The instability of a fluid inside a precessing cylinder is studied
theoretically and experimentally. This study is motivated by
aeronautics and geophysics applications. Precessional motion forces
hydrodynamics waves called Kelvin modes whose structure and
amplitude are predicted by a linear inviscid theory. When a forced
Kelvin mode is resonant, a viscous and weakly nonlinear theory has
been developed to predict its saturated amplitude. We show that this
amplitude scales as Re1/2 for low Reynolds numbers and as
θ1/3 (where θ is the precessing angle) for high
Reynolds numbers. These scalings are confirmed by PIV measurements.
For Reynolds numbers sufficiently large, this forced flow becomes
unstable. A linear stability analysis based on a triadic resonance
between a forced Kelvin mode and two free modes has been carried
out. The precessing angle for which the flow becomes unstable is
predicted and compared successfully to experimental measurements. A
weakly nonlinear theory was developed and allowed to show that the
bifurcation of the instability of precession is subcritical. It also
showed that, depending on the Reynolds number, the unstable flow can
be steady or intermittent. Finally, this weakly nonlinear theory
allowed to predict, with a good agreement with experiments, the mean
flow in the cylinder; even if it is turbulent.