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Multifractal dynamics of turbulent flows in swimming bacterial suspensions.

We experimentally investigate the self-propelled two-dimensional turbulent flows of Escherichia coli suspensions in thin liquid films at two different cell concentrations. It is found that the flow has fluctuating vortices with a broad range of scales and intensities through the nonlinear interaction of the swimming bacteria. Increasing cell concentration increases the total propelling power and the nonlinear interaction. It causes the generation of vortices with larger scale, lower frequency, and higher intensity. It also widens the histograms of the flow velocity and the velocity increment between two spatially separated points with more stretched non-Gaussian tails. From the scaling analysis of the structure function S(q)(r) of the qth moment of the velocity increment between two points with spatial separation r, nonlinear relations between the scaling exponent ζ(q) of S(q)(r) and q are found for both cell concentrations, which manifests the multifractal dynamics. The multifractality can be enhanced by increasing cell concentration.