Helicity — the correlation between velocity and vorticity — is a topological invariant of inviscid fluid flow, measuring the linkage and knottedness of vortex lines. In turbulence, it's conserved alongside energy in the inviscid limit, and both cascade through the inertial range. The standard picture separates forward (small-scale) and inverse (large-scale) cascades cleanly.
Oujia, Briard, Jain, and Bretherton show the picture is wrong when helicity is sign-indefinite. Global helicity can be zero while each circularly polarized branch of the wave field carries sign-definite helicity. The decomposition into polarization branches reveals structure invisible to the global measure.
The key finding: sign-definite helicity per branch enables upscale energy transfer — backscatter — even within a predominantly forward cascade. The energy flows from small to large scales through the helical channel while simultaneously flowing from large to small scales through the total energy channel. The two cascades coexist because they operate on different projections of the same velocity field.
In weak turbulence theory, the helicity spectrum follows H(k) ~ k^{-5/3}, the same scaling as the energy spectrum. But the amplitudes differ by branch: the positive and negative helicity branches carry different energy densities, and their asymmetry controls the net direction of helical energy transfer. When one branch dominates, the transfer is forward. When they're comparable, backscatter appears.
Helicity is not one quantity. It's two, labeled by polarization. The global zero can hide two large, opposite-sign contributions whose imbalance controls the direction of energy flow.