  We explore the near-resonant interaction of inertial waves with geostrophic
modes in rotating fluids via numerical and theoretical analysis. When a single
inertial wave is imposed, we find that some geostrophic modes are unstable
above a threshold value of the Rossby number $kRo$ based on the wavenumber and
wave amplitude. We show this instability to be caused by triadic interaction
involving two inertial waves and a geostrophic mode such that the sum of their
eigen frequencies is non-zero. We derive theoretical scalings for the growth
rate of this near-resonant instability. The growth rate scaled by the global
rotation rate is proportional to $(kRo)^2$ at low $kRo$ and transitions to a
$kRo$ scaling for larger $kRo$. These scalings are in excellent agreement with
direct numerical simulations. This instability could explain recent
experimental observations of geostrophic instability driven by waves.
