The cyclone-anticyclone asymmetry in decaying rotating turbulence

The statistics of the vorticity fluctuations in decaying rotating turbulence is experimentally investigated by means of particle image velocimetry. Two series of experiments have been carried out, one in a small-scale rotating water tank (FAST, Paris), with an aspect ratio $\sim O(1)$, and the other one in the large-scale `Coriolis' plateform (LEGI, Grenoble), with an aspect ratio $\sim O(10)$. In both experiments, turbulence is generated by rapidly towing a grid through the fluid, providing an initial state which is approximately homogeneous and isotropic. The asymmetry between cyclones and anticyclones is characterized by the vorticity skewness $S_\omega = \langle \omega_z^3 \rangle / \langle \omega_z^2 \rangle^{3/2}$ ($\omega_z$ is the vorticity component along the rotation axis). During the decay, for times up to the Ekman timescale, a growth of the asymmetry towards cyclonic vorticity is observed as $S_\omega \sim (\Omega t)^{0.6 \pm 0.1}$. For larger times, a re-symmetrization of the vorticity fluctuations take place, due to the non-linear Ekman pumping which preferentially affects the cyclonic vorticity. While the power-law growth is generic of both experiment, the maximum value of $S_\omega$ is shown to depend on the experiment size.