Anomalous Chained Turbulence in Actively Driven Flows on Spheres.

Area of Science:

• Fluid dynamics
• Nonlinear physics
• Soft matter physics

Background:

• Substrate curvature significantly impacts actively forced fluid dynamics.
• Theoretical challenges persist in covariant formulation of continuum models for nonequilibrium flows on curved surfaces.

Purpose of the Study:

• Introduce and analyze a generalized covariant Navier-Stokes model for active stresses on nonplanar geometries.
• Investigate fluid dynamics on curved surfaces, specifically focusing on active stresses and their emergent behaviors.

Main Methods:

• Developed a generalized covariant Navier-Stokes model.
• Derived exact stationary solutions for spherical bubble geometry.
• Performed direct numerical simulations to observe flow dynamics.

Main Results:

• Identified a curvature-induced transition from a burst phase to an anomalous turbulent phase.
• Observed self-assembly of finite-size vortices into linked chains with antiferromagnetic order.
• Demonstrated an active dynamic network facilitating upward energy transfer, unlike classical 2D Kolmogorov turbulence.

Conclusions:

• The covariant Navier-Stokes model provides analytical tractability for active flows on curved surfaces.
• Active turbulence on curved surfaces exhibits unique characteristics, including vortex chain networks and anomalous energy transfer.
• This work offers a new perspective on turbulence and energy cascades in active systems.