Abstract
In this chapter, we review both theoretical and experimental studies on active turbulence, especially bacterial turbulence. Hydrodynamic flows created by bacteria usually destabilize alignment, leading to turbulent states without any long-range order. Such turbulent states resemble fluid turbulence in spite of their low Reynolds number. Hydrodynamic theories have succeeded in describing the properties of bulk unconstrained bacterial turbulence, but the boundary conditions of active turbulence remain unknown. Recent experiments have found that bacterial turbulence geometrically confined in droplets or in microfluidic devices can self-organize in vortex states, which suggests the importance of boundary conditions to understand macroscopic behavior of bacterial turbulence. At the end of this chapter, we summarize what needs to be experimentally investigated for a better understanding.
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Notes
- 1.
In addition to energy conservation, enstrophy is also conserved in two-dimensional fluid turbulence. This additional conservation law modifies the exponent in two-dimensional turbulence from that in three-dimensional turbulence.
- 2.
Of course, such a model with a few variables might not precisely describe actual phenomena, but this can be a first step toward a full understanding of active turbulence.
- 3.
Puller-type microswimmers swim by pulling fluid in front of them, and consequently the fluid behind the body is drugged toward the swimmers. Therefore, a single puller-type microswimmer can be denoted as a force dipole directing inward.
- 4.
Note that this \(\varvec{v}\) is the velocity field only for bacteria, not for fluid. We neglect the dynamics of ambient fluid.
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Nishiguchi, D. (2020). Active Turbulence. In: Order and Fluctuations in Collective Dynamics of Swimming Bacteria. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-32-9998-6_4
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DOI: https://doi.org/10.1007/978-981-32-9998-6_4
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