Appears in collection : 2026 - T2 - WS2 - Instabilities and transitions in geophysical flows

Turbulence is characterized by energy fluxes, whose direction is determined by conservation laws.

In 3D rotating turbulence, however, energy is observed to flow simultaneously toward large-scale two-dimensional structures and toward small-scale three-dimensional waves. Using a mean–wave kinetic theory, we derive analytical expressions for these competing bi-directional transfers in the presence of a spontaneously emergent 2D mean flow. We show the direction of the energy transfer is determined by the type of allowed 2D-3D interactions: the mean flow is fed by a sector of modes for which only same-sign-helicity interactions are allowed, while modes which have helicity-mixing interactions extract energy from it. The balance between the two sectors changes as the Rossby- and Reynolds-numbers are varied. We obtain the 2D-3D energy partition as a function of Rossby and Reynolds analytically, in agreement with fully nonlinear simulations, presenting a unified picture across rotation rates.

Co-author: Sebastien Gome