Active Flows on Curved Surfaces

Abstract

We consider a numerical approach for a covariant generalised Navier-Stokes equation on general surfaces and study the influence of varying Gaussian curvature on anomalous vortex-network active turbulence. This regime is characterised by self-assembly of finite-size vortices into linked chains of anti-ferromagnet order, which percolate through the entire surface. The simulation results reveal an alignment of these chains with minimal curvature lines of the surface and indicate a dependency of this turbulence regime on the sign and the gradient in local Gaussian curvature. While these results remain qualitative and their explanations are still incomplete, several of the observed phenomena are in qualitative agreement with experiments on active nematic liquid crystals on toroidal surfaces and contribute to an understanding of the delicate interplay between geometrical properties of the surface and characteristics of the flow field, which has the potential to control active flows on surfaces via gradients in the spatial curvature of the surface.

arXiv comment23 pages, 14 figures

References in corpus (33)

• Flocks, herds, and schools: A quantitative theory of flocking
• Meso-scale turbulence in living fluids
• Topology and Dynamics of Active Nematic Vesicles
• Topological Origin of Equatorial Waves
• Vortices in Superfluid Films on Curved Surfaces
• Emergence of active nematic behaviour in monolayers of isotropic cells
• Modelling fluid deformable surfaces with an emphasis on biological interfaces
• Incompressible fluid problems on embedded surfaces: Modeling and variational formulations
• Curvature-Induced Defect Unbinding in Toroidal Geometries
• Higher-order surface FEM for incompressible Navier-Stokes flows on manifolds
• Solving the incompressible surface Navier-Stokes equation by surface finite elements
• 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
• Geometrical control of active turbulence in curved topographies
• A finite element approach for vector- and tensor-valued surface PDEs
• Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes
• Arbitrary Lagrangian--Eulerian finite element method for curved and deforming surfaces. I. General theory and application to fluid interfaces
• Orientational order on surfaces - the coupling of topology, geometry, and dynamics
• Analysis of Finite Element Methods for Vector Laplacians on Surfaces
• Geometry-dependent viscosity reduction in sheared active fluids
• A numerical approach for fluid deformable surfaces
• Anomalous chained turbulence in actively driven flows on spheres
• Divergence-free tangential finite element methods for incompressible flows on surfaces
• Dimension reduction for the Landau-de Gennes model on curved nematic thin films
• Elastic Theory of Defects in Toroidal Crystals
• Condensate formation and multiscale dynamics in two-dimensional active suspensions
• Liquid Crystals on Deformable Surfaces
• Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations
• Nematic liquid crystals on curved surfaces - a thin film limit
• Defect order in active nematics on a curved surface
• Linearly forced fluid flow on a rotating sphere
• Nonuniversal transition to condensate formation in two-dimensional turbulence

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• The interplay of geometry and coarsening in multicomponent lipid vesicles under the influence of hydrodynamics
• Simultaneous solution of incompressible Navier-Stokes flows on multiple surfaces
• A curvilinear surface ALE formulation for self-evolving Navier-Stokes manifolds - Stabilized finite element formulation
• Effects of Rotation on Vorticity Dynamics on a Sphere with Discrete Exterior Calculus
• Vielbein Lattice Boltzmann approach for fluid flows on spherical surfaces