Orographic–convective flows, wave reflection, and gravity-wave momentum fluxes in a two-layer hydrostatic atmosphere

Dynamical aspects of flows forced by either convective heating or a mountain have been extensively studied, but those forced by both convective heating and a mountain have been less studied. Here, we theoretically examine orographic–convective flows, gravity-wave reflection, and gravity-wave momentum fluxes in a stably stratified two-layer hydrostatic atmosphere. The upper layer (stratosphere) has a larger static stability than the lower layer (troposphere), and the basic-state wind has a constant shear in the troposphere and is uniform in the stratosphere. The equations governing small-amplitude perturbations in a two-dimensional, steady-state, inviscid, non-rotating system in the presence of orographic forcing and convective forcing are analytically solved. Then, the analytic solutions are analysed to understand how orographically and convectively forced flows vary with changes in basic-state wind speed, stratospheric static stability, and the location of the convection relative to the mountain. Over the upslope of the mountain, the convectively forced deep upward motion is positively combined with the orographic uplift, thus giving rise to enhanced upward motion there. The ratio of the convectively forced vertical velocity to the orographically forced vertical velocity at the cloud base height over an upslope location of the mountain is analysed to further understand the linear interaction between orographically and convectively forced flows. The gravity-wave reflection at the tropopause plays an important role in orographic–convective flows. The gravity-wave reflection at the tropopause amplifies the symmetric (anti-symmetric) structure of orographically (convectively) forced waves. The vertical fluxes of the horizontal momentum are analytically obtained. The total momentum flux contains the component resulting from the non-linear interaction between orographically and convectively forced waves. It is found that the non-linear interaction component can be as important as each of the orographic and convective components in the total momentum flux depending on the location of the convection relative to the mountain.