Lee Waves Research Articles

Internal gravity waves in flow past a bluff body under different levels of stratification

The flow field of a bluff body, a circular disk, that moves horizontally in a stratified environment is studied using large-eddy simulations. Five levels of stratification (body Froude numbers of ${{Fr}} = 0.5, 1, 1.5, 2$ and $5$ ) are simulated at Reynolds number of ${{Re}} = 5000$ and Prandtl number of $Pr =1$ . A higher ${{Re}} = 50\,000$ database at ${{Fr}} = 2, 10$ and $Pr =1$ is also examined for comparison. The wavelengths and amplitudes of steady lee waves are compared with a linear-theory analysis. Excellent agreement is found over the entire range of ${{Fr}}$ if an ‘equivalent body’ that includes the separation region is employed for the linear theory. For asymptotically large distances, the velocity amplitude varies theoretically as ${{Fr}}^{-1}$ but a correction owing to the dependence of the separation zone on ${{Fr}}$ is needed. The wake waves propagate in a narrow band of angles with the vertical, and have a wavelength that increases with increasing ${{Fr}}$ . The envelope of wake waves, demarcated using buoyancy variance, exhibits self-similar behaviour. The higher ${{Re}}$ results are consistent with the buoyancy effects exhibited at the lower ${{Re}}$ . The wake wave energy is larger at ${{Re}} = 50\,000$ . Nevertheless, independent of ${{Fr}}$ and ${{Re}}$ , the ratio of the wake wave potential energy to the wake turbulent energy increases to approximately 0.6–0.7 in the non-equilibrium stage showing their energetic importance besides suggesting universality in this statistic. There is a crossover of energetic dominance of lee waves at ${{Fr}} <2$ to wake-wave dominance at ${{Fr}} \approx 5$ .

Deep Mesoscale and Submesoscale Circulations Around the Atlantis II Seamount

AbstractThis study investigates the complex interactions between the North Atlantic Current (NAC) and the New England Seamount chain, focusing on the Atlantis II seamount. Employing a high‐resolution submesoscale permitting regional ocean circulation model nested within a basin‐wide simulation, it explores three distinct periods, each 2 weeks long, showcasing varied deep mesoscale and submesoscale circulations around the seamount. The analysis includes Eulerian statistics and Lagrangian particle tracing experiments to explore the transport and mixing impacts of the highly dynamic flow around the seamount. The results reveal significant density variations across the water column, attributed to the seamount's influence on local ocean currents. Specifically, mesoscale and submesoscale vortices, a seamount wake, and lee waves form during periods of increased near‐bottom current flow. These findings highlight the critical role of topographic features in modulating oceanic flows and ocean mixing, which have implications, among others, for nutrient distribution, acoustic propagation, and climate modeling. The variety and variability of the mesoscale and submesoscale circulations that arise in response to the variability in the NAC strength and position in relation to the New England Seamount Chain demonstrate the difficulty in extrapolating general behaviors from isolated observational campaigns.

Impact of mountain-wave-induced temperature fluctuations on the occurrence of polar stratospheric ice clouds: a statistical analysis based on MIPAS observations and ERA5 data

Abstract. Temperature fluctuations induced by mountain waves can play a crucial role in the formation of polar stratospheric clouds (PSCs). In particular, the cold phase of the waves can lower local temperatures sufficiently to trigger PSC formation, even when large-scale background temperatures are too high. To provide new quantitative constraints on the relevance of this effect, this study analyzes a decade (2002–2012) of ice PSC detections obtained from Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) measurements and ERA5 data in the polar winter lower stratosphere. In the MIPAS observations, we find that approximately 52 % of the Arctic ice PSCs and 26 % of the Antarctic ice PSCs are detected at temperatures above the local Tice. Ice PSCs above Tice are concentrated around mountainous regions and their downwind directions. A backward-trajectory analysis is performed to investigate the temperature history of each ice PSC observation. The cumulative fraction of ice PSCs above Tice increases as the trajectory gets closer to the observation point. The most significant change in the fraction of ice PSCs above Tice occurs within the 6 h preceding the observations. At the observation point, the mean fractions of ice PSCs above Tice, taking into account temperature fluctuations along the backward trajectory, are 33 % in the Arctic and 9 % in the Antarctic. The results provide a quantitative assessment of the occurrence of ice PSCs above Tice in connection with orographic waves. Additionally, the observational statistics presented can be utilized for comparison with chemistry climate simulations.

