A model for Convective Boundary Layer development in an alpine valley

A model for the evolution of the convective boundary layer within an alpine valley and the consequent development of up-valley winds is proposed. The model extends previous results on the diurnal evolution of an inversion capped convective boundary layer in order to include the effects induced by a slowly tilted bottom and by the adjacent slopes. Assuming the layer to be well mixed, suitable evolution equations are derived for the depth-averaged horizontal wind velocity components, potential temperature and the boundary layer depth. Further cross-averaging over the valley section - under the hypothesis of transverse homogeneity of the flow - leads to a hypebolic system of three coupled evolution equation for cross averaged values of potential temperature, wind velocity and boundary layer depth. Turbulent fluxes occurring at ground are evaluated with suitable drag and heat transfer coefficients. The effects of different entrainment closures at the inversion height is also evaluated. Various possible solution are found for both steady and unsteady conditions. The results are compared with experimental evidences from ground and airborne measurements. The model is applied to the case study of the valley wind arising in the northern part of Garda Lake and known as Ora del Garda