Reduced dynamical equations for the high-latitude thermosphere: Ion drag balance

Although highly variable on small scales, the middle thermosphere shows evidence of slow-timescale mesoscale dynamics. A reduced set of equations is derived by asymptotic scale analysis. The drag-balance equations describe the nonlinear evolution of the thermosphere during magnetic quiet times under an approximate balance of pressure, Coriolis, and ion-drag forces. The equations explicitly remove gravity and sound oscillations, making them well suited for theoretical study of slow-timescale evolution and efficient for numerical modeling. Linear analysis is used to establish the limits of their validity in terms of timescale separation. The slow-timescale component is only weakly damped for horizontally broad motions, even when the ion-neutral collision frequency is large.