A Three-dimensional Wave Activity Flux of Inertia-Gravity Waves and Its Application to a Rainstorm Event

A three-dimensional transformed Eulerian-mean (3D TEM) equation under a non-hydrostatic and non-geostrophic assumption is deduced in this study. The vertical component of the 3D wave activity flux deduced here is the primary difference from previous studies, which is suitable to mesoscale systems. Using the 3D TEM equation, the energy propagation of the inertia-gravity waves and how the generation and dissipation of the inertia-gravity waves drive the mean flow can be examined. During the mature stage of a heavy precipitation event, the maximum of the Eliassen-Palm (EP) flux divergence is primarily concentrated at the height of 10-14 km, where the energy of the inertia-gravity waves propagates forward (eastward) and upward. Examining the contribution of each term of the 3D TEM equation shows that the EP flux divergence is the primary contributor to the mean flow tendency. The EP flux divergence decelerates the zonal wind above and below the high-level jet at the height of 10 km and 15 km, and accelerates the high-level jet at the height of 12-14 km. This structure enhances the vertical wind shear of the environment and promotes the development of the rainstorm.