It is shown that spiral density waves in astrophysical disks can undergo nonlinear resonance and scatter to waves with lower azimuthal wavenumber. The process is a fluid analog to nonlinear Landau damping, in which two linear modes exchange energy, mediated by a virtual beat mode. The scattering rate is calculated for a thin fluid disk model, using a weak turbulence expansion. It is shown that down-scattering is related to outward angular momentum transport and hence plays a role in mass accretion.
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Mattor et al. (1996) studied this question.