A theory of gravity wave absorption by a houndary layer

A one-layer model of the atmospheric boundary layer (BL) is proposed to explain the nature of lee-wave attenuation and gravity wave absorption seen in numerical simulations. Two complex coefficients are defined: the compliance coefficient and the wave reflection coefficient. A real-valued ratio of reflected to incident wave energy is also useful. The key result is that, due to horizontal friction, the wind response in the BL is shifted upstream compared to the phase of disturbances in the free atmosphere. The associated 4 flow divergence modulates the thickness of the BL so that it partially absorbs incident gravity waves. A simple expression is derived relating the reflection coefficient to the attenuation and wavelength shift of trapped lee waves. Results agree qualitatively with the numerical simulations, including the effects of increased surface roughness and heat flux.