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Through experiments, we studied defect turbulence, a type of spatiotemporalchaos in planar systems of nematic liquid crystals, to clarify the chaoticadvection of weak turbulence. In planar systems of large aspect ratio,structural relaxation which is characterized by the dynamic structure factorexhibits a long-period oscillation that is described well by a combination of asimple exponential relaxation and underdamped oscillation. The simplerelaxation arises as a result of the roll modulation while the dampedoscillation is manifest in the repetitive gliding of defect pairs in a localarea. Each relaxation is derived analytically by the projection operator methodthat separates turbulent transport into a macroscopic contribution andfluctuations. The analysis proposes that the two relaxations are notcorrelated. The nonthermal fluctuations of defect turbulence are consequentlyseparated into two independent Markov processes. Our approach sheds light ondiversity and universality from a unified viewpoint for weak turbulence.

Relaxation with long-period oscillation in defect turbulence of planar nematic liquid crystals