Factors Controlling Nonlinearity in Mechanically Forced Stationary Waves over Orography

Abstract

The forcing of stationary waves by the earth?s large-scale orography is studied using a nonlinear stationary wave model based on the quasigeostrophic equations. The manner in which wind speed, meridional temperature gradient, Ekman pumping parameter, linear damping, orographic shape, and meridional wind structure affect the validity of the linearized equations is examined and the nonlinear response is investigated. A critical mountain height that separates the linear from the nonlinear regime is defined based on the linear quasigeostrophic potential temperature equation applied at the surface. The largest critical heights (those responses in which nonlinearity is least important) are obtained when the surface damping is weak or nonexistent. Also, relative maximums in mountain critical heights are obtained when the ratio of surface wind to surface wind shear does not vary in the meridional direction. These critical height results are validated using the fully nonlinear stationary wave model. The nonlinearly balanced response to imposed orography is diagnosed at the surface and aloft. The nonlinear effects of eddy wind/orography interaction and nonlinear advection are found to be important only in the vicinity of the orography. The structure of the nonlinear response at the surface is found to be robust and is characterized (in the Northern Hemisphere) by a high and low situated to the northwest and southeast, respectively, of the mountain center. This orientation of the surface response leads to a stationary wave train that propagates preferentially toward the equator. The system is sensitive enough to both the surface wind and meridional temperature gradient that the observed seasonal variations in the zonal mean circulation will significantly alter the character of the response. As the meridional temperature gradient decreases, the relative importance of nonlinearity increases while the amplitude of the response at the upper levels decreases. Therefore, this model indicates that summertime mechanically forced stationary waves should be weaker, but more nonlinear, than their wintertime counterparts.