A Three-dimensional Wave Activity Flux of Inertia–Gravity Waves and Its Application to a Rainstorm Event

A three-dimensional transformed Eulerian-mean(3D TEM) equation under a non-hydrostatic and non-geostrophic assumption is deduced in this study. The vertical component of the 3D wave activity flux deduced here is the primary difference from previous studies, which is suitable to mesoscale systems. Using the 3D TEM equation, the energy propagation of the inertia–gravity waves and how the generation and dissipation of the inertia–gravity waves drive the mean flow can be examined. During the mature stage of a heavy precipitation event, the maximum of the Eliassen–Palm(EP) flux divergence is primarily concentrated at the height of 10–14 km, where the energy of the inertia–gravity waves propagates forward(eastward) and upward. Examining the contribution of each term of the 3D TEM equation shows that the EP flux divergence is the primary contributor to the mean flow tendency. The EP flux divergence decelerates the zonal wind above and below the high-level jet at the height of 10 km and 15 km, and accelerates the high-level jet at the height of 12–14 km. This structure enhances the vertical wind shear of the environment and promotes the development of the rainstorm.

Influence of topography on the fine structures of stratospheric gravity waves:An analysis using COSMIC-2 temperature data

We derive the potential energy of gravity waves(GWs)in the upper troposphere and stratosphere at 45°S-45°N from December 2019 to November 2022 by using temperature profiles retrieved from the Constellation Observing System for Meteorology,Ionosphere,and Climate-2(COSMIC-2)satellite.Owing to the dense sampling of COSMIC-2,in addition to the strong peaks of gravity wave potential energy(GWPE)above the Andes and Tibetan Plateau,we found weak peaks above the Rocky,Atlas,Caucasus,and Tianshan Mountains.The land-sea contrast is responsible for the longitudinal variations of the GWPE in the lower and upper stratosphere.At 40°N/S,the peaks were mainly above the topographic regions during the winter.At 20°N/S,the peaks were a slight distance away from the topographic regions and might be the combined effect of nontopographic GWs and mountain waves.Near the Equator,the peaks were mainly above the regions with the lowest sea level altitude and may have resulted from convection.Our results indicate that even above the local regions with lower sea level altitudes compared with the Andes and Tibetan Plateau,the GWPE also exhibits fine structures in geographic distributions.We found that dissipation layers above the tropopause jet provide the body force to generate secondary waves in the upper stratosphere,especially during the winter months of each hemisphere and at latitudes of greater than 20°N/S.

Probing signals of atmospheric gravity waves excited by the July 29,2021 M_(W)8.2 Alaska earthquake

It is commonly believed that the atmosphere is decoupled from the solid Earth.Thus,it is difficult for the seismic wave energy inside the Earth to propagate into the atmosphere,and atmospheric pressure wave signals excited by earthquakes are unlikely to exist in atmospheric observations.An increasing number of studies have shown that earthquakes,volcanoes,and tsunamis can perturb the Earth's atmosphere due to various coupling effects.However,the observations mainly focus on acoustic waves with periods of less than 10 min and inertial gravity waves with periods of greater than 1 h.There are almost no clear observations of gravity waves that coincide with observations of low-frequency signals of the Earth's free oscillation frequency band within 1 h.This paper investigates atmospheric gravity wave signals within1 h of surface-atmosphere observations using the periodogram method based on seismometer and microbarometer observations from the global seismic network before and after the July 29,2021 M_(w)8.2 Alaska earthquake in the United States.The numerical results show that the atmospheric gravity wave signals with frequencies similar to those of the Earth's free oscillations _(0)S_(2) and _(0)T_(2) can be detected in the microbaro meter observations.The results con firm the existence of atmospheric gravity waves,indicating that the atmosphere and the solid Earth are not decoupled within this frequency band and that seismic wave energy excited by earthquakes can propagate from the interior of the Earth to the atmosphere and enhance the atmospheric gravity wave signals within 1 h.

