Memory function of turbulent fluctuations in soft-mode turbulence

TL;DR

This paper investigates the relaxation dynamics of soft-mode turbulence in nematic liquid crystals, revealing a dual structure linked to non-thermal fluctuations and their memory effects, which influence the turbulence's temporal behavior.

Contribution

It introduces a novel analysis of the memory function in soft-mode turbulence, distinguishing Markov and non-Markov contributions and elucidating their roles in relaxation stages.

Findings

Identification of a dual dynamical structure with a crossover point.

Memory effects from turbulent fluctuations cause time-reversible early-stage relaxation.

Spatial coherency called the patch structure underpins the memory effects.

Abstract

Modal relaxation dynamics has been observed experimentally to clarify statistical-physical properties of soft-mode turbulence, the spatiotemporal chaos observed in homeotropically aligned nematic liquid crystals. We found a dual structure, dynamical crossover associated with violation of time-reversal invariance, the corresponding time scales satisfying a dynamical scaling law. To specify the origin of the dual structure, the memory function due to non-thermal fluctuations has been defined by a projection-operator method and obtained numerically using experimental results. The results of the memory function suggest that the non-thermal fluctuations can be divided into Markov and non-Markov contributions, the latter is called the turbulent fluctuation (TF). Consequently, the relaxation dynamics is separated into three characteristic stages: bare-friction, early, and late stages. If the dissipation due to TFs dominates over that of the Markov contribution, the bare-friction stage contracts; the early and late stages then configure the dual structure. The memory effect due to TFs results in the time-reversible relaxation at the early stage, and the disappearance of the memory by turbulent mixing leads to a simple exponential relaxation at the late stage. Furthermore, the memory effect due to TFs is shown to originate from characteristic spatial coherency called the patch structure.