The Rapid Response of Southern Ocean Biological Productivity to Changes in Background Small Scale Turbulence

AbstractBackground subsurface vertical mixing rates in the Southern Ocean (SO) are known to vary by an order of magnitude temporally and spatially, due to variability in their generating mechanisms, which include winds and shear instabilities at the surface, and the interaction of tides and lee waves with rough bottom topography. There is great uncertainty in the parameterization of this mixing in coarse resolution Earth System Models (ESM), and in the impact that this has on SO biological productivity on sub decadal timescales. Using a data assimilating biogeochemical ocean model we show that SO phytoplankton productivity is highly sensitive to differences in background diapycnal mixing over short timescales. Changes in the background vertical mixing rates alter key biogeochemical and physical conditions. The greatest changes to the distribution of physical and biogeochemical tracers occur in regions with very strong tracer vertical gradients. A combination of reduced nutrient limitation and reduced light limitation causes a strong increase in SO phytoplankton productivity with higher background mixing. This leads to increased summer carbon export but reduced wintertime export over the mixed layer depth, which could alter the strength of the SO biological carbon pump and atmospheric concentrations on centennial to millennial timescales. This study demonstrates the importance of accurately representing diapycnal mixing in ESM to predict SO biogeochemical dynamics and their broader climatic implications.

Effects of Stratification on Wind‐Driven Upwelling Over a Coastal Valley

AbstractIn‐situ observations indicate variations in stratified conditions over the coastal valley off the Sansha Bay in the northwestern Taiwan Strait across different years. However, dynamic processes and mechanisms governing the upwelling process over the valley, as influenced by stratification, are still unknown. By employing idealized numerical simulations, we demonstrate that compared to the unstratified case, the surface offshore flow intensifies, upwelling flux and net cross‐shore transport are enhanced, upwelling area expands, and the cross‐shore velocity structure is modified over the valley under stratified conditions. The primary factor controlling the vertical velocity within the valley is the relative vorticity change along a streamline (RVC). Further decomposition of the RVC reveals that the depth‐averaged alongshore velocity () and the depth‐averaged alongshore gradient of vorticity () primarily modulate the magnitude and spatial distribution of the vertical velocity. The negative zone of the expands in the valley, resulting in a larger upwelling area. The magnitude of the in the upper layer is slightly enhanced. The combined influence of these two factors leads to increased upwelling flux in the valley under stratified conditions. The net upslope motion over the valley is intensified under stratified conditions. The augmented advection of relative potential vorticity, originating from the increased amplitude of coastal trapped lee waves, primarily contributes to the enhanced net cross‐shore transport in the valley.

Transient Tropopause Waves

Abstract Flight-level airborne observations have often detected gravity waves with horizontal wavelengths near the tropopause. Here, in situ and remote sensing aircraft data of these short gravity waves trapped along tropopause inversion layer and collected during a mountain-wave event over southern Scandinavia are analyzed to quantify their spectral energy and energy fluxes and to identify nonstationary modes. A series of three-dimensional numerical simulations are performed to explain the origin of these transient wave modes and to investigate the parameters on which they depend. It turns out that mountain-wave breaking in the middle atmosphere and the subsequent modification of the stratospheric flow are the key factors for the occurrence of trapped modes with . In particular, the intermittent and periodic breaking of mountain waves in the lower stratosphere forms a wave duct directly above the tropopause, in which the short gravity waves are trapped. The characteristics of the trapped, downstream-propagating waves are mainly controlled by the sharpness of the tropopause inversion layer. It could be demonstrated that different settings for optimizing the numerical solver have a significantly smaller influence on the solutions.

