Formulation and evaluation of a nonhydrostatic mesoscale vorticity model (TVM)

Abstract

This paper describes the formulation and the application of the nonhydrostatic anelastic vorticity model (TVM). This model is constructed using a method involving two horizontal streamfunctions and two horizontal vorticity components. The evaluation of this formulation is performed by simulating various bidimensional hydrostatic and nonhydrostatic mountain wave cases. Results are compared with analytical solutions and in particular with those developed by Laprise and Peltier for nonlinear forcings. The anelastic formulation is also validated with respect to the highly nonlinear 1972 Boulder windstorm. TVM is shown to accurately reproduce these mountain wave test cases in both its incompressible and anelastic formulations. In the second part of this paper, the adequacy of the hydrostatic and anelastic assumptions in simulating thermally induced circulations is investigated and compared to previous works. For a moderate surface thermal forcing, typical geographical setups are used and show slight differences between hydrostatic and nonhydrostatic horizontal wind speeds. For vertical wind speeds, differences are shown to be much larger and more sensitive to changes in grid resolution. For more stringent thermal surface forcing, differences remain low for horizontal wind speeds but increase considerably for the vertical wind component. The comparison between anelastic and incompressible solutions for the same cases shows the adequacy of the incompressible assumption when circulations are forced by the surface and are characterized by a relatively shallow vertical extent. In such conditions, virtually no differences are observed between the two formulations.