Time-Dependent Diffusion Coefficients for Chaotic Advection due to Fluctuations of Convective Rolls

Kazuma Yamanaka,Megumi Hashiguchi,Takayuki Narumi,Yoshiki Hidaka,Kazuhiro Hara,Hirotaka Okabe

doi:10.3390/fluids3040099

Kazuma Yamanaka, Megumi Hashiguchi + Show 4 more

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https://doi.org/10.3390/fluids3040099

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Abstract

The properties of chaotic advection arising from defect turbulence, that is, weak turbulence in the electroconvection of nematic liquid crystals, were experimentally investigated. Defect turbulence is a phenomenon in which fluctuations of convective rolls arise and are globally disturbed while maintaining convective rolls locally. The time-dependent diffusion coefficient, as measured from the motion of a tagged particle driven by the turbulence, was used to clarify the dependence of the type of diffusion on coarse-graining time. The results showed that, as coarse-graining time increases, the type of diffusion changes from superdiffusion → subdiffusion → normal diffusion. The change in diffusive properties over the observed timescale reflects the coexistence of local order and global disorder in the defect turbulence.

Highlights

Turbulence occurs by the cascade mechanism (Richardson cascade) because of strong nonlinearities; in ideal cases, the Kolmogorov law (K41) holds [1]
The objective of this paper is to clarify the properties of chaotic advection in the defect turbulence using the time-dependent diffusion coefficients
Subdiffusion over intermediate τ is caused by the confinement effect for the particle by being trapped in a convective roll [32]

Summary

Introduction

Turbulence occurs by the cascade mechanism (Richardson cascade) because of strong nonlinearities; in ideal cases, the Kolmogorov law (K41) holds [1]. Disorder in fluids arises even in a weakly nonlinear regime through the interaction of a few modes with long timescales based on the slaving principle [2]. In a convective system in which mean flow is hardly relaxed, the convective structure is destabilized or weakly disturbed by the interaction between the convective flow and the mean flow even in the vicinity of the convective threshold [3,4]. Because the disturbance in such cases is weak, the convective structure is globally disordered while maintaining local convective rolls. Weak turbulence that occurs in a weakly nonlinear regime near a convection threshold has been investigated as one of the experimental subjects of spatiotemporal chaos in spatially extended nonlinear systems [8,9]. Because order and disorder of different scales coexist, clarifying the differences in properties with coarse-graining scales is required in characterizing it

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