Universal scaling of active nematic turbulence

Abstract

A landmark of turbulence is the emergence of universal scaling laws, such as Kolmogorov's $E(q)\sim q^{-5/3}$ scaling of the kinetic energy spectrum of inertial turbulence with the wave vector $q$. In recent years, active fluids have been shown to exhibit turbulent-like flows at low Reynolds number. However, the existence of universal scaling properties in these flows has remained unclear. To address this issue, here we propose a minimal defect-free hydrodynamic theory for two-dimensional active nematic fluids at vanishing Reynolds number. By means of large-scale simulations and analytical arguments, we show that the kinetic energy spectrum exhibits a universal scaling $E(q)\sim q^{-1}$ at long wavelengths. We find that the energy injection due to activity has a peak at a characteristic length scale, which is selected by a nonlinear mechanism. In contrast to inertial turbulence, energy is entirely dissipated at the scale where it is injected, thus precluding energy cascades. Nevertheless, the non-local character of the Stokes flow establishes long-ranged velocity correlations, which lead to the scaling behavior. We conclude that active nematic fluids define a distinct universality class of turbulence at low Reynolds number.

arXiv commentUpdated journal version

References in corpus (37)

• Spontaneous motion in hierarchically assembled active matter
• Meso-scale turbulence in living fluids
• Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles
• Elastic turbulence in a polymer solution flow
• Fluid dynamics of bacterial turbulence
• Generic theory of active polar gels: a paradigm for cytoskeletal dynamics
• Spontaneous flow transition in active polar gels
• Defect dynamics in active nematics
• Velocity Correlations in an Active Nematic
• Turbulent dynamics of epithelial cell cultures
• Onset of meso-scale turbulence in living fluids
• Taming active turbulence with patterned soft interfaces
• Instabilities and Topological Defects in Active Nematics
• Mesoscopic Turbulence and Local Order in Janus Particles Self-Propelling under an AC Electric Field
• Vorticity, Defects and Correlations in Active Turbulence
• Excitable Patterns in Active Nematics
• Tuning the random walk of active colloids
• Complex Spontaneous Flows and Concentration Banding in Active Polar Films
• Cell division: a source of active stress in cellular monolayers
• Minimal continuum theories of structure formation in dense active fluids
• Vortex arrays and meso-scale turbulence of self-propelled particles
• Tunable dynamics of microtubule based active isotropic gels
• Correlation lengths in hydrodynamic models of active nematics
• Nonlinear dynamics and rheology of active fluids: simulations in two dimensions
• Active turbulence in active nematics
• Statistical Properties of Autonomous Flows in 2D Active Nematics
• The propagation of active-passive interfaces in bacterial swarms
• Active nematic materials with substrate friction
• Hydrodynamic length-scale selection and effective viscosity in microswimmer suspensions
• Phase transition to large scale coherent structures in 2d active matter turbulence
• Turbulence and turbulent pattern formation in a minimal model for active fluids
• Spontaneous mirror-symmetry breaking induces inverse energy cascade in 3D active fluids
• Polar Patterns in Active Fluids
• Multi-scale statistics of turbulence motorized by active matter
• Geometry-dependent viscosity reduction in sheared active fluids
• Multi-scale control of active emulsion dynamics
• The nature of triad interactions in active turbulence

Cited by in corpus (60)

• Active Turbulence
• Theory of defect-mediated morphogenesis
• Machine learning active-nematic hydrodynamics
• Active turbulence in microswimmer suspensions -- the role of active hydrodynamic stress and volume exclusion
• Submersed Micropatterned Structures Control Active Nematic Flow, Topology and Concentration
• Confinement controlled bend instability of three-dimensional active fluids
• A first coherent structure in elasto-inertial turbulence
• Anomalous diffusion and Lévy walks distinguish active from inertial turbulence
• Design of nematic liquid crystals to control microscale dynamics
• Pattern formation by turbulent cascades
• Edge Current and Pairing Order Transition in Chiral Bacterial Vortex
• Active boundary layers
• Introduction to topological defects: from liquid crystals to particle physics
• Tangentially Driven Active Polar Linear Polymers -- An Analytical Study
• Intermittency, fluctuations and maximal chaos in an emergent universal state of active turbulence
• Spontaneous Self-Constraint in Active Nematic Flows
• Mesoscopic Simulations of Active-Nematics
• Cascade or not cascade? Energy transfer and elastic effects in active nematics
• Probing active nematics with in-situ microfabricated elastic inclusions
• Inertia drives a flocking phase transition in viscous active fluids
• Motility-Induced Clustering and Meso-Scale Turbulence in Active Polar Fluids
• Self-mixing in microtubule-kinesin active fluid from nonuniform to uniform distribution of activity
• Confinement and collective escape of active particles
• Learning developmental mode dynamics from single-cell trajectories
• Emerging mesoscale flows and chaotic advection in dense active matter
• Coarsening in the two-dimensional incompressible Toner-Tu equation: Signatures of turbulence
• Dispersion of activity at an active-passive nematic interface
• Defect Line Coarsening and Refinement in Active Nematics
• Asymmetric fluctuations and self-folding of active interfaces
• Coexistence of active and hydrodynamic turbulence in two dimensional active nematics
• Scaling regimes of active turbulence with external dissipation
• Helical Flow States in Active Nematics
• Active turbulence and spontaneous phase separation in inhomogeneous extensile active gels
• The role of advective inertia in active nematic turbulence
• Defect Loops in Three-Dimensional Active Nematics as Active Multipoles
• A fast Chebyshev method for the Bingham closure with application to active nematic suspensions
• Lagrangian Manifestation of Anomalies in Active Turbulence
• Chirality, anisotropic viscosity and elastic anisotropy in three-dimensional active nematic turbulence
• Dynamics of a Passive Droplet in Active Turbulence
• Activity induced isotropic-polar transition in active liquid crystals
• Coexistence of defect morphologies in three dimensional active nematics
• Defect turbulence in a dense suspension of polar, active swimmers
• Friction mediated phase transition in confined active nematics
• Onset of Intermittency and Multiscaling in Active Turbulence
• Nonlinear spontaneous flow instability in active nematics
• Hydrodynamics of thermal active matter
• Fractal generation in a two-dimensional active-nematic fluid
• Boundaries control active channel flows
• An analytical and computational study of the incompressible Toner-Tu Equations
• Active Nematic Multipoles: Flow Responses and the Dynamics of Defects and Colloids
• Statistical physics of active matter, cell division and cell aggregation
• Cascades and Kolmogorov's lognormal scaling in two-dimensional bacterial turbulence
• Hydrodynamic stability and pattern formation in hexatic epithelial layers
• Irreversibility in scalar active turbulence: The role of topological defects
• Motility and self propulsion of active droplets
• Dynamical arrest in active nematic turbulence
• Instabilities and turbulence in extensile swimmer suspensions
• Nematic order condensation and topological defects in inertial active nematics
• On the temperature of an active nematic
• Critical Motility-Induced Phase Separation in Three Dimensions is Consistent with Ising Universality