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Activity induced turbulence in driven active matter

J. K. Bhattacharjee

T. R. Kirkpatrick

School of Physical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India

Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA

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Phys. Rev. Fluids 7, 034602 – Published 15 March, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.034602

Abstract

Turbulence in driven stratified active matter is considered. The relevant parameters characterizing the problem are the Reynolds number $Re = \bar{u} L / ν$ and an active matter Rayleigh number, $R = | ζ | S^{2} L / D \bar{u}$ . Here $\bar{u}$ is the mean velocity of flow, $L$ is the system size, $ν$ is the kinematic viscosity, $ζ$ is the activity coefficient, $S$ is the concentration gradient, and $D$ is the active matter diffusion coefficient. In the mixing limit, $Re ≫ 1, R ≪ 1$ , we show that the standard Kolmogorov energy spectrum law, $E (k) \propto k^{- 5 / 3}$ , is realized. On the other hand, in the stratified limit, $Re ≫ 1, R ≪ 1$ , there is a new turbulence universality class with $E (k) \propto k^{- 7 / 5}$ . The crossover from one regime to the other is discussed in detail. Experimental predictions and probes are also discussed.

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Activity induced turbulence in driven active matter

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