  Increasing observational and theoretical evidence points to binary white
dwarf mergers as the origin of some if not most normal Type Ia supernovae (SNe
Ia). In this paper, we discuss the post-merger evolution of binary white dwarf
(WD) mergers, and their relevance to the double-degenerate channel of SNe Ia.
We present 3D simulations of carbon-oxygen (C/O) WD binary systems undergoing
unstable mass transfer, varying both the total mass and the mass ratio. We
demonstrate that these systems generally give rise to a one-armed gravitational
spiral instability. The spiral density modes transport mass and angular
momentum in the disk even in the absence of a magnetic field, and are most
pronounced for secondary-to-primary mass ratios larger than $0.6$. We further
analyze carbon burning in these systems to assess the possibility of
detonation. Unlike the case of a $1.1 + 1.0 M_{\odot}$ C/O WD binary, we find
that WD binary systems with lower mass and smaller mass ratios do not detonate
as SNe Ia up to $\sim8-22$ outer dynamical times. Two additional models do
however undergo net heating, and their secular increase in temperature could
possibly result in a detonation on timescales longer than those considered
here.
