On the instabilities triggered in rotating flows in closed cylinders

Résumé

In this mainly experimental work, a new setup to study rotating flows has been developed. The setup consists of a cylinder split into two parts just at mid-height to let each part rotate independently. For the experimental data procured, the split cylinder is always in a corotation regime with one of the sides rotating slightly faster than the other. For the obtainment of the experimental velocity flow field, noninvasive optical devices are used. The mean and instantaneous flow are studied inside the split cylinder and compared with the literature when possible. The main focus is put on the boundary layers zone where the instabilities may happen since the background rotation is high enough to have the bulk in almost solid-body rotation, confining the instabilities, if they occur, on the boundary layers. Regarding the cylindrical wall boundary layer, time-dependent structures are found on the azimuthal component of the velocity field, whereas the Stewartson sandwich-like boundary layer is found on the axial component. Moreover, a forcing of the flow is found in form of Kelvin waves since the symmetry of the problem is broken because of a little misalignment of the sides. Due to the experimental runs are performed with a resonant aspect ratio of the first Kelvin mode, its contribution to the flow cannot be neglected. The Kelvin mode found creates a global recirculation flow and its behavior has been addressed using the linear inviscous theory. A modal analysis of the split-cylinder flow is performed to find modes that cannot be observed directly on the experimental velocity field. This analysis reveals some modes and their respective frequencies and amplitudes. A reconstruction of the flow following the linear inviscous theory is performed to corroborate the presence of the found modes. On the other hand, a pre-doctoral stay has been performed where an experimental flow created inside a cylinder in precession has been studied. This experiment has improved the knowledge of another experimental technique and the inviscous theory. The experimental runs performed have been compared with a more recent nonlinear and viscous theory finding a good agreement.