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 moun tain pass, is derived. It is based on the one-dimensional reduced-gravity s hallow-water theory generalized to a three-dimensional orography with moder ate streamwise variations by introducing a variable effective flow cross-se ction. In this way, the hydraulic jump and gap flow are accommodated within the same model. The resulting steady hyperbolic problem is shown to requir e the boundary conditions to be expressed in terms of Riemann invariants. T he latter yield the flow between two given sites in a unique way. In partic ular, it is possible to relate unambiguously the existence of a hydraulic j ump/gap flow and its energy discontinuity to the boundary conditions. A sim ple method of flow interpolation and energy discontinuity calculation betwe en two sites is presented.