Applicability of Reduced-Gravity Shallow-Water Theory to Atmospheric Flow over Topography

Applicability of the reduced-gravity shallow-water (RGSW) theory to a shallow atmospheric layer capped by an inversion underneath a deep stratified atmosphere over a two-dimensional ridge has been investigated using linear analysis and nonlinear numerical simulations. Two key nondimensional parameters are identified, namely, and , where is the reduced gravity acceleration, H0 is the RGSW layer depth, and N and U are the buoyancy frequency and wind speed in the layer above the inversion. If J and ƒ× are around unity or larger, the response of the RGSW flow response over the ridge can be significantly modified by pressure perturbations aloft. Any jump like perturbations in the RGSW layer decay rapidly as they propagate away from the ridge by radiating perturbation energy into the upper layer. The RGSW theory is more adequate for describing RGSW flows with J andƒnƒ× much less than unity, In addition, inversion-splitting occurs downstream of a jump when , where Ni is the buoyancy frequency in the inversion and hm stands for the ridge height. A less stratified upper layer with slower winds in general has less influence on the RGSW flow below and favors the application of the RGSW theory. For a thick inversion (d), the equivalent RGSW flow depth is approximately given by H + d/2, where H is the depth of the neutral layer below the inversion.