What is the energy dissipation rate in rotating turbulence?

The scaling of the energy dissipation rate $\epsilon$ is one of the most fundamental open issues for rapidly rotating turbulence. For non-rotating 3D turbulence at large Reynolds number, it takes the classical form $\epsilon_{3D}\simeq U^3/L$, with $U$ and $L$ the characteristic velocity and length scales. Here, we propose a simple experiment aiming to probe directly the influence of the background rotation on $\epsilon$: we measure the torque $\Gamma$ acting on a propeller rotating at constant rate $\omega$ in a large volume of fluid rotating at $\Omega$ (the torque measurement being performed in the rotating frame). The normalized torque $K_p=\Gamma/(\rho R^4 H \omega^2)$ (where $R$ and $H$ are the propeller radius and height) provides a direct measure of the normalized dissipation $\epsilon / \epsilon_{3D}$ as a function of the Rossby number $Ro=\omega/\Omega$. For cyclonic propeller rotation ($Ro>0$) we find a transition between $K_p =$constant at large $Ro$ (no rotation) and $K_p\simeq Ro$ at small $Ro$ (large rotation), in agreement with weakly nonlinear rotating turbulence prediction. The situation is more intricate for anticyclonic rotation ($Ro<0$), showing a peak dissipation at intermediate $Ro$, and a decrease at small $Ro$ but with a different scaling.