Interaction between Trapped Waves and Boundary Layers

The absorption of trapped lee waves by the atmospheric boundary layer (BL) is investigated based on numerical simulations and theoretical formulations. It is demonstrated that the amplitude of trapped waves decays exponentially with downstream distance due to BL absorption. The decay coefficient, α, defined as the inverse of the e-folding decay distance, is found to be sensitive to both surface momentum and heat fluxes. Specifically, α is larger over a rougher surface, associated with a more turbulent BL. On the other hand, the value of α decreases with increasing surface heating and increases with increasing surface cooling, implying that a stable nocturnal BL is more efficient in absorbing trapped waves than a typically deeper and more turbulent convective BL. A stagnant layer could effectively absorb trapped waves and increase α. Over the range of parameters examined, the absorption coefficient shows little sensitivity to wave amplitude. A relationship is derived to relate the surface reflection factor and the wave decay coefficient. Corresponding to wave absorption, there are positive momentum and negative energy fluxes across the boundary layer top, indicating that an absorbing BL serves as a momentum source and energy sink to trapped waves. Wave reflection by a shallow viscous layer with a linear shear is examined using linear theory, and its implication on BL wave absorption is discussed.