Gravity Waves Research Articles

Efficient spectral element method for the Euler equations on unbounded domains

Mitigating the impact of waves leaving a numerical domain has been a persistent challenge in numerical modeling. Reducing wave reflection at the domain boundary is crucial for accurate simulations. Absorbing layers, while common, often incur significant computational costs. This paper introduces an efficient application of a Legendre-Laguerre basis for absorbing layers for two-dimensional non-linear compressible Euler equations. The method couples a spectral-element bounded domain with a semi-infinite region, employing a tensor product of Lagrange and scaled Laguerre basis functions. Semi-infinite elements are used in the absorbing layer with Rayleigh damping. In comparison to existing methods with similar absorbing layer extensions, this approach, a pioneering application to the Euler equations of compressible and stratified flows, demonstrates substantial computational savings. The study marks the first application of semi-infinite elements to mitigate wave reflection in the solution of the Euler equations, particularly in nonhydrostatic atmospheric modeling. A comprehensive set of tests demonstrates the method's versatility for general systems of conservation laws, with a focus on its effectiveness in damping vertically propagating mountain gravity waves, a benchmark for atmospheric models. Across all tests, the model presented in this paper consistently exhibits notable performance improvements compared to a traditional Rayleigh damping approach.

Observation of Post-Sunset Equatorial Plasma Bubbles with BDS Geostationary Satellites over South China

An equatorial plasma bubble (EPB) is characterized by ionospheric irregularities which disturb radio waves by causing phase and amplitude scintillations or even signal loss. It is becoming increasingly important in space weather to assure the reliability of radio systems in both space and on the ground. This paper presents a newly established GNSS ionospheric observation network (GION) around the north equatorial ionization anomaly (EIA) crest in south China, which has a longitudinal coverage of ∼30° from 94°E to 124°E. The measurement with signals from geostationary earth orbit (GEO) satellites of the BeiDou navigation satellite system (BDS) is capable of separating the temporal and spatial variations of the ionosphere. A temporal fluctuation of TEC (TFT) parameter is proposed to characterize EPBs. The longitude of the EPBs’ generation can be located with TFT variations in the time–longitude dimension. It is found that the post-sunset EPBs have a high degree of longitudinal variability. They generally show a quasiperiodic feature, indicating their association with atmospheric gravity wave activities. Wave-like structures with different scale sizes can co-exist in the same night.

Main features of the geomagnetic effect of the October 14, 2023 annular solar eclipse in the Americas

The purpose of this paper is to investigate temporal variations in the northward, X, eastward, Y, and downward, Z, components of the geomagnetic field recorded during the October 14, 2023 annular solar eclipse, which main features include its annularity, the eclipse occurrence from local dawn to local dusk, its magnitude variation from 0.30 to 0.86, and the longest ever-observed path across the mainland of the Americas, covering latitudes from ∼65°N to 12°S. The analysis was made possible due to the data on temporal variations in the northward, X, eastward, Y, and downward, Z, components of the geomagnetic field collected at thirteen International Real-time Magnetic Observatory Network magnetometer stations (https://imag-data.bgs.ac.uk/GIN_V1/GINForms2). The solar eclipse acted to cause non-sinusoidal and quasi-sinusoidal perturbations having temporal durations of 180–240 min in all geomagnetic field components on a global scale (∼8000 km). The X-component experienced the largest perturbations attaining 10–20 nT, and the Z-component underwent the smallest disturbances. The quasi-sinusoidal perturbation amplitude did not exceed 5–6 nT, and the period most often showed variations within 15–40 min. The magnetic effect exhibited a tendency to increase with solar eclipse magnitude, while the magnitude of the effect has been shown to be significantly dependent on geographic coordinates, local time, ionospheric state, and the patterns of ionospheric currents as well. During the solar eclipse, the electron density depletion was estimated to be ∼0.10 to ∼0.40–0.60 when the eclipse obscuration Amax varied from 19% to 82%. The movement of the lunar shadow was accompanied by the generation of atmospheric gravity waves with period of ∼10–80 min and by electron density perturbations with amplitudes of the order of 0.01–0.03. The estimates made on the assumption that the magnetic effect is due to the ionospheric current disruptions show good agreement with the observations.

