  A mechanism of excitation of the large-scale inertial waves in a rotating
inhomogeneous turbulence due to an excitation of a large-scale instability is
found. This instability is caused by a combined effect of the inhomogeneity of
the turbulence and the uniform mean rotation. The source of the large-scale
instability is the energy of the small-scale turbulence. We determined the
range of parameters at which the large-scale instability occurs, the growth
rate of the instability and the frequency of the generated large-scale inertial
waves. Geophysical and astrophysical applications of the obtained results are
discussed.
