Large scale flow instabilities in rotating flows

Background rotation affects the dynamics of fluid flows with a combination of linear and nonlinear effects, according to the relative importance of the Coriolis acceleration compared to the convective and forcing terms in the Navier-Stokes equation. We perform experiments on a turbulent flow ($Re_{\lambda}\sim150$) electromagnetically forced in a confined tank put on a rotating table, and we measure the flow using Particle Tracking Velocimetry. We focus here on the anisotropic effects of rotation at the large scales, and we define the Rossby number $Ro_f=\frac{U_f^2/L}{2\Omega U_f}$ based on the forced velocity scale $U_f$. With a mild rotation of $0.2~\mathrm{s^{-1}}$ ($Ro_f\sim1.8$), we observe an enhancement of horizontal and vertical velocity gradients of the large scale flow, but the overall forced flow pattern remains stable. When the rotation is increased to $2.0~\mathrm{s^{-1}}$ ($Ro_f\sim0.2$), we observe instead the dampening of the velocity gradients at large scales, while the forced flow pattern strongly fluctuates. With a strong rotation of $5.0~\mathrm{s^{-1}}$ ($Ro_f\sim0.07$), the stability of the forced mean flow structures is finally restored.