  We demonstrate that nonlocally coupled limit-cycle oscillators subject to
spatiotemporally white Gaussian noise can exhibit a noise-induced transition to
turbulent states. After illustrating noise-induced turbulent states with
numerical simulations using two representative models of limit-cycle
oscillators, we develop a theory that clarifies the effective dynamical
instabilities leading to the turbulent behavior using a hierarchy of dynamical
reduction methods. We determine the parameter region where the system can
exhibit noise-induced turbulent states, which is successfully confirmed by
extensive numerical simulations at each level of the reduction.
