  We present predictions for the gravitational-wave (GW) emission of
three-dimensional supernova (SN) simulations performed for a 15 solar-mass
progenitor with the Prometheus-Vertex code using energy-dependent, three-flavor
neutrino transport. The progenitor adopted from stellar evolution calculations
including magnetic fields had a fairly low specific angular momentum (j_Fe <~
10^{15} cm^2/s) in the iron core (central angular velocity ~0.2 rad/s), which
we compared to simulations without rotation and with artificially enhanced
rotation (j_Fe <~ 2*10^{16} cm^2/s; central angular velocity ~0.5 rad/s). Our
results confirm that the time-domain GW signals of SNe are stochastic, but
possess deterministic components with characteristic patterns at low
frequencies (<~200 Hz), caused by mass motions due to the standing accretion
shock instability (SASI), and at high frequencies, associated with gravity-mode
oscillations in the surface layer of the proto-neutron star (PNS). Non-radial
mass motions in the post-shock layer as well as PNS convection are important
triggers of GW emission, whose amplitude scales with the power of the
hydrodynamic flows. There is no monotonic increase of the GW amplitude with
rotation, but a clear correlation with the strength of SASI activity. Our
slowly rotating model is a fainter GW emitter than the non-rotating model
because of weaker SASI activity and damped convection in the post-shock layer
and PNS. In contrast, the faster rotating model exhibits a powerful SASI spiral
mode during its transition to explosion, producing the highest GW amplitudes
with a distinctive drift of the low-frequency emission peak from ~80-100 Hz to
~40-50 Hz. This migration signifies shock expansion, whereas non-exploding
models are discriminated by the opposite trend.
