Flow splitting at the bifurcation between two valleys:: idealized simulations in comparison with Mesoscale Alpine Programme observations

This paper investigates the characteristics of channelled airflow in the vicinity of a junction of three idealized valleys (one valley carrying the incoming flow and two tributaries carrying the outflow), using a two-dimensional single-layer shallow water model. Particular attention is given to the flow splitting occurring at the junction. Nondimensionalized, the model depends on the valley geometry, the Reynolds number, which is related to the eddy viscosity, and on the difference of the hydrostatic pressure imposed at the exit of the tributaries. At the spatial scale considered in this study, the Rossby number relating the inertial and Coriolis forces is always larger than 1, implying that the effect of earth rotation can be neglected to a first approximation. The analysis of the flow structure within the three valleys as well as the calculation of the split ratio (fraction of the air flow diverted into one of the two downstream valleys with respect to the total mass flux in the upstream valley) show that (i) the flow pattern depends strongly on the Reynolds number while the split ratio is comparatively insensitive; (ii) the valley geometry and the difference between the upstream and downstream hydrostatic pressures affect the flow pattern, the location of the split point and the split ratio; (iii) the relative contribution of flow deflection by the sidewalls and the blocking/splitting mechanism differs between the settings of a "Y-shape" valley and a "T-shape" valley. Quantitative comparison of the present results with numerical simulations of realistic cases and with observations collected in the region of the Rhine and Seez valleys Switzerland) ("Y-shape'' valley) and in the region of the Inn and Wipp valleys (Austria) ("T-shape'' valley) during the Mesoscale Alpine Programme (MAP) field experiment shows good agreement provided that the normalized valley depth N Delta H/U-u significantly exceeds 1, i.e., when "flow around'' is expected. A structural disagreement between the idealized simulations and the observed wind field is found only when N Delta H/U-u similar or equal to 1, that is, in the "flow over'' regime. This shows that the dimensionless valley depth Delta H is indeed a good indicator for flow splitting, implying that the stratification is a key player in reality.