A three-dimensional numerical model based on the inviscid and adiabatic primitive equations in the Boussinesq approximation is used to investigate the retardation of cold fronts by high two and three-dimensional mountains, approximately the same size as the Alps. Initial and boundary conditions are specified according to an analytical model for an idealized front with constant potential vorticity. The study covers cases with uniform, neutral or stable stratification in both the cold and warm air masses. The model results are compared with previous analytical solutions of a shallow water flow model. A scale analysis and a parameter study identify the conditions under which a front is strongly influenced by mountains.
For two-dimensional cases, the study shows that the foot of the front is strongly retarded if the kinetic energy is too small to let the cold air climb over the mountain. The bulk of the front is strongly retarded if the Froude number and the relative front/mountain height are small, and if the mountain is steep. For Froude numbers of order one and for high mountains, hydraulic jumps arise in accordance with theories for layered flows. Stable stratification further enhances retardation of the front and disperses possible hydraulic jumps. In three dimensions, the front experiences deformation due to anticyclonic motion. This deformation is enhanced by stratification. The model explains the magnitude of surface-front deformation for two observed cases where cold fronts are strongly retarded at the Alps.