Observations of waves and currents on the fore-reef and reef flat of a coral reef atoll in the South China Sea

Understanding the wave and current conditions of coral reef ecosystems is essential for maintaining their health, as many reef processes are controlled by these hydrodynamic conditions. In this study, high-frequency measurements of tides, waves, and currents were made using acoustic, electromagnetic, and pressure instruments over a 28-d period on the fore-reef and reef flat of a coral reef atoll in the South China Sea. The research revealed wave transformation, tidal and wave modulation of flow, and wave setup conditions for the first time at this typical atoll. Three large wave processes dominated by gravity waves (GWs) are observed in the fore-reef. The GWs are significantly attenuated on the reef flat, whereas infragravity (IG) waves strengthened. The tidal modulation of GWs and IG waves on the reef flat is significant when the incident wave height exceeded 1 m. In the fore-reef, the modulation of progressive tidal waves and large waves leads to relatively stronger upper-layer currents, and weak near-bottom currents are primarily attributed to the dissipation of tidal wave energy by the rough coral terrain. In calm conditions, flow variations on the reef flat are modulated by tides, thereby allowing seawater flow to pass through the reef flat during spring tides. Conversely, during periods with large waves, tidal modulation of flow on the reef flat is less significant, and the cross-reef flow velocity increases with increasing incident wave height. The occurrence of wave setup on the reef flat enhances cross-reef flow towards the lagoon. The wave setup is positively linearly correlated with the incident wave height. The magnitude of wave setup is associated with the distance between the measurement sites on the fore-reef and reef flat.

Diurnal off-mountain propagation of rainfall and low-level vertical velocity over the leeside of the Yungui Plateau

Abstract Diurnal off-mountain propagation is a distinctive feature of rainfall over terrestrial areas, whereas the causes of this phenomenon are not well understood. Focused on the rainfall downstream of the Yungui Plateau (YGP), this study aims to examine whether the gravity waves stimulated by an assumed terrain-related thermal forcing could explain the feature. The results show that rainfall diurnal phase propagates eastward at a speed of approximately 13 m s−1 over the leeside of YGP during warm seasons. The diurnal amplitude reaches its zonally maximum over the slope of the YGP and drops sharply downstream the terrain. The low-level vertical velocity exhibits similar diurnal characteristics. A linear model forced by a hollow heating is proposed to mimic the thermal forcing related to a mountain. Experiments with the model show that there are mainly two branches of waves around the terrain. One is over the upstream with upwind tilting phase lines that moves towards −z and −x directions. The other branch exists over the leeside of terrain with downwind tilting phase lines that moves towards −z and +x directions, which is considered to be relevant to the off-mountain propagation feature. The wave behavior over the YGP is then reproduced using the model. It is shown that the main features of the diurnal phase lag and the zonal amplitude distribution pattern of the low-level updraft could be captured by the model, suggesting an important role of the gravity wave in driven the diurnal propagation of vertical velocity and rainfall downstream large terrains.

Hetero-Bäcklund Transformation for a (2+1)-Dimensional Generalized Modified Dispersive Water-Wave System

This work is designed for a (2+1)-dimensional generalized modified dispersive water-wave system for the nonlinear and dispersive long gravity waves travelling along two horizontal directions in the shallow water of uniform depth, with our results as a hetero-B acklund transformation, from that system to a known generalized (2+1)-dimensional dispersive long-wave system. As for the height of the water surface and horizontal velocity of the water wave, our hetero-Backlund transformation depends on the shallow-water coefficients in that system.

Virtual Reflection Height of Nighttime Equatorial Ionosphere Estimated With Low‐Frequency Magnetic Sferics Measured in Malacca

AbstractThe return stroke of cloud‐to‐ground (CG) lightning is an impulsive radiator of very low‐frequency/low‐frequency (VLF/LF) electromagnetic signals allowing for the remote sensing of lower ionosphere over large spatial coverage. In this study, we examined the LF magnetic fields measured in Malacca, Malaysia, to probe reflection heights of the lower ionosphere near the equator on three different nights in 2021. The results show that the virtual ionospheric height at nighttime typically ranged from 82.0 to 90.0 km, with a mean value of 85.3 km. Our measurements also revealed significant variations in the virtual ionospheric height across different regions over a spatial scale of about 800 km. The maximum height difference was about 5.0 km. Moreover, the fluctuation characteristics are observed in both estimated ionospheric height and calculated peak reflection ratio during similar periods. This fluctuation may be related to atmospheric gravity waves in the nighttime ionosphere. In addition, we compared the virtual ionospheric height estimated from CG strokes of different polarities, and the results showed that the virtual reflection height for positive CG strokes is lower than that for negative ones.

