  Two-dimensional axisymmetric simulations have shown that the post-bounce
accretion shock in core collapse supernovae is subject to the Spherical
Accretion Shock Instability, or SASI. Recent three-dimensional simulations have
revealed the existence of a non-axisymmetric mode of the SASI as well, where
the postshock flow displays a spiral pattern. Here we investigate the growth of
these spiral modes using two-dimensional simulations of the post-bounce
accretion flow in the equatorial plane of a core-collapse supernova. By
perturbing a steady-state model we are able to excite both one, two and
three-armed spiral modes that grow exponentially with time, demonstrating that
these are linearly unstable modes closely related to the original axisymmetric
sloshing modes. By tracking the distribution of angular momentum, we show that
these modes are able to efficiently separate the angular momentum of the
accretion flow (which maintains a net angular momentum of zero), leading to a
significant spin-up of the underlying accreting proto-neutron star.
