Gravity wave breaking in two-layer hydrostatic flow

To better understand mountain-induced gravity wave breaking and potential vorticity generation in the troposphere, a two-layer hydrostatic flow over a three-dimensional Witch-of-Agnesi type of mountain is investigated. It is suggested that a two-layer model is the simplest model in which the partitioning of upper- and lower-level wave breaking and dissipation can be studied. High-resolution shallow water model runs are carried out with unsheared upstream flow and a wide variety of mountain heights. A regime diagram is constructed, in which gravity wave breaking is classified based on shock number, location, and type. It is demonstrated that different types of shocks identified in the numerical simulations can be consistently described using a shock regime diagram, derived from viscous shock theory. Four curious shock properties are shown to influence orographic flow: the steepening requirement, the tendency for external jumps to amplify shear, the bifurcation in external jumps, and the "double shock.'' Some results are compared with continuously stratified flow simulations by a nonhydrostatic mesoscale model. It is demonstrated that vertical wind shear controls the vertical distribution of wave breaking and potential vorticity generation.