Transition from Direct to Inverse Cascade in Three-Dimensional Turbulence*

We study a model system [1] where the triadic interactions in Navier-Stokes equations are enhanced or suppressed in a controlled manner without affecting neither the total number of degrees of freedom nor the ideal invariants and without breaking any of the symmetries of original equations. Our numerical simulations are based on the helical decomposition of velocity Fourier modes. We introduced a parameter (0 ≤ λ ≤ 1) that controls the relative weight among homochiral and heterochiral triads in the nonlinear evolution. We show that by using this weighting protocol the turbulent evolution displays a sharp transition, for a critical value of the control parameter, from forward to backward energy transfer but still keeping the dynamics fully three dimensional, isotropic, and parity invariant. [1] G Sahoo, A Alexakis and L Biferale, Phys. Rev. Lett 118, 164501 (2017).