  We present a model of a pulsar-driven supernova remnant, by using a
hydrodynamics code, which simulates the evolution of a pulsar wind nebula when
the pulsar is moving at a high velocity through its expanding supernova
remnant. The simulation shows four different stages of the pulsar wind nebula:
the supersonic expansion stage, the reverse shock interaction stage, the
subsonic expansion stage and ultimately the bow shock stage. Due to the high
velocity of the pulsar, the position of the pulsar is located at the head of
the pulsar wind bubble, after the passage of the reverse shock. The resulting
morphology of the pulsar wind bubble is therefore similar to the morphology of
a bow shock pulsar wind nebula. We show how to distinguish these two different
stages, and apply this method to the SNR G327.1-1.1, for which we argue that
there is no bow shock around its pulsar wind nebula.