Study of the Mountain Wave Generation over the European Part of Russia and Assessment of Forecasting Capabilities for Aviation Using the COSMO-Ru6.6 Model

Study of the Mountain Wave Generation over the European Part of Russia and Assessment of Forecasting Capabilities for Aviation Using the COSMO-Ru6.6 Model

Modification of the microclimate and fire danger by Berg winds in the midlands of KwaZulu-Natal

ABSTRACT Wildfires have the potential to result in significant loss of life and property damage. Mountain wave flow events (Berg winds) are integrally linked to periods of enhanced fire danger. The basis for enhanced fire danger during periods of mountain winds has long been established, supported by evidence from a number of case studies. A fuzzy logic model, applied to hourly meteorological data from four different sites varying in elevation, allowed for an in-depth study of the effects of Berg winds on the microclimate and fire danger. Results indicate that night-time Berg wind events occur less frequently than daytime events, also having a significantly reduced influence on the microclimate. Daytime Berg wind events were shown to result in a significant change in the microclimate and fire danger across all sites. Night-time Berg wind events did not result in significant change to air temperature and relative humidity but when combined with significant changes to wind speed did result in significant increases in fire danger. The sensitivity of the Lowveld Fire Danger Index was also tested. The study emphasizes the need for boundary layer processes such as Berg winds to be taken into account when forecasting and monitoring fire danger.

Mountain waves developing inside and aloft stably stratified turbulent boundary layers

AbstractA linear theory of the trapped mountain waves that develop in a turbulent boundary layer is presented. The theory uses a mixing‐length turbulence model based on Monin–Obukhov similarity theory. First, the backward reflection of a stationary gravity wave propagating toward the ground is examined. Three parameters are investigated systematically: the Monin–Obukhov length , the roughness length , and the limit value of the mixing length aloft the “inner” layer. The reflection coefficient appears to depend strongly on the Richardson number aloft the inner layer (, with the von Kármán constant), with the reflection decreasing when the stability increases. The influence of the roughness and mixing lengths on the reflection is explained in terms of the depth of a “pseudo”‐critical level located below the surface, with the reflection decreasing when the depth of the “pseudo”‐critical level decreases. The preferential modes of oscillations occurring in the presence of mountain forcing are then analysed, with the decay rate of the trapped waves downstream increasing when the reflection decreases. At a certain point nevertheless, when the absorption is large but the boundary‐layer depth deep enough, trapped modes appear that interact little with the surface.

Modulation of the wake of a horizontal cylinder by pycnocline thickness in stratified flow

This study investigates the modulating effect of the pycnocline thickness in two-dimensional stratified flow on a cylinder. It encompasses three typical flow regimes identified by Boyer in experiments conducted within the Reynolds number range of Re = 260–2000. Quantitative control of the modulation effect of internal interface waves on the cylinder wake is achieved by varying the thickness of the pycnocline. Under appropriate thickness of the pycnocline, a multiple-centerline-structure can transition to isolated-mixed-structure flow regimes and Double-Eddy-Wavy-Wake flow regimes. Similar modulation patterns are also observed in isolated-mixed flow regimes. Normalized pressure distribution and velocity fields indicate that in low Reynolds number flow regimes (Re < 600), downstream isolated mixed regions generate dynamic pressure that periodically cascades upstream. This periodic reverse energy transfer provides favorable adverse pressure gradients, cyclically reducing the drag force on the cylinder. The cyclic period is, for the first time, classified into four stages: dynamic pressure storage stage, dynamic pressure transfer stage, dynamic pressure consumption stage, and dynamic pressure exhaustion stage. Despite the highly nonlinear modulation effect of internal interface waves in low Reynolds number conditions, the linear predictive theory of lee waves based on streamline equations remains instructive in predicting the trend of lee waves wavelength variation with pycnocline thickness. Drawing upon the modulation study results concerning the pycnocline thickness on lee waves, a regime map is constructed, illustrating the directional evolution of lee waves flow patterns based on variations in pycnocline thickness.

Study of nonlinear trapped lee waves in the modified β-plane approximation

In the modified β-plane approximation, we derive exact solutions to the nonlinear governing equations of three-dimensional trapped lee waves influenced by Coriolis forces or Coriolis forces and centripetal forces, respectively. Further, we obtain the dispersion relation and qualitatively analyze the pressure, density, and vorticity in two cases. In this process, we find more accurate representations of solutions caused by the incorporation of a gravitational-correction term and investigate the influence of centripetal forces on trapped lee waves.

