Self-acceleration and instability of gravity wave packets: 1. Effects of temporal localization

An anelastic numerical model is used to explore the dynamics accompanying the attainment of large amplitudes by gravity waves (GWs) that are localized in altitude and time. GW momentum transport induces mean flow variations accompanying a GW packet that grows exponentially with altitude, is localized in altitude, and induces significant GW phase speed, and phase, variations across the GW packet. These variations arise because the GW occupies the region undergoing accelerations, with the induced phase speed variations referred to as "self-acceleration." Results presented here reveal that self-acceleration of a GW packet localized in time and altitude ultimately leads to stalling of the vertical propagation of the GW packet and accompanying two-and three-dimensional (2-D and 3-D) instabilities of the superposed GW and mean motion field. The altitudes at which these effects occur depend on the initial GW amplitude, intrinsic frequency, and degree of localization in time and altitude. Larger amplitudes and higher intrinsic frequencies yield strong self-acceleration effects at lower altitudes, while smaller amplitudes yield similar effects at higher altitudes, provided the Reynolds number, Re, is sufficiently large. Three-dimensional instabilities follow 2-D "self-acceleration instability" for sufficiently high Re. GW packets can also exhibit self-acceleration dynamics at more than one altitude because of continued growth of the GW packet leading edge above the previous self-acceleration event.