  We quantify the strength of the waves and their impact on the energy cascade
in rotating turbulence by studying the wave number and frequency energy
spectrum, and the time correlation functions of individual Fourier modes in
numerical simulations in three dimensions in periodic boxes. From the spectrum,
we find that a significant fraction of the energy is concentrated in modes with
wave frequency $\omega \approx 0$, even when the external forcing injects no
energy directly into these modes. However, for modes for which the period of
the inertial waves $\tau_\omega$ is faster than the turnover time
$\tau_\textrm{NL}$, a significant fraction of the remaining energy is
concentrated in the modes that satisfy the dispersion relation of the waves. No
evidence of accumulation of energy in the modes with $\tau_\omega =
\tau_\textrm{NL}$ is observed, unlike what critical balance arguments predict.
From the time correlation functions, we find that for modes with $\tau_\omega <
\tau_\textrm{sw}$ (with $\tau_\textrm{sw}$ the sweeping time) the dominant
decorrelation time is the wave period, and that these modes also show a slower
modulation on the timescale $\tau_\textrm{NL}$ as assumed in wave turbulence
theories. The rest of the modes are decorrelated with the sweeping time,
including the very energetic modes modes with $\omega \approx 0$.
