  We study the phase ordering dynamics of a uniform Bose gas in two dimensions
following a quench into the ordered phase. We explore the crossover between
dissipative and conservative evolution by performing numerical simulations
within the classical field methodology. Regardless of the dissipation strength,
we find clear evidence for universal scaling, with dynamical critical exponent
$z$ characterising the growth of the correlation length. In the dissipative
limit we find growth consistent with the logarithmically corrected law
$[t/\log(t/t_0)]^{1/z}$, and exponent $z=2$, in agreement with previous
studies. Decreasing the dissipation towards the conservative limit, we find
strong numerical evidence for the expected growth law $t^{1/z}$. However, we
observe a smooth crossover in $z$ that converges to an anomalous value
distinctly lower than $2$ at a small finite dissipation strength. We show that
this lower exponent may be attributable to a power-law vortex mobility arising
from vortex--sound interactions.
