  We investigate the dynamical instability of the one-armed spiral m=1 mode in
differentially rotating stars by means of 3+1 hydrodynamical simulations in
Newtonian gravitation. We find that both a soft equation of state and a high
degree of differential rotation in the equilibrium star are necessary to excite
a dynamical m=1 mode as the dominant instability at small values of the ratio
of rotational kinetic to potential energy, T/|W|. We find that this spiral mode
propagates outward from its point of origin near the maximum density at the
center to the surface over several central orbital periods. An unstable m=1
mode triggers a secondary m=2 bar mode of smaller amplitude, and the bar mode
can excite gravitational waves. As the spiral mode propagates to the surface it
weakens, simultaneously damping the emitted gravitational wave signal. This
behavior is in contrast to waves triggered by a dynamical m=2 bar instability,
which persist for many rotation periods and decay only after a
radiation-reaction damping timescale.
