Observational evidence and modelling of an internal hydraulic jump at the atmospheric boundary-layer top during a Tramontane event

A hydraulic jump has been observed with the airborne backscatter lidar LEANDRE 1 (Lidar embarque pour l'Etude des Aerosols, des Nuages, des interactions Dynamique-Rayonnement et du cycle de l'Eau) at the top of the atmospheric boundary layer (ABL) during a Tramontane event in the framework of the Pyrenees experiment. An analytical fluid mechanics model is used to interpret lidar observations in connection with in situ measurements and to study the sensitivity of the hydraulic jump triggering to the boundary conditions. This model, which generalizes the reduced-gravity shallow-water theory for two-dimensional stratified flows over a topograpy, is diagnostic (i.e., the reduced gravity g' = g Delta theta (v)/theta (v) is prescribed) and uses boundary conditions defined in terms of Riemann invariants. Using inflow and outflow boundary conditions as well as the reduced gravity prescribed from in situ measurements, the model is able to diagnose the presence of a hydraulic jump at the location suspected from the lidar observations. The wind speed, ABL height and Froude number derived from the model are in good agreement with the observations (within about 20-30%).