Abstract

Three-dimensional (3D) turbulence is characterized by a dual forward cascade of both kinetic energy and helicity, a second inviscid flow invariant besides energy, 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 (reversed) energy cascade can be observed analogous to that of two-dimensional turbulence (2D) where enstrophy, a second positive-definite flow invariant, 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 shown 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 an inverse energy cascade depending on the specific triad interaction geometry.