Research on internal gravity waves in the Martian atmosphere based on Tianwen-1 and Mars Global Surveyor occultation data

Internal gravity waves(IGWs)are critical in driving Martian atmospheric motion and phenomena.This study investigates Martian IGWs by using high-resolution data from China’s Tianwen-1 mission and the National Aeronautics and Space Administration’s Mars Global Surveyor(MGS)by the radio occultation(RO)technique.Key IGW parameters,such as vertical and horizontal wavelengths,intrinsic frequency,and energy density,are extracted based on vertical temperature profiles from the Martian surface to~50 km altitude.Data reveal that the Martian IGWs are predominantly small-scale waves,with vertical wavelengths between 6 and 13 km and horizontal wavelengths extending to thousands of kilometers.These waves propagate almost vertically and exhibit low intrinsic frequencies close to the inertial frequency,with the characteristic of low-frequency inertial IGWs.Tianwen-1 data indicate stronger IGW activity,higher energy density,and less dissipation than MGS data in the northern hemisphere.Moreover,MGS data in the southern hemisphere show higher buoyancy frequencies and lower vertical wavelengths,suggesting more stable atmospheric conditions conducive to IGW propagation.These extracted IGW characteristics can enhance our understanding of the atmospheric dynamics on Mars and contribute valuable information for parameterization in global circulation models.

Analysis of gravity wave activity during stratospheric sudden warmings in the northern hemisphere

Due to the significant changes they bring to high latitude stratospheric temperature and wind,stratospheric sudden warmings(SSWs)can have an impact on the propagation and energy distribution of gravity waves(GWs).The variation characteristics of GWs during SSWs have always been an important issue.Using temperature data from January to March in 2014−2016,provided by the Constellation Observing System for Meteorology,Ionosphere and Climate(COSMIC)mission,we have analyzed global GW activity at 15−40 km in the Northern Hemisphere during SSW events.During the SSWs that we studied,the stratospheric temperature rose in one or two longitudinal regions in the Northern Hemisphere;the areas affected extended to the east of 90°W.During these SSWs,the potential energy density(E_(p)of GWs expanded and covered a larger range of longitude and altitude,exhibiting an eastward and downward extension.The E_(p)usually increased,while partially filtered by the eastward zonal winds.When zonal winds weakened or turned westward,E_(p)began to strengthen.After SSWs,the E_(p)usually decreased.These observations can serve as a reference for analyzing the interaction mechanism between SSWs and GWs in future work.

Gravitomagnetic Waves Predicted by the Theory of Informatons

In this article we show that the description of the gravitational field as a cloud of g-information implies the phenomenon of “gravitomagnetic” or “gravitational waves”1 and that accelerated mass particles and radioactive decay are sources of such waves. It is also shown that a gravitomagnetic wave propagating in a certain direction can be understood as the macroscopic manifestation of a spatial sequence of informatons whose characteristic angle is fluctuating along that—with the speed of light—speeding “train”. Finally, it is shown that gravitomagnetic waves transport energy in the form of packages carried by informatons. These entities are called “gravitons”.

On Scalar Planck Waves

The sound of space-time at the large scale is observed in the form of gravitational waves, which are disturbances in space-time produced by wavelike distortions (or kinks) in the gravitational field of an accelerating parcel or distribution of energy. In this study, we investigate a hypothetical wave mode of quantum space-time, which suggests the existence of scalar Planck waves. According to this hypothesis, the sound of quantum space-time corresponds to kinks propagating in the gravitational displacement field of an oscillating energy density. In evaluating the emission of scalar Planck waves and their effect on the geometry of space-time, one finds that they not only transport a vanishingly small amount of energy but can also be used to simulate gravity.

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

To investigate the stratosphere-troposphere exchange(STE)process induced by the gravity waves(GWs)caused by Typhoon Molave(2020)in the upper troposphere and lower stratosphere,we analyzed the ERA5 reanalysis data provided by the European Centre for Medium-Range Weather Forecasts and the CMA Tropical Cyclone Best Track Dataset.We also adopted the mesoscale forecast model Weather Research and Forecasting model V4.3 for numerical simulation.Most of the previous studies were about typhoon-induced STE and typhoon-induced GWs,while our research focused on the STE caused by typhoon-induced gravity waves.Our analysis shows that most of the time,the gravity wave signal of Typhoon Molave appeared below the tropopause.It was stronger on the east side of the typhoon center(10°-20°N,110°-120°E)than on the west side,suggesting an eastward tilted structure with height increase.When the GWs in the upper troposphere and lower stratosphere region on the west side of the typhoon center broke up,it produced strong turbulence,resulting in stratosphere-troposphere exchange.At this time,the average potential vorticity vertical flux increased with the average ozone mass mixing ratio.The gravity wave events and STE process simulated by the WRF model were basically consistent with the results of ERA5 reanalysis data,but the time of gravity wave breaking was different.This study indicates that after the breaking of the GWs induced by typhoons,turbulent mixing will also be generated,and thus the STE.

