Implications of the Hydrostatic Assumption on Atmospheric Gravity Waves

Abstract

The validity of the hydrostatic approximation is examined for use in predicting the dynamics of topographically generated atmospheric gravity waves (lee waves) propagating in an atmosphere with realistic wind shear. To isolate nonhydrostatic effects, linear, analytic solutions derived both with and without the hydrostatic assumption are compared. The atmospheric profiles of wind and stability are chosen both to render the governing equations analytically tractable and be representative of typical atmospheric conditions. Two atmospheric models are considered: 1) a troposphere-only model in which the wind increases linearly with height and the stability is constant and 2) a troposphere-stratosphere model, which retains the important effect of the vertical wind shear in the troposphere and adds the essential feature of a stability jump at the tropopause. The nonhydrostatic trapping effect of wind shear on gravity wave modes is clearly illustrated in the troposphere-only atmospheric model. In the troposphere-stratosphere model the vertical wind shear partially traps nonhydrostatic waves in the troposphere, which leak energy into the stratosphere; this effect is completely eliminated in the hydrostatic solution. Solutions for both hydrostatic and nonhydrostatic cases are examined for a range of tropospheric Richardson numbers and tropopause depths. Results show that the hydrostatic approximation radically alters the character of the gravity wave reflection and transmission through the tropopause, as well as both the magnitude and distribution of the momentum flux in the troposphere and stratosphere. Of particular importance is the downstream shift of momentum flux by the nonhydrostatic component, which can lead to misinterpretation of momentum flux measurements in both aircraft data and numerical models. It is found that the nonhydrostatic component is significant in this strongly sheared environment, even when the mountain is broad. Thus, even for relatively large-scale topographic forcing, the hydrostatic assumption may not be justified for gravity wave calculations.