Reflection of nonlinear mountain waves by critical levels: behaviour of the reflection coefficient

Abstract

AbstractCritical levels, where the wind vanishes in the atmosphere, are of key importance for gravity wave drag parametrization. The reflectivity of these levels to mountain waves is investigated here using a combination of high‐resolution numerical simulations and insights from linear theory. A methodology is developed for relating the reflection coefficient of 2D hydrostatic orographic gravity waves to the extrema of the associated drag as a function of an independent flow parameter. This method is then used to infer the variation of the reflection coefficient with flow nonlinearity. To isolate the effect of critical levels, a wind profile with negative shear is adopted, which is characterized by its Richardson number and the dimensionless mountain height , based on the mountain height , Brunt‐Väisälä frequency and surface incoming wind speed . Subject to the assumptions of linear theory, the drag is shown to be modified by wave refraction and reflection. The modulation of the drag by wave reflection is used to derive the reflection coefficient from the drag diagnosed from the numerical simulations. Despite considerable uncertainty, the critical level is found to have an that first increases with for low values of this parameter, and for stronger nonlinearity saturates to a value of about 0.6. The flow configuration in this saturated regime is characterized in the case of high‐drag states by constructive wave interference, resembling downslope windstorms. Wave reflection by critical levels enhances the flow nonlinearity and the associated drag amplification, more than doubling it for values of as low as 0.12. These results emphasize the need to represent this process in orographic gravity wave drag parametrizations, and suggest a possible way of doing it using a prescribed critical level reflection coefficient, derived using the present methodology.