Helicity conservation simplifies the weak-turbulence kinetic equation, yielding a unique scale-invariant spectrum for constant energy flux while same-branch triads produce systematic backscatter even in direct cascades.
Fjørtoft, On the changes in the spectral distribution of kinetic energy for two-dimensional, nondivergent flow, Tellus5, 225 (1953)
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Sign-Indefinite Helicity and the Structure of Weak Turbulence in Inertial and Non-Hermitian Waves
Helicity conservation simplifies the weak-turbulence kinetic equation, yielding a unique scale-invariant spectrum for constant energy flux while same-branch triads produce systematic backscatter even in direct cascades.