Internal gravity waves in a saturated moist neutral atmosphere

This work is motivated by an unusual feature associated with the start-up of a moist nearly neutral atmospheric flow over a mountain ridge that was previously observed in a full-physics numerical model. In that study, the upstream propagation of a wave of subsidence precluded the establishment of upward-displaced and saturated flow that might be expected upstream of the topography. This phenomenon was hypothesized to be a consequence of the peculiar property of saturated moist neutral flow: an upward air parcel displacement produces zero buoyancy, while a downward displacement desaturates the air parcel and produces a positive buoyancy anomaly. In the present study, this hypothesis is confirmed within numerical solutions to a reduced system of equations that incorporates the saturated-atmosphere property in a particularly simple manner. The relatively uncomplicated nature of these solutions motivates the numerical solution of a further simplified initial-value problem for both nonhydrostatic and hydrostatic flow. Exact analytic solutions are developed for the latter hydrostatic case, which explains the upstream-propagating wave of subsidence as a shock phenomenon.