  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.
