Lee Waves on the Boundary-Layer Inversion and Their Dependence on Free-Atmospheric Stability

Abstract

This study examines gravity waves that develop at the boundary-layer capping inversion in the lee of a mountain ridge. By comparing different linear wave theories, we show that lee waves that form under these conditions are most accurately described as forced interfacial waves. Perturbations in this type of flow can be studied with a linear two-dimensional model with constant wind speed and a sharp density discontinuity separating two layers, a neutral one below and a stable one above. Defining the model parameters on the basis of observations taken in the Madeira archipelago, we highlight the impact of upper-level stability on interfacial waves. We demonstrate that stable stratification aloft limits the possible range of lee wavelengths and modulates the length of the stationary wave mode. Finally, we show that the stable stratification aloft strongly constrains the validity of the shallow-water (or long-wave) approximation by permitting only short-wave modes to be trapped at the interface.

Exchange Processes in the Atmospheric Boundary Layer Over Mountainous Terrain

“…• Inversion layers above mountain tops control the amplitude and wavelength of propagating and trapped wave modes (Figure 5b). Low-level inversions exceeding critical strength or located above critical height trap wave energy in the underlying boundary layer [213]. Some authors described the impact of stable layers on gravity waves as if it were that of a virtual topography [214].…”

Water Tank Experiments on Stratified Flow over Double Mountain-Shaped Obstacles at High-Reynolds Number

“…Although this effect may account for the small discrepancies between the single obstacle regime diagram (Figure 6a) and the one from Vosper [35], it cannot explain the occurrence of trapped lee waves at very high Froude numbers for double obstacle experiments (Figure 6b-d) since NH 1 /U did not vary much between the relevant single and double obstacle experiments. As shown in [37], the stratification above has additionally relatively little influence on the non-linearity of the waves on the inversion.…”

“…Following Sachsperger et al [37] the changes in the stable stratification above have a two-fold influence on the waves forming on the interface. The first one is reducing the lee-wave wavelength; the second is modulating which waves are able to propagate through the interface.…”

“…The flow was classified as trapped lee waves when regular undulations formed in the lee of the obstacles, without noticeable mixing and the wavelength of the wave was smaller than the maximum wavelength for which waves can be trapped on the inversion (cf. [37])…”

“…Given that waves trapped on the inversion (i.e., density jump) are surface waves and therefore different in nature to those trapped by positive shear (cf. [36,37]), the overall goals of HyIV-CNRS-SecORo experiments were to:…”