Orographic Drag Associated with Lee Waves Trapped at an Inversion

The drag produced by 2D orographic gravity waves trapped at a temperature inversion and waves propagating in the stably stratified layer existing above are explicitly calculated using linear theory, for a two-layer atmosphere with neutral static stability near the surface, mimicking a well-mixed boundary layer. For realistic values of the flow parameters, trapped-lee-wave drag, which is given by a closed analytical expression, is comparable to propagating-wave drag, especially in moderately to strongly nonhydrostatic conditions. In resonant flow, both drag components substantially exceed the single-layer hydrostatic drag estimate used in most parameterization schemes. Both drag components are optimally amplified for a relatively low-level inversion and Froude numbers Fr ≈ 1. While propagating-wave drag is maximized for approximately hydrostatic flow, trapped-lee-wave drag is maximized for l2a = O(1) (where l2 is the Scorer parameter in the stable layer and a is the mountain width). This roughly happens when the horizontal scale of trapped lee waves matches that of the mountain slope. The drag behavior as a function of Fr for l2H = 0.5 (where H is the inversion height) and different values of l2a shows good agreement with numerical simulations. Regions of parameter space with high trapped-lee-wave drag correlate reasonably well with those where lee-wave rotors were found to occur in previous nonlinear numerical simulations including frictional effects. This suggests that trapped-lee-wave drag, besides giving a relevant contribution to low-level drag exerted on the atmosphere, may also be useful to diagnose lee-rotor formation.