On a possible mechanism for the generation of cyclonic vortices regime in a precessing cylindrical container

We report experimental observations obtained by particle image velocimetry of the behavior of a flow driven by rotation and precession in a cylindrical container. This study is motivated by dynamo effect and geophysics applications. Precessional motion forces inertial waves whose amplitude are predicted by a linear inviscid theory. But, various flow regimes are identified experimentally according to the value of the control parameter $\varepsilon $ the precession rate : the ratio of the precession frequency $\Omega_{\mathrm{P}}$ to the rotation frequency $\Omega_{\mathrm{R}}$ ($\varepsilon =\frac{\Omega_{P} }{\Omega_{R} })$. When $\varepsilon $ is increased from small values, after a linear regime, we have observed a differential rotation followed by the apparition of four permanent cyclonic vortices as a consequence of instability (eruption of jets from the lateral edges of the cylinder). We propose a mechanism for this instability based on a precedent study : we have proved that the nonlinear mode coupling of two inertial waves of azimuthal wave number $m =$ 0 and $m =$ 1 (mode forced by the precession) in the inviscid regime creates differential rotation also observed experimentally at small $\varepsilon $. The profile of the azimuthal mean velocity and the corresponding axial mean vorticity both show an inflexion point in their radial profile. We show that when the control parameter $\varepsilon $ is increased from low values, the forced mode $m =$ 1 can become instable in this induced differential rotation. It could be responsible for the observed instability and for the cyclones formation within the volume after a subsequent Kelvin-Helmholtz type instability.