  Measurements of solar wind turbulence reveal the ubiquity of discontinuities.
In this study, we investigate how the discontinuities, especially rotational
discontinuities (RDs), are formed in magnetohydrodynamic (MHD) turbulence. In a
simulation of the decaying compressive three-dimensional (3-D) MHD turbulence
with an imposed uniform background magnetic field, we detect RDs with sharp
field rotations and little variations of magnetic field intensity as well as
mass density. At the same time, in the de Hoffman-Teller (HT) frame, the plasma
velocity is nearly in agreement with the Alfv\'{e}n speed, and is field-aligned
on both sides of the discontinuity. We take one of the identified RDs to
analyze in details its 3-D structure and temporal evolution. By checking the
magnetic field and plasma parameters, we find that the identified RD evolves
from the steepening of the Alfv\'{e}n wave with moderate amplitude, and that
steepening is caused by the nonuniformity of the Alfv\'{e}n speed in the
ambient turbulence.
