Diagnostics of hydraulic jump and gap flow in stratified flows over topography

A criterion, allowing one to assess conditions likely to generate gap flows and/or hydraulic jumps in stratified flows over a mountain ridge or a mountain pass, is derived. It is based on the one-dimensional reduced-gravity shallow-water theory generalized to a three-dimensional orography with moderate streamwise variations by introducing a variable effective flow cross-section. In this way, the hydraulic jump and gap flow are accommodated within the same model. The resulting steady hyperbolic problem is shown to require the boundary conditions to be expressed in terms of Riemann invariants. The latter yield the flow between two given sites in a unique way. In particular, it is possible to relate unambiguously the existence of a hydraulic jump/gap flow and its energy discontinuity to the boundary conditions. A simple method of flow interpolation and energy discontinuity calculation between two sites is presented.