On the Applicability of Reduced Gravity Shallow-Water Theory to Continuously-Stratified Flows over Topography

Applicability of the reduced-gravity shallow-water (RGSW) theory to a shallow atmospheric layer underneath an inversion over topography is investigated through linear analysis and nonlinear numerical simulations. According to linear theory, when the dimensionless inversion strength, is large (i.e., J>>1), the impact of perturbations above the inversion on the momentum conservation in the shallow lower layer is negligible and accordingly, the RGSW theory is applicable. For a relatively weak inversion with J near unity or less, perturbation energy leaks through the inversion into the free atmosphere, and the associated horizontal pressure gradient exerted above the inversion invalidates the momentum conservation in the shallow flow underneath. In addition, the inversion needs to be thin for RGSW to work. If the inversion is too thick (i.e., nondimensional thickness, >1), wave breaking may occur in the upper portion of the inversion and cause the inversion to split.