Helicity controls the direction of fluxes in rotating turbulence

Abstract: Turbulence sustains out-of-equilibrium fluxes that are shaped by conservation laws. Three-dimensional flows conserve energy and sign-indefinite helicity, both being transferred to small scales. Here, we uncover a dual organization of energy fluxes in 3D rotating flows, shaped by helicity. When sufficiently-fast inertial waves interact with a large-scale 2D flow, they conserve their helicity separately by sign. This causes an inverse energy transfer, from 3D to 2D motions, which promotes self-organization and spectral condensation. In contrast, slower modes exchange helicity with modes of opposite helicity sign, similarly to non-rotating 3D turbulence. This generates a forward energy transfer, from the large-scale 2D flow to small 3D scales, coexisting with the inverse transfer. We determine analytically these bi-directional energy transfers to the 2D mean flow via a quasi-linear wave-kinetic theory. The theory captures the main Reynolds number and rotation rate dependence of the mean-flow amplitude in Navier-Stokes simulations from zero to infinite rotation rates.