Gravity wave momentum flux in directional shear flows over three‐dimensional mountains: Linear and nonlinear numerical solutions as compared to linear analytical solutions

Abstract

Gravity waves forced by circular bell‐shaped mountains are simulated using the Advanced Regional Prediction System model for four directionally sheared wind profiles W1, W2, W2a, and W2b. W1 is eastward at the surface, while the latter three are southeastward. With the vertical shear directed northward, W1 shows an increasing speed with height, whereas W2, W2a, and W2b are first decelerated in the bottom layer (beneath different heights). Gravity wave momentum flux (WMF) and its vertical divergence at four different Froude numbers (Fr) are investigated. At a large Froude number Fr = 80 where the waves are essentially linear, the simulated WMF and WMF divergence agree well with their linear analytic counterparts, thus providing a numerical validation for the analytical solutions of Xu et al. For moderately nonlinear waves at Fr = 1.6, the simulated WMFs are qualitatively similar to the analytical values but are amplified due to nonlinear effect. For more nonlinear waves at lower Froude numbers, an enhanced drag is found at the lower Fr = 0.4 in W1, W2a, and W2b, and a low drag is found at higher Fr = 0.8 in W2, in contrast to the corresponding constant‐flow solutions. Analyses on the mountain flow structure show that the height variation of the ambient wind speed has an important influence on the airflow behavior (e.g., flow over versus flow around a mountain), which in turn affects the drag. Thus, unlike the constant‐flow case, the wave drag state in turning flows cannot be determined from the surface‐based Froude number alone, and new wave drag parameterization schemes would be needed to properly account for directional shear effects. Additionally, directional wind shear can also introduce asymmetric development in the wake flow to trigger lee vortex shedding, which is observed in W2 at Fr = 0.4.