Boundary layer dynamics in a simple model for convectively coupled gravity waves

A simplified model of intermediate complexity for convectively coupled gravity waves that incorporates the bulk dynamics of the atmospheric boundary layer is developed and analyzed. The model comprises equations for velocity, potential temperature, and moist entropy in the boundary layer as well as equations for the free tropospheric barotropic (vertically uniform) velocity and first two baroclinic modes of vertical structure. It is based on the multicloud model of Khouider and Majda coupled to the bulk boundary layer-shallow cumulus model of Stevens. The original multicloud model has a purely thermodynamic boundary layer and no barotropic velocity mode. Here, boundary layer horizontal velocity divergence is matched with barotropic convergence in the free troposphere and yields environmental downdrafts. Both environmental and convective downdrafts act to transport dry midtropospheric air into the boundary layer. Basic states in radiative--convective equilibrium are found and are shown to be consistent with observations of boundary layer and free troposphere climatology. The linear stability of these basic states, in the case without rotation, is then analyzed for a variety of tropospheric regimes. The inclusion of boundary layer dynamics--specifically, environmental downdrafts and entrainment of free tropospheric air--enhances the instability of both the synoptic-scale moist gravity waves and nonpropagating congestus modes in the multicloud model. The congestus mode has a preferred synoptic-scale wavelength, which is absent when a purely thermodynamic boundary layer is employed. The weak destabilization of a fast mesoscale wave, with a phase speed of 26 m [s.sup.-1] and coupling to deep convection, is also discussed.