Anomalous chained turbulence in actively driven flows on spheres

TL;DR

This paper develops a covariant Navier-Stokes model for active flows on curved surfaces, revealing a curvature-induced transition to a novel active turbulence characterized by vortex chains and energy transfer mechanisms.

Contribution

It introduces a generalized covariant model for active turbulence on curved surfaces and demonstrates exact solutions and novel turbulence regimes not seen in classical models.

Findings

Curvature induces a transition from burst to active turbulence.

Active turbulence features vortex chains with anti-ferromagnetic order.

Energy transfer occurs via vortex chain networks, differing from classical cascades.

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.