Interaction of inhomogeneous geomagnetic field with the planetary usually Rossby waves generates the magnetized Rossby-type wavy perturbations in the upper atmosphere and ionosphere. An effective linear mechanism responsible for the intensification and mutual transformation of large scale magnetized Rossby type and small scale inertial waves in the shear wind driven ionosphere is found. To study the interaction of shear flow (inhomogeneous wind) and wave structures in the atmosphere-ionosphere regions, more adequate is nonmodal mathematical analysis. Using nonmodal approach and numerical modeling, it is illustrated the peculiar features of the interaction of magnetized Rossby waves with the background flow as well as the mutual transformation of Rossby-inertial wave disturbances in the ionosphere. It has been shown that the shear flow driven magnetized Rossby wave perturbations effectively extract energy of the shear flow increasing own energy and amplitude. These perturbations undergo self organization in the form of the nonlinear solitary vortex structures due to nonlinear twisting of the perturbation’s front. Such nonlinear vortex structures are often observed in different regions of the atmosphere-ionosphere layers of the Earth.