Helicity controls the direction of fluxes in rotating turbulence

Abstract

Turbulence sustains out-of-equilibrium energy fluxes shaped by conservation laws. Three-dimensional flows conserve energy and sign-indefinite helicity, both being transferred to small scales. Yet in 3D rotating turbulence, energy is observed to flow simultaneously toward large-scale two-dimensional structures and toward small-scale three-dimensional waves. We uncover the origin of this dual behavior. When sufficiently fast inertial waves interact with a large-scale 2D flow, they conserve their helicity separately by sign, enforcing an inverse transfer of energy from 3D waves to 2D motions and promoting spectral condensation. Slower modes, by contrast, exchange helicity across opposite-sign sectors and thus behave as in non-rotating turbulence, driving a forward transfer. Using a mean-wave kinetic theory, we derive analytical expressions for these competing bi-directional transfers and quantitatively predict the rotation- and Reynolds-number dependence of the large-scale 2D flow in fully nonlinear simulations, unifying the picture from zero to infinite rotation.