Weak nonlinear theory of the ionospheric response to atmospheric gravity waves in the F-region

The nonlinear ionospheric response to atmospheric gravity waves is studied in an approximate fashion using a new approach. The concept of nonlinear travelling ionospheric disturbances (TIDs) is outlined, and the nonlinear behaviour of atmospheric gravity waves is calculated. A principal result is that harmonics are generated which cause the wave velocity perturbation to deform. The ionospheric response is investigated by solving the continuity equation for ionization in the F-region. The distortion of the TIDs waveform produced by the nonlinear interactions is depicted. The nonlinear TIDs depart seriously from a cosinusoidal wave described by previous linear TID theory. The distorted TIDs appear as ‘sharp peak’ and ‘sawtooth’ waveform shapes. The ‘peaks’ can be upward or downward, and the ‘sawteeth’ forward or backward, depending on the wave parameters. The nonlinearly distorted TIDs show a good agreement with various observed ionospheric irregularities produced by atmospheric gravity waves.