Decaying turbulence and developing chaotic attractors

TL;DR

This paper investigates how competing attractors related to homogeneity and isotropy influence the decay of turbulence, revealing that rotational symmetry can dominate during intermediate decay stages, supported by DNS data.

Contribution

It demonstrates the dominance of rotational symmetry attractors in intermediate turbulence decay stages, highlighting the role of different integrals in controlling chaotic attractors.

Findings

Rotational symmetry attractor dominates in intermediate decay stages

DNS data supports the dominance of Loitsyanskii integral-controlled attractor

Translational symmetry attractor develops later in the decay process

Abstract

Competition between two main attractors of the distributed chaos, one associated with translational symmetry (homogeneity) and another associated with rotational symmetry (isotropy), has been studied in freely decaying turbulence. It is shown that, unlike the case of statistically stationary homogeneous isotropic turbulence, the attractor associated with rotational symmetry (and controlled by Loitsyanskii integral) can dominate turbulent local dynamics in an intermediate stage of the decay, because the attractor associated with translational symmetry (and controlled by Birkhoff-Saffman integral) is still not developed enough. The DNS data have been used in order to support this conclusion.