Drift towards isotropization during the 3D hydrodynamic turbulence onset

TL;DR

This paper investigates the evolution of anisotropy in 3D hydrodynamic turbulence, showing a slow drift towards isotropy during the onset of turbulence despite persistent pancake structures.

Contribution

It provides numerical evidence of slow isotropization in 3D turbulence, analyzing the evolution of isotropy markers during turbulence onset.

Findings

Isotropy markers drift slowly towards unity.

Anisotropy persists despite pancake alignment.

Isotropization occurs without viscous scale activation.

Abstract

The incompressible three-dimensional Euler equations develop very thin pancake-like regions of exponentially increasing vorticity. The characteristic thickness of such regions decreases exponentially with time, while the other two dimensions do not change considerably, making the flow near each pancake strongly anisotropic. The pancakes emerge in increasing number with time, which may enhance the anisotropy of the flow, especially if they orient similarly in space. In the present paper, we study numerically the anisotropy by analyzing the evolution of the so-called isotropy markers [Phys. Rev. Fluids 10, L022602 (2025)]. We show that these functions drift slowly towards unity, indicating the process of slow isotropization, which takes place without the viscous scales getting exited and despite the similar orientation of the emerging pancakes.