at that Re_{\tau}, the oscillatory flow either
relaminarises or reaches a conditionally turbulent or strongly asymmetric state
depending on Wo. The numerical method is validated by demonstrating excellent
agreement of our DNS results with experimental data and analytical predictions
from literature for the limiting cases of non-oscillating but turbulent and
oscillating but laminar pipe flow. For an oscillating turbulent pipe flow we
further found a very good agreement between qualitative descriptions of the
characteristic flow features observed in experiments and our DNS. Here, we
focus on the observation of a strongly asymmetric behaviour between the
positive and the negative half-cycles of the oscillatory pipe flow at Wo=6.5.
