Inverse energy cascade in three-dimensional isotropic turbulence

TL;DR

This paper demonstrates that an inverse energy cascade can occur in three-dimensional isotropic turbulence, highlighting the role of helicity and challenging the notion that such phenomena are solely due to external anisotropic effects.

Contribution

The study shows that inverse energy cascade occurs in 3D isotropic flows by modifying Navier-Stokes equations to include only specific helical interactions, revealing intrinsic 3D mechanisms.

Findings

Inverse energy cascade observed in 3D isotropic turbulence.

Helicity plays a key role in energy transfer.

Both 2D and 3D turbulence properties coexist naturally.

Abstract

In turbulent flows kinetic energy is spread by nonlinear interactions over a broad range of scales. Energy transfer may proceed either toward small scales or in the reverse direction. The latter case is peculiar of two-dimensional (2D) flows. Interestingly, a reversal of the energy flux is observed also in three-dimensional (3D) geophysical flows under rotation and/or confined in thin layers. The question is whether this phenomenon is enforced solely by external anisotropic mechanisms or it is intimately embedded in the Navier-Stokes (NS) equations. Here we show that an inverse energy cascade occurs also in 3D isotropic flow. The flow is obtained from a suitable surgery of the NS equations, keeping only triadic interactions between sign-defined helical modes, preserving homogeneity and isotropy and breaking reflection invariance. Our findings highlight the role played by helicity in the energy transfer process and show that both 2D and 3D properties naturally coexist in all flows in nature.