Anomalous chained turbulence in actively driven flows on spheres

Abstract

Recent experiments demonstrate the importance of substrate curvature for actively forced fluid dynamics. Yet, the covariant formulation and analysis of continuum models for non-equilibrium flows on curved surfaces still poses theoretical challenges. Here, we introduce and study a generalized covariant Navier-Stokes model for fluid flows driven by active stresses in non-planar geometries. The analytical tractability of the theory is demonstrated through exact stationary solutions for the case of a spherical bubble geometry. Direct numerical simulations reveal a curvature-induced transition from a burst phase to an anomalous turbulent phase that differs distinctly from externally forced classical 2D Kolmogorov turbulence. This new type of active turbulence is characterized by the self-assembly of finite-size vortices into linked chains of anti-ferromagnetic order, which percolate through the entire fluid domain, forming an active dynamic network. The coherent motion of the vortex chain network provides an efficient mechanism for upward energy transfer from smaller to larger scales, presenting an alternative to the conventional energy cascade in classical 2D turbulence.

arXiv comment13 pages, supplementary movies available on request; typo in fig 3(b) corrected

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• A finite element approach for vector- and tensor-valued surface PDEs
• Condensate formation and multiscale dynamics in two-dimensional active suspensions
• Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations
• Active Flows on Curved Surfaces
• Active nematodynamics on curved surfaces -- the influence of geometric forces on motion patterns of topological defects
• A numerical approach for fluid deformable surfaces with conserved enclosed volume
• Defect order in active nematics on a curved surface
• Linearly forced fluid flow on a rotating sphere
• Hydrodynamics of Quantum Vortices on a Closed Surface
• The interplay of geometry and coarsening in multicomponent lipid vesicles under the influence of hydrodynamics
• Stokes' second problem and reduction of inertia in active fluids
• Hydrodynamic interactions in polar liquid crystals on evolving surfaces
• An optimal complexity spectral method for Navier--Stokes simulations in the ball