Evolution of disturbances in a three-layer model of the atmosphere with shear instability

A three-layer model with constant vorticity and density in each layer is re garded as a simple model of the atmosphere with sheer instability, Model eq uations that describe the evolution of wave packets against the background of a long-wavelength random noise are derived. Packet wave numbers are loca lized near the instability region, which is assumed to be narrow. It is sho wn that the long-wavelength noise can reduce the growth rate of an unstable mode and can even remove the instability.