Simulations of mountain waves and lee vortices using an explicit, semi-Lagrangian numerical model

We have recently developed a nonhydrostatic numerical model to study a wide range of spatial scales of atmospheric systems. The model is based on a fully compressible and three-dimensional system of equations with a terrain-following vertical coordinate. A major advantage of the model is the use of a forward-backward integration scheme to treat both high-frequency sound waves and internal gravity waves explicitly. The numerical procedure is shown in one of authors' earlier work to be quite accurate and also is free from unstable computational modes. In addition, we use a forward semi-Lagrangian advection scheme which performs much better than a second order finite difference advection scheme. Our numerical procedure appears to be particularly suited to study mountain wave situations, since little numerical damping or diffusion is required for a very stable numerical scheme.

The simulated airflow reached a steady-state for the simulation of a 3D, nonhydrostatic linear mountain wave situation. The model result is validated against the corresponding analytical solution in details. The dissipation and dispersion errors of the model results are calculated as well as the total mass and the total energy of the simulated flow fields. The simulations for the airflow past idealized mountains under a low Froude number are consistent with previous studies with features like lee vortices and hydraulic jump, etc.