Applicability of the Reduced Gravity Shallow Water Model to Gap Flow

The reduced gravity shallow water model (RGSW) is widely used for studying atmospheric flows through gaps. Despite its relative simplicity, it provides a fully nonlinear model, but it also assumes a gross idealization of the atmospheric structure, which is not always justified. A quantitative comparison is therefore presented between nonlinear simulations of shallow-water and continuously stratified flow through an idealized channel with a sill or a lateral constriction.

The continuously stratified simulations all involved weakly stratified flow capped by a inversion, which allows optimal comparison with the RGSW model. In addition, these simulations are divided into two classes: type I, with a typical atmospheric stratification of N=0.01 s^-1) above the inversion, and type II, with very weak stratification (N=0.002 s^-1) above the inversion. Simulations for both types of continuous stratification, and for the true shallow-water model were compared for the same channel topography, fluid depth, and upstream Froude numbers, but for different inversion strengths by making appropriate adjustments to the upstream flow speed.

For type II soundings, the resulting flow showed almost no dependence on the inversion strength (as would be expected from RGSW model since the topography and upstream Froude numbers remained the same), whereas for type I soundings, the flow response was much weaker in those cases with a weak inversion. In all cases, both with sills and with constrictions, there were significant differences in the maximum wind speed and the relative acceleration across the sill or constriction between the type I simulations and the type II and fully shallow-water models.