Underestimates of Orographic Precipitation in Idealized Simulations. Part II: Underlying Causes

Abstract Warm-sector orographic precipitation in a midlatitude cyclone encountering a ridge is simulated in a “Cyc+Mtn” experiment. A second “Shear” simulation is conducted with horizontally uniform unidirectional flow over the same mountain having thermodynamic and cross-mountain wind profiles identical to those on the centerline in the “Cyc+Mtn” simulation. The relationship between integrated vapor transport (IVT) and orographic precipitation in the Mtn+Cyc case is consistent with observations, yet the same IVT in the Shear simulation produces far less precipitation. The difference between the precipitation rates in the Cyc+Mtn and Shear cases is traced to differences in the cross-mountain moisture-flux convergence and is further isolated to differences in the cross-mountain-velocity convergence over the windward slope. The winds at the ridge crest are stronger in the Shear case, leading to more velocity divergence and decreased moisture-flux convergence. The stronger ridge-crest winds in the Shear case are produced by a stronger mountain wave, which persists after being generated during the artificial startup of the Shear simulation. Initializing with a gradually ramped-up unidirectional flow and integrating to a quasi-steady state fails to adequately capture the processes regulating the leeside circulations. Even worse results are obtained if the shear flow is instantaneously accelerated from rest. An alternative microphysical explanation for the precipitation difference between the Cyc+Mtn and Shear simulations is examined using additional numerical experiments that enhance the seeder–feeder process. Although such enhancements increase precipitation, the increase is too small to account for the differences between the Cyc+Mtn and Shear simulations. Significance Statement Our results highlight the difficulty in conducting studies of mesoscale atmospheric circulations in isolation from their surrounding environment. This approach often allows for more computationally efficient and detailed analysis of the target phenomena by reducing the size of the computational domain. But, at least in the case of orographic precipitation, such isolation can significantly limit the realism of the simulated process.

The Meteorology of the August 2023 Maui Wildfire

Abstract On 8 August 2023, a wind-driven wildfire pushed across the city of Lahaina, located in West Maui, Hawaii, resulting in at least 100 deaths and an estimated economic loss of 4–6 billion dollars. The Lahaina wildfire was associated with strong, dry downslope winds gusting to 31–41 m s−1 (60–80 kt; 1 kt ≈ 0.51 m s−1) that initiated the fire by damaging power infrastructure. The fire spread rapidly in invasive grasses growing in abandoned agricultural land upslope from Lahaina. This paper describes the synoptic and mesoscale meteorology associated with this event, as well as its predictability. Stronger-than-normal northeast trade winds, accompanied by a stable layer near the crest level of the West Maui Mountains, resulted in a high-amplitude mountain-wave response and a strong downslope windstorm. Mesoscale model predictions were highly accurate regarding the location, strength, and timing of the strong winds. Hurricane Dora, which passed approximately 1300 km to the south of Maui, does not appear to have had a significant impact on the occurrence and intensity of the winds associated with the wildfire event. The Maui wildfire was preceded by a wetter-than-normal winter and near-normal summer conditions. Significance Statement The 2023 Maui wildfire was one of the most damaging of the past century, with at least 100 fatalities. This paper describes the meteorological conditions associated with the event and demonstrates that excellent model forecasts made the threat foreseeable.

Subtropical Foehn Winds, Southeast Queensland, Australia

AbstractFoehn winds have been a focus of research in mid‐latitude mountainous regions for more than 150 years, where their onset is typically associated with warm, dry, and gusty winds. This research has now extended into high latitude regions, yet research of foehn winds in subtropical and tropical regions remains scarce. Here we present results from the first investigation of foehn winds in the subtropics of Southeast Queensland (SEQ), Australia. Analysis of meteorological records found that foehn winds occur throughout the year with peak frequency and duration in late winter (August) associated with the passage of shortwave troughs over southern Australia. Modeling of wind fields and atmospheric boundary layer conditions for three case studies was conducted using the Weather Research and Forecasting (WRF) model. Results showed foehn events in SEQ can be associated with mountain waves and hydraulic jump features in the lee of topographic barriers. Over lee slopes, acceleration of wind speeds and topographic channeling of foehn winds was found to occur, along with substantial increases in air temperature, and decreases in relative humidity. Warming of the foehn airstream is believed to occur primarily through isentropic drawdown with a likely contribution from surface sensible heat flux. Recommendations for future research are made in light of the importance of foehn winds to wildfire management and mitigation in SEQ.

