Temporal Evolution of Ionospheric Gravity Waves in the Presence of a Strong Constant Magnetic Field

A time-dependent nonlinear model is presented to describe internal gravity waves propagating upwards in the F-region of the Earth’s ionosphere. The model is based on a configuration where the background neutral velocity is constant, the geomagnetic field is approximately constant, and the angular gyrofrequency of the ions is much larger than the ion-neutral collision frequency, which is in turn larger than the angular frequency of the gravity waves. For small-amplitude waves the equations are linearized, and a time-dependent analytical solution is obtained for the special case corresponding to the limit of zero vertical-to-horizontal aspect ratio. This analytical solution and the linear numerical results for general aspect ratio show that in the limit of infinite time the linear solution approaches a steady state in which the ion damps the wave amplitude in the vertical direction. For the more general configuration that includes larger amplitude waves, time-dependent nonlinear numerical simulations show that, in the presence of the ion drag, there are wave mean-flow interactions even in the absence of vertical shear in the background neutral flow. With time, the perturbation develops a zero-wavenumber component corresponding to a wave-induced mean flow acceleration, which depends on the dip angle of the geomagnetic field and on the aspect ratio.