The Nonlinear Response of the Atmosphere to Large-Scale Mechanical and Thermal Forcing

Abstract

The subject of large-scale mountain waves is reviewed briefly. Existing mountain wave theory based on a linear system is shown to give an inadequate description of the balance of angular momentum. The response of the atmosphere to mechanical forcing in a nonlinear framework is then discussed, using a two-level quasi-geostrophic long-wave spectral model based on spherical coordinates, including diabatic heating, surface friction and mountains. The nonlinear theory shows that there exists a critical mountain height Hc, which is a function of the frictional coefficient as well as the phase difference between the mountain and the surface pressure field. If, and only if, the mountain height is less than this critical value, can the deflection effect of the mountain be neglected and the response regarded as approximately linear. This critical mountain height is only about 1 km. Thus most of the atmospheric response to large-scale mountains must be nonlinear. In the nonlinear case, as the mountain height is increased the deflection effect becomes more and more important. Therefore, although in the upper atmosphere the mountain wave is intensified, at the surface the pressure perturbation decreases and the zonal surface winds become dominant and approach an asymptotic value. It is also shown that the combined effect of mechanical and thermal forcing is nonlinear. Despite the fact that the formation of surface pressure systems is mainly a result of thermal forcing, orography affects, to some extent their intensities and locations. Considering the balance requirement of angular momentum, it is concluded that purely mechanical forcing cannot be the case in the real atmosphere. Although the mountain torque owes its existence to unevenness of the earth's surface, its sign and intensity depend critically upon the relative locations of mechanical and thermal forcing.