  Evolution of the parametric decay instability (PDI) of a circularly polarized
Aflv\'en wave in a turbulent low-beta plasma background is investigated using
3D hybrid simulations. It is shown that the turbulence reduces the growth rate
of PDI as compared to the linear theory predictions, but PDI can still exist.
Interestingly, the damping rate of ion acoustic mode (as the product of PDI) is
also reduced as compared to the linear Vlasov predictions. Nonetheless,
significant heating of ions in the direction parallel to the background
magnetic field is observed due to resonant Landau damping of the ion acoustic
waves. In low-beta turbulent plasmas, PDI can provide an important channel for
energy dissipation of low-frequency Alfv\'en waves at a scale much larger than
the ion kinetic scales, different from the traditional turbulence dissipation
models.
