  Following the exact decomposition in eigenstates of helicity for the
Navier-Stokes equations in Fourier space [F. Waleffe, Phys. Fluids A 4, 350
(1992)] we introduce a modified version of helical shell models for turbulence
with non-local triadic interactions. By using both an analytical argument and
numerical simulation, we show that there exists a class of models, with a
specific helical structure, that exhibits a statistically stable inverse energy
cascade, in close analogy with that predicted for the Navier-Stokes equations
restricted to the same helical interactions. We further support the idea that
turbulent energy transfer is the result of a strong entanglement among triads
possessing different transfer properties.

Fluid Dynamics