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 nonequilibrium 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 nonplanar 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 antiferromagnetic 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.

Linearly forced fluid flow on a rotating sphere

“…Figures 1(a-i) show snapshots of the statistically stationary state of the dimensionless relative vorticity ζτ for a range of R/Λ and Ωτ at t/τ = 15. For Ωτ = 0, we attain solutions akin to those obtained by Mickelin et al (2018) in the non-rotating case. When the dimensionless rotation rate of the sphere Ωτ is increased, the flow becomes zonalised, that is, the φ−variation in the vorticity field decreases.…”

“…The dynamics at the poles are similar to those on a non-rotating flat plane and the non-inertial effects matter the most at the equator. method with a basis of spin-weighted spherical harmonics Vasil et al 2019); more details on the method can be found in the appendix of Mickelin et al (2018). A spectral expansion with a cut-off max = 256 was found to be sufficient to obtain converged solutions.…”

“…In all simulations, we fix the dimensionless bandwidth κΛ = 1. Narrower driving leads to a "burst mode" (Mickelin et al 2018) and wider driving leads to classical turbulence (Frisch 1995). We explore the phase space by varying the parameters R/Λ and Ωτ .…”

“…Exact stationary solutions reported previously include 3D Beltrami flows (S lomka & Dunkel 2017b) and 2D vortex lattices (S lomka & Dunkel 2017a). Furthermore, Mickelin et al (2018) recently explored GNS flows on 2D curved surfaces and constructed stationary solutions for the case of a non-rotating sphere. Here, we generalize their work by deriving exact time-dependent solutions for GNS flows on rotating spheres, and by comparing them with direct numerical simulations (figure 1).…”

Collective transport of polar active particles on the surface of a corrugated tube

“…Ellis [16] studied the effect of self-propulsion and curvature on the degree of defect unbinding. On the other hand, curvature can induce spontaneous flow and flocking [22][23][24][25][26][27][28]. Sanchez and coworkers [22] experimentally studied selfpropelled microtubule bundles on curved surfaces and reported the spontaneous generation of a streaming flow.…”