  The transition from complex-periodic to chaotic behavior is investigated in
oscillatory media supporting spiral waves. We find turbulent regimes
characterized by the spontaneous nucleation, proliferation and erratic motion
of synchronization defect lines which separate domains of different oscillation
phases. The line defect dynamics is controlled by the competition between
diffusion, which reduces line length and curvature, and phase-gradient-induced
growth. The onset of each type of defect-line turbulence is identified with a
non-equilibrium phase transition characterized by non-trivial critical
exponents.
