  We present results from a suite of three-dimensional global hydrodynamic
simulations which show that spiral density waves propagating in circumstellar
disks are unstable to the growth of a parametric instability that leads to
break-down of the flow into turbulence. This spiral wave instability (SWI)
arises from a resonant interaction between pairs of inertial waves, or
inertial-gravity waves, and the background spiral wave. The development of the
instability in the linear regime involves the growth of a broad spectrum of
inertial modes, with growth rates on the order of the orbital time, and results
in a nonlinear saturated state in which turbulent velocity perturbations are of
a similar magnitude to those induced by the spiral wave. The turbulence induces
angular momentum transport, and vertical mixing, at a rate that depends locally
on the amplitude of the spiral wave (we obtain a stress parameter $\alpha \sim
5 \times 10^{-4}$ in our reference model). The instability is found to operate
in a wide-range of disk models, including those with isothermal or adiabatic
equations of state, and in viscous disks where the dimensionless kinematic
viscosity $\nu\le 10^{-5}$. This robustness suggests that the instability will
have applications to a broad range of astrophysical disk-related phenomena,
including those in close binary systems, planets embedded in protoplanetary
disks (including Jupiter in our own Solar System) and FU Orionis outburst
models. Further work is required to determine the nature of the instability,
and to evaluate its observational consequences, in physically more complete
disk models than we have considered in this paper.
