Pseudo-invariants causing inverse energy cascades in three-dimensional turbulence

TL;DR

This paper reveals that in 3D turbulence, certain triad interactions conserve a pseudo-invariant, leading to inverse energy cascades similar to 2D turbulence, expanding understanding of flow invariants and cascade directions.

Contribution

It identifies a new pseudo-invariant conserved by specific triad interactions in 3D turbulence, explaining inverse energy cascades.

Findings

Existence of a pseudo-invariant affecting energy cascade direction.

Triad interactions can either promote forward or inverse cascades.

Theoretical and numerical evidence supports the pseudo-invariant's role.

Abstract

Three-dimensional (3D) turbulence is characterized by a dual forward cascade of both kinetic energy and helicity, a second inviscid flow invariant, from the integral scale of motion to the viscous dissipative scale. In helical flows, however, such as strongly rotating flows with broken mirror symmetry, an inverse energy cascade can be observed analogous to that of two-dimensional turbulence (2D) where a second positive-definite flow invariant, enstrophy, unlike helicity in 3D, effectively blocks the forward cascade of energy. In the spectral-helical decomposition of the Navier-Stokes equation it has previously been show that a subset of three-wave (triad) interactions conserve helicity in 3D in a fashion similar to enstrophy in 2D, thus leading to a 2D-like inverse energy cascade in 3D. In this work, we show both theoretically and numerically that an additional subset of interactions exist conserving a new pseudo-invariant in addition to energy and helicity, which contributes either to a forward or inverse energy cascade depending on the specific triad interaction geometry.