  We present hydrodynamical models of the grand design spiral M51 (NGC 5194),
and its interaction with its companion NGC 5195. Despite the simplicity of our
models, our simulations capture the present day spiral structure of M51
remarkably well, and even reproduce details such as a kink along one spiral
arm, and spiral arm bifurcations. We investigate the offset between the stellar
and gaseous spiral arms, and find at most times (including the present day)
there is no offset between the stars and gas to within our error bars. We also
compare our simulations with recent observational analysis of M51. We compute
the pattern speed versus radius, and like the observations, find no single
global pattern speed. We also show that the spiral arms cannot be fitted well
by logarithmic spirals. We interpret these findings as evidence that M51 does
not exhibit a quasi-steady density wave, as would be predicted by density wave
theory. The internal structure of M51 derives from the complicated and
dynamical interaction with its companion, resulting in spiral arms showing
considerable structure in the form of short-lived kinks and bifurcations.
Rather than trying to model such galaxies in terms of global spiral modes with
fixed pattern speeds, it is more realistic to start from a picture in which the
spiral arms, while not being simple material arms, are the result of tidally
induced kinematic density `waves' or density patterns, which wind up slowly
over time.
