Interaction between lee-waves and a planetary boundary layer

Lee-waves are often described as standing waves trapped between a flat solid surface and an elevated wave-ducting layer, where the Scorer parameter decreases with height sharply. A missing component in this classical lee-wave model is the planetary boundary layer, which may modulate lee-waves through momentum and energy exchanges. The interaction between lee-waves and the boundary layer underneath is investigated in this model-based theoretical study. It is demonstrated that a turbulent boundary layer could act as a sponge that partially absorbs downward propagating wave energy. As a result, the lee-wave amplitude and wave energy decay exponentially with increasing downstream distance, i.e., w(x) = w(x=0) exp(-x/L), where L, referred to as the decay distance, is a characteristic length scale. Corresponding to the boundary absorption, the momentum and energy fluxes averaged over lee-waves are positive and negative respectively between the boundary layer top and the wave-ducting layer aloft, indicating a net downward transfer of wave energy. The loss of momentum in the boundary layer tends to increase the boundary layer depth.

The sensitivity of the decay distance L to different types of boundary layers has been examined. In general, L increases with the boundary layer depth, and L is significantly larger in the presence of a stagnant layer underneath the boundary layer. To understand absorption mechanisms, high-resolution simulations have been performed to test two hypotheses; wave-absorption through interaction between lee-waves and the viscous boundary layer, and wave-absorption associated with a critical level in the boundary layer. Preliminary results suggest that both mechanisms are relevant to lee-wave absorption.