Do inertial wave interactions control the rate of energy dissipation of rotating turbulence?

The scaling law of the energy dissipation rate, $\epsilon\propto U^3/L$ (with $U$ and $L$ the characteristic velocity and lengthscale), is one of the most robust features of fully developed turbulence. How this scaling is affected by a background rotation is still a controversial issue with importance for geo and astrophysical flows. At asymptotically small Rossby numbers $Ro=U/\Omega L$, i.e. in the weakly nonlinear limit, wave-turbulence arguments suggest that $\epsilon$ should be reduced by a factor $Ro$. Such scaling has however never been evidenced directly, neither experimentally nor numerically. We report here direct measurements of the injected power, and therefore of $\epsilon$, in an experiment where a propeller is rotating at a constant rate in a large volume of fluid rotating at $\Omega$. In co-rotation, we find a transition between the wave-turbulence scaling at small $Ro$ and the classical Kolmogorov law at large $Ro$. The transition between these two regimes is characterized from experiments varying the propeller and tank dimensions. In counter-rotation, the scenario is much richer with the observation of an additional peak of dissipation, similar to the one found in Taylor-Couette experiments.