Intermittency measurement in two dimensional bacterial turbulence

Abstract

In this paper, an experimental velocity database of a bacterial collective motion , e.g., \textit{B. subtilis}, in turbulent phase with volume filling fraction $84\%$ provided by Professor Goldstein at the Cambridge University UK, was analyzed to emphasize the scaling behavior of this active turbulence system. This was accomplished by performing a Hilbert-based methodology analysis to retrieve the scaling property without the $\beta -$limitation. A dual-power-law behavior separated by the viscosity scale ${\ell }_{\nu }$ was observed for the $q$th-order Hilbert moment ${\mathcal{L}}_q(k)$. This dual-power-law belongs to an inverse-cascade since the scaling range is above the injection scale $R$, e.g., the bacterial body length. The measured scaling exponents $\zeta (q)$ of both the small-scale \red{(resp. $k>k_{\nu }$) and large-scale (resp. $k<k_{\nu }$)} motions are convex, showing the multifractality. A lognormal formula was put forward to characterize the multifractal intensity. The measured intermittency parameters are ${\mu }_S=0.26$ and ${\mu }_L=0.17$ respectively for the small- and large-scale motions. It implies that the former cascade is more intermittent than the latter one, which is also confirmed by the corresponding singularity spectrum $f(\alpha )$ vs $\alpha$. Comparison with the conventional two-dimensional Ekman-Navier-Stokes equation, a continuum model indicates that the origin of the multifractality could be a result of some additional nonlinear interaction terms, which deservers a more careful investigation.

23 pages, 7 figures. This paper is published on Physical Review E, 93, 062226, 2016

References in corpus (15)

• Meso-scale turbulence in living fluids
• The multifractal nature of turbulent energy dissipation
• Fluid dynamics of bacterial turbulence
• Turning bacteria suspensions into a "superfluid"
• Effective viscosity of microswimmer suspensions
• An amplitude-frequency study of turbulent scaling intermittency using Empirical Mode Decomposition and Hilbert Spectral Analysis
• Arbitrary-order Hilbert spectral analysis for time series possessing scaling statistics: a comparison study with detrended fluctuation analysis and wavelet leaders
• Minimal continuum theories of structure formation in dense active fluids
• Vortex arrays and meso-scale turbulence of self-propelled particles
• Vorticity statistics in the two-dimensional enstrophy cascade
• Second order structure function in fully developed turbulence
• Lagrangian single particle turbulent statistics through the Hilbert-Huang Transform
• Influence of Friction on the Direct Cascade of the 2d Forced Turbulence
• Fluid Velocity Fluctuations in a Suspension of Swimming Protists
• Hilbert Statistics of Vorticity Scaling in Two-Dimensional Turbulence

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• Taylor dispersion in two-dimensional bacterial turbulence
• Hidden Turbulence in van Gogh's \textbf{\textit{The Starry Night}}
• Cascades and Kolmogorov's lognormal scaling in two-dimensional bacterial turbulence
• Turbulent lithosphere deformation in the Tibetan Plateau