Excitation of large-scale inertial waves in a rotating inhomogeneous turbulence

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.