  Through experiments, we studied defect turbulence, a type of spatiotemporal
chaos in planar systems of nematic liquid crystals, to clarify the chaotic
advection of weak turbulence. In planar systems of large aspect ratio,
structural relaxation which is characterized by the dynamic structure factor
exhibits a long-period oscillation that is described well by a combination of a
simple exponential relaxation and underdamped oscillation. The simple
relaxation arises as a result of the roll modulation while the damped
oscillation is manifest in the repetitive gliding of defect pairs in a local
area. Each relaxation is derived analytically by the projection operator method
that separates turbulent transport into a macroscopic contribution and
fluctuations. The analysis proposes that the two relaxations are not
correlated. The nonthermal fluctuations of defect turbulence are consequently
separated into two independent Markov processes. Our approach sheds light on
diversity and universality from a unified viewpoint for weak turbulence.
