  Recent observations of the Mira AB binary system have revealed a surrounding
arc-like structure and a stream of material stretching 2 degrees away in
opposition to the arc. The alignment of the proper motion vector and the
arc-like structure shows the structures to be a bow shock and accompanying
tail. We have successfully hydrodynamically modelled the bow shock and tail as
the interaction between the asymptotic giant branch (AGB) wind launched from
Mira A and the surrounding interstellar medium. Our simulations show that the
wake behind the bow shock is turbulent: this forms periodic density variations
in the tail similar to those observed. We investigate the possiblity of
mass-loss variations, but find that these have limited effect on the tail
structure. The tail is estimated to be approximately 450,000 years old, and is
moving with a velocity close to that of Mira itself. We suggest that the
duration of the high mass-loss phase on the AGB may have been underestimated.
Finally, both the tail curvature and the rebrightening at large distance can be
qualitatively understood if Mira recently entered the Local Bubble. This is
estimated to have occured 17 pc downstream from its current location.
