Abstract
An approximate solution of the eigenvalue problem governing the stability of the zonal wind with respect to small disturbances of long wavelength is developed for profiles with strong, positive-definite vertical shear. It is found that certain disturbances, characterized by positive phase velocities, appear to be stable on the basis of a first approximation but are unstable in higher approximations. The results, together with the previously established instability for short wavelengths and/or weak vertical shear, support the conjecture that typical zonal-wind configurations are unstable with respect to small disturbances of almost all wavelengths at almost all windspeeds.
