  The merger of two white dwarfs (WDs) creates a differentially rotating
remnant which is unstable to magnetohydrodynamic instabilities. These
instabilities can lead to viscous evolution on a time-scale short compared to
the thermal evolution of the remnant. We present multi-dimensional hydrodynamic
simulations of the evolution of WD merger remnants under the action of an
$\alpha$-viscosity. We initialize our calculations using the output of eight WD
merger simulations from Dan et al. (2011), which span a range of mass ratios
and total masses. We generically find that the merger remnants evolve towards
spherical states on time-scales of hours, even though a significant fraction of
the mass is initially rotationally supported. The viscous evolution unbinds
only a very small amount of mass $(< 10^{-5} M_\odot)$. Viscous heating causes
some of the systems we study with He WD secondaries to reach conditions of
nearly dynamical burning. It is thus possible that the post-merger viscous
phase triggers detonation of the He envelope in some WD mergers, potentially
producing a Type Ia supernova via a double detonation scenario. Our
calculations provide the proper initial conditions for studying the long-term
thermal evolution of WD merger remnants. This is important for understanding WD
mergers as progenitors of Type Ia supernovae, neutron stars, R Coronae Borealis
stars and other phenomena.
