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.

The island of Madeira is well known for giving rise to atmospheric wakes. Strong and unsteady atmospheric wakes, resembling a von Kármán vortex street, are frequently observed in satellite images leeward of Madeira, especially during summer months, when conditions favoring the formation of atmospheric wakes occur frequently under the influence of the Azores high. Reported here is the analysis of the first airborne measurements of Madeira’s wake collected during the 2010 Island-induced Wake (I-WAKE) campaign. High-resolution in situ and remote sensing data were collected in the I-WAKE by a research aircraft. The measurements reveal distinctive wake signatures, including strong lateral wind shear zones and warm and dry eddies downwind of the island. A strong anticorrelation of the horizontal wind speed and sea surface temperature (SST) was found within the wake. High-resolution numerical simulations with the Weather Research and Forecasting (WRF) Model were used to study the dynamics of the wake generation and its temporal evolution. The comparison of the model results and observations reveals a remarkable fidelity of the simulated wake features within the marine boundary layer (MBL). Strong potential vorticity (PV) anomalies were found in the simulated MBL wake, emanating from the flanks of the island. The response of the wake formation within the MBL to surface friction and enhanced thermal forcing is explored through the model sensitivity analyses.

This study presents an analytical model for the amplitude of lee waves on the boundary-layer inversion in two-dimensional flow. Previous linear lee wave models, in which the amplitude depends on the power spectrum of topography, can be inaccurate if the amplitude is large. Our model incorporates nonlinear effects by assuming that lee waves originate at a region of transition between super-and subcritical flow (internal jump) downstream of topography. Energy flux convergence at this location is compensated by the radiation of laminar lee waves. The available energy is estimated using a hydraulic jump model and the resulting wave amplitude is determined from linear theory. According to this model, the amplitude of lee waves depends essentially on their wavelength and on the inversion height difference across the jump. The new amplitude model is verified against numerical simulations and water tank experiments. The agreement between the model and the numerical results is excellent, while the verification with water tank experiments reveals that the accuracy of the model is comparable to that of numerical simulations. Finally, we derive a nonlinearity parameter for interfacial lee waves and discuss the regime transition from lee waves to hydraulic jumps in terms of the Froude number and the non-dimensional mountain and inversion heights.

The coupling between mountain waves in the free atmosphere and rotors in the boundary layer is investigated using a two-dimensional numerical model and linear wave theory. Uniformly stratified flow past a single mountain is examined.Depending on background stratification and mountain width, different wave regimes are simulated, from weakly to strongly nonlinear and from hydrostatic to non-hydrostatic. Acting in conjunction with surface friction, mountain waves cause the boundary layer to separate from the ground, causing the development of atmospheric rotors in the majority of the simulated flows.The rotors with largest vertical extent and strongest reverse flow near the ground are found to develop when the wave field is nonlinear and moderately non-hydrostatic, in line with linear theory predictions showing that the largest wave amplitudes develop in such conditions. In contrast, in near-hydrostatic flows boundary-layer rotors form even if the wave amplitude predicted by linear theory is relatively small. In such cases, rotors appear to be decoupled from the wave field aloft by low-level wave breaking. In fact, rotor formation is caused by short-wavelength modes propagating horizontally along an elevated and stably stratified jet below the neutrally stratified wave-breaking region. Once formed, atmospheric rotors trigger non-hydrostatic wave modes that can penetrate through the finite-depth neutral layer above the jet and propagate into the free atmosphere.In all simulated cases, non-hydrostatic effects -i.e. sharp vertical accelerations -appear to be essential for rotor formation, regardless of the degree of hydrostaticity in the primary wave field.