Transition from Direct to Inverse Cascade in Three-Dimensional Turbulence

Direction of energy transfer among the scales in a turbulent flow has asignificant role in the macroscopic properties of the flow. It has been arguedthat the dimensionality and the ideal invariants of the flow determine thedirection of the cascade of energy. Because of two sign definite invariants,energy and enstrophy, of two-dimensional turbulence, energy is transferredbackwards from small scales to larger scales and enstrophy is transferred tosmaller scales. However in three-dimensions, while energy is sign-definite, theother invariant helicity does not have a definite sign and therefore there isno constraint on the direction of transfer. It is merely an empiricalobservation that the energy and helicity cascade to the smaller scales in athree-dimensional turbulent flow. Many systems, however, show bidirectionalsplit energy transfer, e.g., flows under strong rotation and stratification, inthin layers or under external magnetic field. The appearance of inverse energyflux in such systems are often considered as a result of enhancement ofquasi-2D Fourier interactions in a 3D background. We designed a model system[1] where the triadic interactions in Navier-Stokes equations are enhanced orsuppressed in a controlled manner without affecting the degrees of freedom,ideal invariants or breaking any of the symmetries of NSE. In our numericalsimulations that uses the tool of helical decomposition of velocity Fouriermodes, we introduced a parameter (0 ≤ λ ≤ 1) that controls therelative weight among homochiral triads and all the others in the nonlinearevolution. We show that by using this weighting protocol the turbulentevolution displays a sharp transition, for a critical value of the controlparameter, from forward to backward energy transfer but still keeping thedynamics fully three dimensional, isotropic, and parity invariant. [1] G Sahoo, A Alexakis and L Biferale, Phys. Rev. Lett. 118, 164501 (2017).