Tropical Aviation Turbulence Induced by the Interaction Between a Jet Stream and Deep Convection

AbstractOn 18 December 2022, Hawaiian Airlines flight HA35 encountered severe turbulence without warning in a cloud‐free height. We reproduced this incident using the Weather Research and Forecasting Model (WRF) at a convection‐permitting resolution. We found that this case of tropical upper‐level turbulence occurred primarily due to the fast‐growing convective tower in the unstable layer created by gravity wave breaking. At lower altitudes, a mesoscale convective system (MCS) caused a decrease in wind speed in both upstream and downstream regions. At upper levels, a large‐scale jet descended and accelerated after flowing over the top of the MCS, which acted like a barrier and produced a situation similar to a downslope windstorm due to mountain terrain. Upper‐level turbulence is 2–3 km higher than the top of the MCS. The critical level above the jet and the locally self‐induced critical level created the locally enhanced descending jet stream, which destabilized the flow through Kelvin–Helmholtz instabilities. The convective tower existed near the flight route and played an important role in triggering turbulence in the unstable environment through its convective gravity waves.

Slowly Traveling Gravity Waves for Darcy Flow: Existence and Stability of Large Waves

Slowly Traveling Gravity Waves for Darcy Flow: Existence and Stability of Large Waves

Scalar induced gravity waves from ultra slow-roll galileon inflation

We consider the production of secondary gravity waves in Galileon inflation with an ultra-slow roll (USR) phase and show that the spectrum of scalar-induced gravitational waves (SIGWs) in this case is consistent with the recent NANOGrav 15-year data and with sensitivities of other ground and space-based missions, LISA, BBO, DECIGO, CE, ET, HLVK (consists of aLIGO, aVirgo, and KAGRA), and HLV(03). Thanks to the non-renormalization property of Galileon theory, the amplitude of the large fluctuation is controllable at the sharp transitions between SR and USR regions. We show that the behavior of the GW spectrum, when one-loop effects are included in the scalar power spectrum, is preserved under a shift of the sharp transition scale with peak amplitude ΩGWh2∼O(10−6), and hence it can cover a wide range of frequencies within O(10−9Hz−107Hz). An analysis of the allowed mass range for primordial black holes (PBHs) is also performed, where we find that mass values ranging from O(1M⊙−10−18M⊙) can be generated over the corresponding allowed range of low and high frequencies.

Wave resonances and the time-dependent capillary gravity wave motion

The interconnection of time and frequency domains for capillary gravity wave motion in the presence of current is discussed in this article. The general time-dependent problem is solved using Green’s function technique, and the asymptotic solution is derived using the method of stationary phase for large time and space. Also, the frequency domain solution is derived as a special case using the Cauchy Residue theorem. Different types of wave resonances like Trapping, Blocking and Bragg resonances are discussed. The existence of the trapped mode below the cutoff frequency is justified theoretically, and numerical results are obtained using the multipole expansion method. The blocking and Bragg resonances are analyzed above the cutoff frequency. It is found that in the presence of current, when the ripple wavenumber of the bottom undulation equals twice the cosine angle of incidence of wave times the wavenumber of the wave, Bragg resonance occurs. It is found that three propagating modes exist in the case of wave blocking, and the trapped modes exist only for the first propagating mode. Furthermore, because of the negative group velocity inside the blocking zone, the Bragg reflection increases while decreasing outside. The effect of current on the wave energy propagation in the form of group velocity is analyzed and the same is verified in the case of time-dependent problem.

Turbulence of internal gravity waves in the laboratory

Turbulence of internal gravity waves in the laboratory

Steady-state interfacial gravity waves with one-dimensional class-III triad resonance

Steady-state interfacial gravity waves with one-dimensional class-III triad resonance

The Response of Stratospheric Gravity Waves to the 11-Year Solar Cycle

Atmospheric gravity waves are one of the important dynamic processes in near space and are widely present in the atmosphere. They play a crucial role in the transfer of energy and momentum between different regions of the atmosphere. The Sun, as the ultimate source of gravity wave energy, significantly influences the intensity of gravity wave disturbances through its activity variations. This paper utilizes data from the Global Navigation Satellite System Occultation Sounder (GNOS) onboard the Fengyun-3C (FY-3C) satellite to invert global stratospheric gravity wave disturbances. It provides the global stratospheric gravity wave distribution from 2015 to 2023, nearly covering one solar activity cycle, and focuses on analyzing the response of gravity waves at different latitudes, altitudes, and wavelengths to the solar activity cycle. We found that short-wavelength gravity waves respond more noticeably to solar activity compared to long-wavelength gravity waves. Through analyzing the intensity of stratospheric gravity wave disturbances across different latitude bands, we found that in high-latitude regions, stratospheric gravity wave disturbances are most sensitive and respond most quickly to variations in solar activity. Furthermore, the Southern Hemisphere exhibits a stronger response to the current year’s solar activity changes compared to the Northern Hemisphere. In the mid-latitude and equatorial regions, the response to changes in solar activity intensity is delayed. The correlation gradually strengthens with this lag, reaching a very strong level after a 2-year lag. Additionally, the correlation between the Southern Hemisphere and solar activity is generally higher than that of the Northern Hemisphere.

