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 LEAN DRE 1 (Lidar embarque pour l'Etude des Aerosols, des Nuages, des interactio ns Dynamique-Rayonnement et du cycle de l'Eau) at the top of the atmospheri c boundary layer (ABL) during a Tramontane event in the framework of the Py renees experiment. An analytical fluid mechanics model is used to interpret lidar observations in connection with in situ measurements and to study th e 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 b oundary 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 hydr aulic jump at the location suspected from the lidar observations. The wind speed, ABL height and Froude number derived from the model are in good agre ement with the observations (within about 20-30%).