A mathematical model for the numerical simulations of traveling ionospheric disturbances/atmospheric gravity waves generated by the Joule heating

Traveling ionospheric disturbances (TIDs) and atmospheric gravity waves (AGWs) generated by the Joule heating produced from intensified auroral electrojet and/or intense particle precipitation in the auroral and subauroral regions during geomagnetic storms and which propagate downward toward the lower (neutral) atmosphere are numerically simulated using a simple two-dimensional mathematical model for internal gravity waves propagating in the lower atmosphere. An explicit expression for the Joule heating is obtained, and the characteristics of the simulated TIDs/AGWs (e.g., buoyancy frequency, wavenumbers, cutoff wavelength, speed, structures) are also examined and compared with the results obtained from observations. As may be seen in the observations, small-scale TIDs/AGWs with wavelengths shorter than 100 km, medium-scale TIDs/AGWs with wavelengths of several hundred kilometers, and large-scale TIDs/AGWs with wavelengths longer than 1000 km generated by the Joule heating were modeled and numerically simulated. For example, observations have revealed that the Joule heating can generate TID/AGW pairs. The developed numerical model was used to simulate medium-scale TID/AGW wave packet pairs, and the results (wavelength, speed, structure) are in agreement with SuperDARN observations reported by Sofko and Huang, 2000. TIDs/AGWs with shorter horizontal wavelengths are more trapped than those with longer wavelengths (medium- and large-scale TIDs/AGWs). Their cutoff horizontal wavelength was approximated using the linear stability theory of AGWs. The approximated cutoff horizontal wavelength suggests that not all simulated small-scale disturbances with horizontal wavelengths shorter than 100 km are traveling as may be seen in the observations.