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Area of Science:

  • Physics
  • Fluid Dynamics
  • Biophysics

Background:

  • Active turbulence in bacterial suspensions like Bacillus subtilis exhibits complex dynamics.
  • Understanding scaling behavior is crucial for characterizing these systems.
  • Experimental data from Professor Goldstein's lab provides a unique dataset.

Purpose of the Study:

  • To analyze the scaling behavior of bacterial active turbulence.
  • To investigate multifractality without beta-limitation using Hilbert-based methods.
  • To compare experimental findings with continuum models.

Main Methods:

  • Analysis of an experimental velocity database of Bacillus subtilis.
  • Application of a Hilbert-based methodology for scaling property retrieval.
  • Characterization of multifractal intensity using a log-normal formula.

Main Results:

  • Observed a dual-power-law behavior in the qth-order Hilbert moment, separated by the viscosity scale.
  • Identified convex scaling exponents indicating multifractality in both small- and large-scale motions.
  • Measured intermittency parameters (μS=0.26, μL=0.17) showing higher intermittency in small-scale motion.

Conclusions:

  • The observed dual-power-law scaling is characteristic of an inverse cascade in active turbulence.
  • Multifractality is a key feature of this bacterial collective motion.
  • Additional nonlinear terms in continuum models may explain the observed multifractality.