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.

Abstract:In this article, we present an overview of the HyIV-CNRS-SecORo (Hydralab IV-CNRS-Secondary Orography and Rotors Experiments) laboratory experiments carried out in the CNRM (Centre National de Recherches Météorologiques) large stratified water flume. The experiments were designed to systematically study the influence of double obstacles on stably stratified flow. The experimental set-up consists of a two-layer flow in the water tank, with a lower neutral and an upper stable layer separated by a sharp density discontinuity. This type of layering over terrain is known to be conducive to a variety of possible responses in the atmosphere, from hydraulic jumps to lee waves and highly turbulent rotors. In each experiment, obstacles were towed through the tank at a constant speed. The towing speed and the size of the tank allowed high Reynolds-number flow similar to the atmosphere. Here, we present the experimental design, together with an overview of laboratory experiments conducted and their results. We develop a regime diagram for flow over single and double obstacles and examine the parameter space where the secondary obstacle has the largest influence on the flow. Trapped lee waves, rotors, hydraulic jumps, lee-wave interference and flushing of the valley atmosphere are successfully reproduced in the stratified water tank. Obstacle height and ridge separation distance are shown to control lee-wave interference. Results, however, differ partially from previous findings on the flow over double ridges reported in the literature due to the presence of nonlinearities and possible differences in the boundary layer structure. The secondary obstacle also influences the transition between different flow regimes and makes trapped lee waves possible for higher Froude numbers than expected for an isolated obstacle.