Seamounts generate efficient active transport loops to nourish the twilight ecosystem.

Seamounts are ecological oases nurturing abundant fisheries resources and epibenthic megafauna in the vast oligotrophic ocean. Despite their significance, the formation mechanisms underlying these seamount ecological oases remain uncertain. To shed light on this phenomenon, this study conducted interdisciplinary in situ observations focusing on a shallow seamount in the oligotrophic ocean. The findings show that the seamount's topography interferes with the oceanic current to generate lee waves, effectively enhancing the nutrient supply to the euphotic layer downstream of the seamount. This continuous supply enhances phytoplankton biomass and subsequently the grazing and diurnal vertical migration of zooplankton, rapidly transporting the augmented phytoplankton biomass to the aphotic layer. Unlike the cyclonic eddies that move in the upper ocean, seamounts stand at fixed locations creating a more efficient and steady active transport loop. This active transport loop connects the euphotic and twilight zones, potentially conveying nourishment to benthic ecosystems to create stereoscopic oases in the oligotrophic ocean.

On the role of seamounts in upwelling deep-ocean waters through turbulent mixing

Turbulent mixing in the ocean exerts an important control on the rate and structure of the overturning circulation. However, the balance of processes underpinning this mixing is subject to significant uncertainties, limiting our understanding of the overturning's deep upwelling limb. Here, we investigate the hitherto primarily neglected role of tens of thousands of seamounts in sustaining deep-ocean upwelling. Dynamical theory indicates that seamounts may stir and mix deep waters by generating lee waves and topographic wake vortices. At low latitudes, stirring and mixing are predicted to be enhanced by a layered vortex regime in the wakes. Using three realistic regional simulations spanning equatorial to middle latitudes, we show that layered wake vortices and elevated mixing are widespread around seamounts. We identify scalings that relate mixing rate within seamount wakes to topographic and hydrographic parameters. We then apply such scalings to a global seamount dataset and an ocean climatology to show that seamount-generated mixing makes an important contribution to the upwelling of deep waters. Our work thus brings seamounts to the fore of the deep-ocean mixing problem and urges observational, theoretical, and modeling efforts toward incorporating the seamounts' mixing effects in conceptual and numerical ocean circulation models.

Additional Clearance over Obstacles to Determine Minimum Flight Altitude in Mountainous Terrain

The International Civil Aviation Organization (ICAO) specifies that in the design phase of instrument flight procedures, an additional clearance may be added to an obstacle when flights are over mountainous terrain. This clearance increase can be up to 100 per cent of the minimum obstacle clearance (MOC). Airspace and instrument flight procedure designers usually face the problem of determining what value should be applied, since setting the maximum value of 100% often implies operational penalties, but there are no standardized criteria to determine lower values. The ICAO PANS-OPS indicates that the additional clearance over obstacles in mountainous areas is caused by two effects, both related to orography and wind speed. The first effect is due to the altimeter indication error. The second one is related to the loss of altitude when an aircraft is exposed to turbulence produced by mountain waves. This paper presents a methodology for determining the additional clearance to be applied over obstacles when, in the flight procedure design phase, the overflight of mountainous terrain is expected. Through this methodology, results have been achieved for the proposal of an appropriate additional clearance. The development of graphs and tables allows us to identify which additional value should be considered in each case.