Characteristics of Gravity Waves in Opposing Phases of the QBO: A Reanalysis Perspective with ERA5

Abstract Gravity waves dispersing upward through the tropical stratosphere during opposing phases of the QBO are investigated using ERA5 data for 1979–2019. Log–log plots of two-sided zonal wavenumber–frequency spectra of vertical velocity, and cospectra representing the vertical flux of zonal momentum in the tropical lower stratosphere, exhibit distinctive gravity wave signatures across space and time scales ranging over two orders of magnitude. Spectra of the vertical flux of momentum are indicative of a strong dissipation of westward-propagating gravity waves during the easterly phase and vice versa. This selective “wind filtering” of the waves as they disperse upward imprints the vertical structure of the zonal flow on the resolved wave spectra, characteristic of (re)analysis and/or free-running models. The three-dimensional structures of the gravity waves are documented in composites of the vertical velocity field relative to grid-resolved tropospheric downwelling events at individual reference grid points along the equator. In the absence of a background zonal flow, the waves radiate outward and upward from their respective reference grid points in concentric rings. When a zonal flow is present, the rings are displaced downstream relative to the source and they are amplified upstream of the source and attenuated downstream of it, such that instead of rings, they assume the form of arcs. The log–log spectral representation of wind filtering of equatorial waves by the zonal flow in this paper can be used to diagnose the performance of high-resolution models designed to simulate the circulation of the tropical stratosphere.

On equatorial spread F occurrence: A multi-dimensional quantitative assessment

The present study investigates the role of gravity wave induced seed perturbations in the occurrence of Equatorial Spread F (ESF) under the influence of the post sunset background conditions modulated by prevailing electrodynamics and neutral wind. Ionospheric foF2 data sets over geomagnetic equatorial station Trivandrum (8.5°N, 77°E and magnetic dip 0.68°N-corresponding to the period of study) corresponding to vernal and autumnal equinoctial periods encompassing high, low and moderate solar activity years, are used for the study. Meridional wind data is obtained either from ESA’s sun-synchronous satellite GOCE (Gravity field and steady-state Ocean Circulation Explorer) or derived using ionosonde h’F (base height of ionosphere at 2.5 MHz) data from Trivandrum (TVM- 8.5°N, 77°E and magnetic dip 0.68°N) and Sriharikota (SHAR−13.7°N, 80.2°E and magnetic dip 6.9°N-for period of study). This particular study is carried out for geomagnetically quiet days of Vernal Equinox (VE) and Autumnal Equinox (AE) seasons, which are most favoured for ESF occurrence over Indian longitudes. Considering thermospheric wind, ion-neutral collisions, and electric field effects in association with gravity wave seed, threshold curve is generated, which clearly demarcates ESF and NSF (Non spread F) days. Previous studies have addressed ESF variability in electrodynamical domain alone (wherein the layer is above a threshold level). The present study, for the first time, succeeds in demarcating ESF and NSF days by incorporating effects of electric field, neutral wind, collisional RT instability term, and gravity wave seed perturbations simultaneously irrespective of threshold height.

In Situ Generation of Planetary Waves in the Mesosphere by Zonally Asymmetric Gravity Wave Drag: A Revisit

Abstract This study investigates the in situ generation of planetary waves (PWs) by zonally asymmetric gravity wave drag (GWD) in the mesosphere using a fully nonlinear general circulation model extending to the lower thermosphere. To isolate the effects of GWD, we establish a highly idealized but efficient framework that excludes stationary PWs propagating from the troposphere and in situ PWs generated by barotropic and baroclinic instabilities. The GWD is prescribed in a zonally sinusoidal form with a zonal wavenumber (ZWN) of either 1 or 2 in the lower mesosphere of the Northern Hemisphere midlatitude. Our idealized simulations clearly show that zonally asymmetric GWD generates PWs by serving as a nonconservative source Z′ of linearized disturbance quasigeostrophic potential vorticity q′. While Z′ initially amplifies PWs through enhancing q′ tendency, the subsequent zonal advection of q′ gradually balances with Z′, thereby attaining steady-state PWs. The GWD-induced PWs predominantly have the same ZWN as the applied GWD with minor contributions from higher ZWN components attributed to nonlinear processes. The amplitude of the induced PWs increases in proportion with the magnitude of the peak GWD, while it decreases in proportion to the square of ZWN. Moreover, the amplitude of PWs increases as the meridional range of GWD expands and as GWD shifts toward lower latitudes. These PWs deposit substantial positive Eliassen–Palm flux divergence (EPFD) of ∼30 m s−1 day−1 at their origin and negative EPFD of 5–10 m s−1 day−1 during propagation. In addition, the in situ PWs exhibit interhemispheric propagation following westerlies that extend into the Southern Hemisphere.

