Turbulence is ubiquitous in nature, but only now has the universal nature of active turbulence been revealed!

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Turbulence is chaotic but has universal statistical properties, and in recent years, seemingly turbulent flows have been found in active fluids such as bacterial suspensions, epithelial cell monolayers, biopolymers, and mixtures of molecular motors. In a new study published in the journal Nature Physics, scientists from the University of Barcelona, ​​Princeton University, and the Ecole Polytechnique in France have found that chaotic flows in active nematic fluids can be described by unique universal scaling laws.

Turbulence is ubiquitous in nature, from plasma flows in stars, to large-scale atmospheric and oceanic flows on Earth, to air currents caused by airplanes. Turbulence is chaotic, constantly emerging and breaking up into smaller eddies. However, when this complex chaotic behavior is considered in a statistical sense, turbulence obeys universal scaling laws. This means that the statistical properties of turbulence are independent of both how turbulence is generated and the properties of the specific fluid observed, such as its viscosity and density.

The scientists revisited this universal concept in the context of active fluids, where flows and eddies are not generated by the action of some external factor (such as temperature gradients in the atmosphere), but by the active fluid itself. The active nature of these fluids depends on their ability to generate forces internally, for example, due to bacterial swimming or the action of molecular motors on biopolymers. "When these active forces are strong enough, the fluid begins to flow spontaneously, powered by the energy injected by the active processes," explains Richard Alter, a postdoctoral researcher at Princeton University.

When the forces acting on them are strong, these spontaneous flows turn into a chaotic mixture of self-generated vortices - called active turbulence. The researchers focused on a specific type of active fluid: two-dimensional active nematic liquid crystals. They describe experimental systems such as cell monolayers, as well as suspensions of biopolymers and molecular motors. Large-scale simulations show that active flows organize into a disordered pattern of vortices of a characteristic size; studies of flows much larger than the characteristic size of the vortices show that the statistical properties of these large-scale flows follow clear scaling laws.

Professor Jaume Casademut from the Institute of Complex Systems (UBICS) of the University of Barcelona points out: "We have shown that this scaling law is universal and independent of the specific properties of the active fluid. This scaling law in active nematic fluids is equivalent to the scaling law of Andrei Kolmogorov's 1941 classical turbulence, but with a different exponent. It is the result of the combined effects of inertia-free viscous flow and the self-organizing forces within the active fluid."

Another striking result of the study is that all energy injected by active forces at a given scale is dissipated by viscous effects at the same scale. Therefore, in stark contrast to classical turbulence, no energy can be transferred to other scales. Both in simulations and analysis, the researchers demonstrated that a minimal active nematic fluid self-organizes in such a way that active energy injection precisely balances the energy dissipation at each scale.

Bo Ke Yuan | Research/From: University of Barcelona

Reference journal Nature Physics

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