Variability of the Southern Andes rain shadow

The southern Andes mountain range plays a determinant role in separating humid Chilean climate from dry Argentinian climate. However, there is substantial event-to-event variability in rain shadow strength, such that some precipitation events are able to produce significant spillover precipitation over the Argentinian side. This study investigates the mechanisms modulating the rain shadow strength across the Southern Andes. Rain gauge measurements from Chile and Argentina were used to classify events according to their rain shadow strength, as strong rain shadow (SRS) or weak rain shadow (WRS). ERA5 reanalysis was used to analyze synoptic conditions during these events. Differences between events show that the 0 °C isotherm is higher during SRS events. SRS cases exhibit a larger windward deceleration of cross-barrier wind than WRS events, indicating a blocking signature. Strong mountain wave activity increases precipitation upwind of the Andes and suppresses precipitation on the lee for SRS events, while WRS events exhibit weaker wave activity. Zonal moisture flux offshore is larger for SRS events than for WRS. Analysis of the drying ratio suggests that more water vapor is precipitated out or deflected by the mountains and does not reach the leeside in the SRS events compared to WRS events. The following mechanisms controlling the rain shadow strength are suggested: (1) A higher 0 °C causes more liquid precipitation to fall upstream and over the windward slope of the Andes for SRS events, while WRS cases with a lower 0 °C level allow ice particles and snow at the top of the mountain to be advected to the leeside, decreasing the rain shadow, (2) the low-level impinging flow is blocked by the Andes during SRS events, forcing the flow to rise upstream, increasing precipitation upwind and on the windward slope of the Andes, increasing the rain shadow, (3) leeside descent for SRS events suppresses precipitation on the leeside, while weaker wave activity for WRS cases allows for spillover precipitation decreasing the rain shadow, (4) SRS events that are also characterized by strong orographic enhancement could be produced by the landfall of atmospheric rivers to the area, increasing precipitation upstream and decreasing the rain shadow, as a result of the northerly orientation of the flow in contrast with the more zonal orientation of WRS cases.

Behavior and mechanisms of Doppler wind lidar error in complex terrain: stable flow case study at Perdigão

A numerical experiment is carried out investigating the magnitude of biases in ground-based lidar measurements in complex flow conditions. Biases assessed include those arising from flow curvature and from the interaction of turbulence with the wind field reconstruction (WFR) algorithms used by a WindCube lidars and anemometers. RANS-CFD and WRF-LES simulations were performed for the Perdig˜ao Field Experiment site for a range of atmospheric conditions. Virtual anemometer and lidar data were generated for four locations: two near exposed ridge tops and two in low-speed regions in the valley. The LES data at these four locations show that the scalar inflation terms (the relation between scalar and vector averaged wind speed) for virtual lidar and virtual cups agree very well with predictions using perturbation theory. While the lidar errors vary greatly with location and height, the contribution from the flow curvature tends to be larger than the differences arising from scalar inflation. For one lidar/mast pair near the ridge top, comparisons between simulations and measurements are carried out for a resonant mountain wave event on June 14th, 2017, and for the whole duration of the Perdig˜ao campaign for winds perpendicular to the ridges. The lidar error during the mountain wave, a period of strong stability and low inversion height, is significantly larger than the campaign average. The sensitivity of the lidar error to atmospheric stability is confirmed by the RANS simulations, which suggests strong sensitivity of flow curvature error to stability conditions and to the shape of the wind speed profile near the top of the boundary layer.

Influence of air flow features on alpine wind energy potential

Wind energy is one of the potential options to fill the gap in renewable energy production in Switzerland during the winter season when the energy demand exceeds local production capacities. With likely further rising energy consumption in the future, the winter energy deficit may further increase. However, a reliable assessment of wind energy potential in complex terrain remains challenging. To obtain such information, numerical simulations are performed using a combination of the “Consortium for Small-scale Modeling” and “Weather Research and Forecasting” (COSMO-WRF) models initialized and driven by COSMO-1E model, which allows us to simulate the influence of topography at a horizontal resolution of 300 m. Two LiDAR measurement campaigns were conducted in the regions of Lukmanier Pass and Les Diablerets, Switzerland. Observational LiDAR data and measurements from nearby wind sensor networks are used to validate the COSMO-WRF simulations. The simulations show an improved representation of wind speed and direction near the ground compared to COSMO-1E. However, with increasing height and less effect of the terrain, COSMO-WRF tends to overestimate the wind speeds, following the bias that is already present in COSMO-1E. We investigate two characteristic mountain–terrain flow features, namely waves and Foehn. The effect of mountain-induced waves of the flow is investigated through an event that occurred in the area of Diablerets. One-year analysis for the frequency of conditions that are favorable for mountain wave formation is estimated. The Foehn impact on wind was observed in the Lukmanier domain. We attempt quantification of the probability of occurrence using the Foehnix model. The result shows a high probability of Foehn occurrence during the winter and early spring seasons. Our study highlights the importance of incorporating complex terrain-related meteorological events into the wind energy assessment. Furthermore, for an accurate assessment of wind speed in complex terrain, our study suggests the necessity to have a better representation of the topography compared to COSMO-1E.