Gravity Wave Activity and Stratosphere-Troposphere Exchange During Typhoon Molave (2020)

Gravity Wave Activity and Stratosphere-Troposphere Exchange During Typhoon Molave (2020)

The impact of asteroseismically calibrated internal mixing on nucleosynthetic wind yields of massive stars

Context. Asteroseismology gives us the opportunity to look inside stars and determine their internal properties, such as the radius and mass of the convective core. Based on these observations, estimations can be made for the amount of the convective boundary mixing and envelope mixing of such stars and for the shape of the mixing profile in the envelope. However, these results are not typically included in stellar evolution models. Aims. We aim to investigate the impact of varying convective boundary mixing and envelope mixing in a range based on asteroseismic modelling in stellar models up to the core collapse, both for the stellar structure and for the nucleosynthetic yields. In this first study, we focus on the pre-explosive evolution and we evolved the models to the final phases of carbon burning. This set of models is the first to implement envelope mixing based on internal gravity waves for the entire evolution of the star. Methods. We used the MESA stellar evolution code to simulate stellar models with an initial mass of 20 M⊙ from zero-age main sequence up to a central core temperature of 109 K, which corresponds to the final phases of carbon burning. We varied the convective boundary mixing, implemented as ‘step-overshoot’, with the overshoot parameter (αov) in the range 0.05−0.4. We varied the amount of envelope mixing (log(Denv/cm2 s−1)) in the range 0−6 with a mixing profile based on internal gravity waves. To study the nucleosynthesis taking place in these stars in great detail, we used a large nuclear network of 212 isotopes from 1H to 66Zn. Results. Enhanced mixing according to the asteroseismology of main-sequence stars, both at the convective core boundary and in the envelope, has significant effects on the nucleosynthetic wind yields. This is especially the case for 36Cl and 41Ca, whose wind yields increase by ten orders of magnitude compared to those of the models without enhance envelope mixing. Our evolutionary models beyond the main sequence diverge in yields from models based on rotational mixing, having longer helium-burning lifetimes and lighter helium-depleted cores. Conclusions. We find that the asteroseismic ranges of internal mixing calibrated from core hydrogen-burning stars lead to similar wind yields as those resulting from the theory of rotational mixing. Adopting the seismic mixing levels beyond the main sequence, we find earlier transitions to radiative carbon burning compared to models based on rotational mixing because they have lower envelope mixing in that phase. This influences the compactness and the occurrence of shell mergers, which may affect the supernova properties and explosive nucleosynthesis.

Dynamical response of a floating ice sheet due to a forced oscillation in a running stream

This paper explores the response of a floating ice sheet to a forced, time-harmonic oscillatory pressure applied to the ice-covered surface of a uniform, finite depth fluid. The floating ice sheet is modeled as a thin elastic plate following the Euler–Bernoulli beam equation, with the additional consideration of in-plane compressive forces acting on the ice. Employing linear wave theory, the problem is presented as an initial boundary value problem and is solved using Laplace and Fourier transforms to obtain a mathematical expression for the ice sheet's deflection in terms of infinite integrals. These integrals are thereafter solved asymptotically for large time and distance using the stationary phase method. The asymptotic analysis indicates a growing response over time when the poles and stationary points of the phase functions coalesce. The deflection of the floating ice sheet is graphically presented, highlighting the effects of various non-dimensional parameters, such as flexural rigidity, compressive force, uniform current speed, and the angular frequency of the oscillatory pressure. Additionally, the group velocity and phase velocity of flexural gravity waves are derived from the dispersion relation and elucidated using diagrams. The results show that compressive force and current speed significantly influence wave amplitude, enhancing the oscillatory nature, while the flexural rigidity of the elastic plate and the angular frequency of the applied pressure have a substantial impact on the plate's deflection.