Self-organization and transition to turbulence in isotropic fluid motion driven by negative damping at low wavenumbers

TL;DR

This paper reports a symmetry-breaking transition from turbulence to a self-organized, large-scale flow in low Reynolds number isotropic fluid motion driven by negative damping, revealing new insights into flow organization.

Contribution

It demonstrates the existence of a transition to a self-organized state in isotropic turbulence at low Reynolds number through direct numerical simulation.

Findings

Transition to a flow with energy only at the lowest wavenumber

Vanishing skewness indicating symmetry breaking

Flow becomes a Beltrami flow with aligned vorticity and velocity vectors

Abstract

We observe a symmetry-breaking transition from a turbulent to a self-organized state in direct numerical simulation of the Navier-Stokes equation at very low Reynolds number. In this self-organized state the kinetic energy is contained only in modes at the lowest resolved wavenumber, the skewness vanishes, and visualization of the flows shows a lack of small-scale structure, with the vorticity and velocity vectors becoming aligned (a Beltrami flow).