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

• Published in: Quarterly journal of the Royal Meteorological Society Vol. 146; no. 727; pp. 1009 - 1025
• Main Authors: Teixeira, M. A. C., Argaín, J. L., Xu, Xin
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.01.2020; Wiley Subscription Services, Inc
• Subjects: Brunt-Vaisala frequency; critical levels; Drag; Gravitational waves; Gravity wave drag; Gravity waves; Height; hydrostatic flow; Lee waves; Methods; Mountain waves; Mountains; nonlinear effects; Nonlinear systems; Nonlinearity; Numerical simulations; Orographic gravity waves; Reflectance; Reflection; Richardson number; Wave drag; Wave reflection; Wave refraction; Wind speed
• ISSN: 0035-9009; 1477-870X
• DOI: 10.1002/qj.3722

Critical 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 R 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 Ri and the dimensionless mountain height Nh0/U0, based on the mountain height h0, Brunt‐Väisälä frequency N and surface incoming wind speed U0. 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 R that first increases with Nh0/U0 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 Nh0/U0 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. The reflection coefficient R of a critical level for orographic gravity waves incident from below is shown as a function of the dimensionless mountain height Nh0/U0. R was obtained using a method developed here from the maxima (red circles) and minima (blue circles) of the drag force as a function of the Richardson number and their geometric mean (black circles), diagnosed from nonlinear numerical simulations of stratified flow where the wind decreases linearly with height over a 2D mountain ridge.