Geometry and topology of turbulence in active nematics

By L. Giomi. 2014

255 citations recorded by the source corpus.

The problem of low Reynolds number turbulence in active nematic fluids is theoretically addressed. Using numerical simulations I demonstrate that an incompressible turbulent flow, in two-dimensional active nematics, consists of an ensemble of vortices whose areas are exponentially distributed within a range of scales. Building on this evidence, I construct a mean-field theory of active turbulence by which several measurable quantities, including the spectral densities and the correlation functions, can be analytically calculated. Because of the profound connection between the flow geometry and the topological properties of the nematic director, the theory sheds light on the mechanisms leading to the proliferation of topological defects in active nematics and provides a number of testable predictions. A hypothesis, inspired by Onsager's statistical hydrodynamics, is finally introduced to account for the equilibrium probability distribution of the vortex sizes.

Subfields: Condensed Matter Physics, Materials Chemistry, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/385112fa02d260cb6df0ffa915e2d896e4b62ea0

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In Condensed Matter Physics

In Materials Chemistry

In Statistical and Nonlinear Physics

Citations in the corpus

Topological active matter (2020, background): “The consequences of self-propelled defects have been explored predominantly in 2D active nematics [67, 77, 78, 108– 110].”
Universal scaling of active nematic turbulence (2019, background): “However, he could not access sufficiently large scales to verify this prediction in simulations [40].”
Active Turbulence (2021, methodology): “Giomi analyzed the turbulent regime in two-dimensional simulations (with parameters ν 1 and γ ∼ η), focusing first on the statistical properties of the vorticity pattern [116].”
Active Particles in Complex and Crowded Environments (2016, background): “…(Sanchez et al., 2012; Schaller et al., 2010; Sumino et al., 2012), to topological defects in nematic vesicles (Keber et al., 2014), vortices in active nematics (Giomi, 2015), agitated granular matter (Narayan et al., 2007), and schools of fish and flocks of birds (Vicsek and Zafeiris, 2012).”
Symmetry, Thermodynamics, and Topology in Active Matter (2021, background): “[40] Luca Giomi, “Geometry and topology of turbulence in ac-”