It is shown that sheared Rossby–Khantadze waves can propagate due to inhomogeneities, taking into account the Earth's angular velocity and the magnetic field. Along with the Hall conductivity, these waves can couple in the ionospheric E region.The novelty of the present work is the consideration of magnetic field inhomogeneity, which was not considered before and reduced our considered system of equations to a 1D modified KdV equation.

Detection of Ionosphere Anomalies (DIA) for detection, identification, and analysis of ionosphere anomalies from satellite spectrograms and time series row data from instruments onboard the DEMETER satellite was designed. Using this software, the analyses of ionosphere parameter variations caused by various factors are provided. The scientific data processing and visualization technologies used in the development of DIA can be used in the creation of software for other scientific space missions.

The paper analytically and numerically treats the new theoretical basis for ground-based and satellite monitoring of the most powerful processes in the lower atmosphere and Earth (hurricanes, earthquakes, etc.), solar-wind magnetosphere (magnetic storms) and ionosphere (lightning discharges, thunderstorms, etc.). This can be provided by the determination of phases and amplitudes of radio waves in the Earth and ionosphere. In perspective, damage from the natural disasters can be decreased.

The interaction of waves can lead to inverse cascades, when energy is transferred from small scales to large ones. In dynamo theory, this corresponds to the alpha-effect, where turbulence generates large-scale magnetic field, in two-dimensional hydrodynamic turbulence transfer of kinetic energy from small scales to large ones is observed. We suggest simple analytical model that explains existence of inverse cascades of kinetic energy in rapidly rotating turbulence.