Instability of precession driven Kelvin modes: Evidence of a detuning effect

We report an experimental study of the instability of a nearly-resonant Kelvin mode forced by precession in a cylindrical vessel. The instability is detected above a critical precession ratio via the appearance of peaks in the temporal power spectrum of pressure fluctuations measured at the end-walls of the cylinder. The corresponding frequencies can be grouped into frequency sets satisfying resonance conditions with the forced Kelvin mode. We show that one triad is associated with a parametric resonance of Kelvin modes. For the first time, we observe a significant frequency variation of the unstable modes with the precession ratio. We explain this frequency modification by considering a detuning mechanism due to the slowdown of the background flow. By introducing a semi-analytical model, we show that the departure of the flow from the solid body rotation leads to a modification of the dispersion relation of Kelvin modes and to a detuning of the resonance condition. Our calculations reproduce the features of experimental measurements. We also show that a second frequency set, including one very low frequency as observed in the experiment, does not exhibit the properties of a parametric resonance between Kelvin modes. Our observations suggest that it may correspond to the instability of a geostrophic mode.