First observation of turbulence in dense algal suspensions

TL;DR

The study reports the first observation of turbulence in dense algal suspensions that lack nematic or polar order, demonstrating that turbulence can arise in isotropic, non-swarming micro-swimmer systems. Through velocity-field reconstruction and statistics such as $E(k)$ and $\Phi(k)$ spectra, non-Gaussian velocity PDFs, intermittency metrics, and Okubo-Weiss analysis, the authors identify a distinct regime of active turbulence in algal monolayers, with $E(k) \sim k^{1/4}$ at small $k$ and $E(k) \sim k^{-9/2}$ at large $k$ and strong intermittency. They compare wild-type and mbo2 mutant strains, find dynamic heterogeneity without a full active-glass transition at studied densities, and argue that existing models fail to capture algal-turbulence statistics, suggesting a potential universal aspect of active turbulence and implications for biological mixing and transport.

Abstract

Active turbulence arises typically in systems ranging from microorganisms and biopolymers to synthetic colloids, where chaotic flows are closely associated with motile topological defects in collectively swarming suspensions. Here, we report the first experimental observation of turbulence in a fundamentally different class of systems: dense monolayers of motile unicellular alga Chlamydomonas reinhardtii that exhibit neither orientational order nor topological defects. Nevertheless, the system displays rich spatiotemporal flow patterns with pronounced small-scale intermittency. We uncover strongly non-Gaussian velocity distribution, a feature distinct from both bacterial and classical fluid turbulence. Furthermore, we observe power-law regimes in the kinetic energy spectra, characterized by unique scaling exponents. Not only do our results provide compelling evidence for active turbulence in systems devoid of nematic or polar structures, but they also challenge current theoretical models. Our work opens new avenues for understanding emergent dynamics in active-matter systems and suggests intriguing biological implications, including enhanced mixing and transport in dense cell suspensions.

Figures (26)

• Figure 1: Time-lapse images of the motion of an isolated (a) wild-type (WT) and (b) mbo2 C. reinhardtii cell [scale bar, $10$ microns]. The flagella of the cells in these images have been highlighted manually for clarity. Experimentally measured beat-averaged flow-fields of isolated (c) WT and (d) mbo2 C. reinhardtii cells; the arrow indicates the direction of motion. (e) Interpolated velocity-vectors, overlaid on the image of a dense suspension of WT C. reinhardtii cells. The supplementary video V7 shows its spatiotemporal evolution.
• Figure 2: (a) Optical image of a suspension of WT C. reinhardtii cells, with average density $\bar{\rho} = 0.63$ [scale bar, $50$ microns]; pseudocolor plots of (b) the density and (c) the vorticity $\omega$ fields, for the image shown in (a). Panels (d), (e), and (f) are the mbo2 C. reinhardtii counterparts of (a), (b), and (c), respectively.
• Figure 3: (a)-(b) Log-log plots of the energy spectra $E(k)$, compensated by different powers of $k$ and plotted versus $ka_w$ for WT cells with $\bar{\rho} = 0.47, 0.61, 0.74$; (c) Log-log plots of the concentration spectra $\Phi(k)$, plotted versus $ka_w$. Panels (d), (e), and (f) are the mbo2 C. reinhardtii counterparts of (a), (b), and (c), respectively. Dark-gray shading indicates scaling regions. Our data are averaged over different samples with similar values of $\bar{\rho}$ (within $\simeq 10\%$ of the mean); the error-bars denote one-standard-deviation ($\varsigma$), i.e., $\pm \varsigma (E(k)/E_0)(ka_w)^\frac{-1}{4})$, $\pm \varsigma ((E(k)/E_0)(ka_w)^\frac{9}{2})$ and $\pm \varsigma (\Phi(k)$. We define $E_0 = \sum E(k)$.
• Figure 4: Semilog plots of different probability distribution functions (PDFs): PDFs of (a) the $x$-component of the velocity field $\bm{u}$ and (b) the Okubo-Weiss parameter $\Lambda$ [Eq. \ref{['eq:Okubo']}] for WT C. reinhardtii cells and different mean densities $\bar{\rho}$. Panels (c) and (d) are the mbo2 C. reinhardtii counterparts of (a) and (b), respectively.
• Figure 5: Semilog plots, for WT C. reinhardtii cells, of (a) the PDFs of longitudinal-velocity increments of the velocity field $\bm{u}$, for different mean densities $\bar{\rho}$ and the separation $l/a_w = 5.37$. (b) the flatness $F_4$ [Eq. \ref{['eq:flat']}] versus $l/a_w$ for different values of $\bar{\rho}$. The plots in (c) and (d) are the mbo2-mutant counterparts of those in (a) and (b), respectively. Our data are averaged over different samples with similar values of $\bar{\rho}$ (within $\simeq 10\%$ of the mean); the error bars denote $\pm \varsigma(F_4)$.