Intermittency measurement in twodimensional bacterial turbulence
Abstract
In this paper, an experimental velocity database of a bacterial collective motion, e.g., Bacillus subtilis, in turbulent phase with volume filling fraction 84 % provided by Professor Goldstein at Cambridge University (UK), was analyzed to emphasize the scaling behavior of this active turbulence system. This was accomplished by performing a Hilbertbased methodology analysis to retrieve the scaling property without the β limitation. A dualpowerlaw behavior separated by the viscosity scale ℓ_{ν} was observed for the q th order Hilbert moment L_{q}(k ) . This dualpowerlaw belongs to an inversecascade since the scaling range is above the injection scale R , e.g., the bacterial body length. The measured scaling exponents ζ (q ) of both the smallscale (k >k_{ν} ) and largescale (k <k_{ν} ) motions are convex, showing the multifractality. A lognormal formula was put forward to characterize the multifractal intensity. The measured intermittency parameters are μ_{S}=0.26 and μ_{L}=0.17 , respectively, for the small and largescale motions. It implies that the former cascade is more intermittent than the latter one, which is also confirmed by the corresponding singularity spectrum f (α ) versus α . Comparison with the conventional twodimensional EkmanNavierStokes 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.
 Publication:

Physical Review E
 Pub Date:
 June 2016
 DOI:
 10.1103/PhysRevE.93.062226
 arXiv:
 arXiv:1607.07940
 Bibcode:
 2016PhRvE..93f2226Q
 Keywords:

 Physics  Fluid Dynamics;
 Physics  Biological Physics
 EPrint:
 23 pages, 7 figures. This paper is published on Physical Review E, 93, 062226, 2016