Detection of Gravitational Waves with Semi Classical Features and Resulting Cosmological Implications

The author argues in this document that initial vacuum state values possibly responsible for GW generation in relic conditions in the initial onset of inflation may have a temporary unsqueezed, possibly even coherent initial value, which would permit in certain models classical coherent initial gravitational wave states. Furthermore, several arguments pro and con as to if or not initial relic GW should be high frequency will be presented, with the reason given why earlier string models did NOT favor low frequency relic GW from the big bang. What is observed is that large higher dimensions above our 4 Dimensional space time, if recipients of matter-energy from collapse and re birth of the universe are enough to insure low relic GW. The existence of higher dimensions, in itself if the additional dimensions are small and compact will have no capacity to lower the frequency limit values of relic GW, as predicted by Giovannini, et al. in 1995.

Absorbing Boundary Conditions for Simulating Water Waves Near Solid Bodies

The objective of this paper is to present a new method for designing absorbing or non-reflective boundary conditions (ABC) or (NRBC), illustrated by the case study of the modelling of a solid body in water, specifically the capillary gravity waves generated by its motion at the surface. The study analyses the flow of an inviscid, barotropic, and compressible fluid around the stationary solid body. The dynamic behaviour of the fluid is analysed using a two-dimensional coupled Neumann-Kelvin model extended with capillarity and inertia terms. For computational purposes, it is necessary to truncate the unbounded spatial domain with artificial boundaries and then introduce appropriate absorbing boundary conditions. The propagation of short wavelength waves in a convective fluid medium with significant differences in properties between the interior and the surface of the fluid presents a number of difficulties in the design of these conditions. The results are illustrated numerically and commented upon.

Analysis of the Characteristics of Inertia-Gravity Waves during an Orographic Precipitation Event

A numerical experiment was performed using the Weather Research and Forecasting（WRF） model to analyze the generation and propagation of inertia-gravity waves during an orographic rainstorm that occurred in the Sichuan area on 17 August 2014. To examine the spatial and temporal structures of the inertia-gravity waves and identify the wave types, three wavenumber-frequency spectral analysis methods（Fourier analysis, cross-spectral analysis, and wavelet cross-spectrum analysis）were applied. During the storm, inertia-gravity waves appeared at heights of 10-14 km, with periods of 80-100 min and wavelengths of 40-50 km. These waves were generated over a mountain and propagated eastward at an average speed of 15-20 m s^（-1）. Meanwhile, comparison between the reconstructed inertia-gravity waves and accumulated precipitation showed there was a mutual promotion process between them. The Richardson number and Scorer parameter were used to demonstrate that the eastward-moving inertia-gravity waves were trapped in an effective atmospheric ducting zone with favorable reflector and critical level conditions, which were the primary causes of the long lives of the waves. Finally, numerical experiments to test the sensitivity to terrain and diabatic heating were conducted, and the results suggested a cooperative effect of terrain and diabatic heating contributed to the propagation and enhancement of the waves.

Inertial gravity waves observed by a Doppler wind LiDAR and their possible sources

In this paper,we use wind observations by a Doppler wind LiDAR near Delingha(37.4°N,97.4°E),Qinghai,Northwestern China to study the characteristics of inertial gravity waves in the stratosphere.We focus on 10–12 December 2013,a particularly interesting case study.Most of the time,the inertial gravity waves extracted from the LiDAR measurements were stationary with vertical wavelengths of about 9–11 km and horizontal wavelengths of about 800–1000 km.However,for parts of the observational period in this case study,a hodograph analysis indicates that different inertial gravity wave propagation features were present at lower and upper altitudes.In the middle and upper stratosphere(~30–50 km),the waves propagated downward,especially during a period of stronger winds,and to the northwest–southeast.In the lower stratosphere and upper troposphere(~10–20 km),however,waves with upward propagation and northeast–southwest orientation were dominant.By taking into account reanalysis data and satellite observations,we have confirmed the presence of different wave patterns in the lower and upper stratosphere during this part of the observational period.The combined data sets suggest that the different wave patterns at lower and upper height levels are likely to have been associated with the presence of lower and upper stratospheric jet streams.

Some Possible Solutions of Nonlinear Internal Inertial Gravity Wave Equations in the Atmosphere

In this paper, the nonlinear internal inerntial gravity wave equation is derived by the analysis method of phase plane and is solved by integration method. The results showed that this nonlinear equation not only has ordinary solitary wave solution but also has another extra-ordinary solutions, and the form of solution is related to stratification stability, wave velocity and direction of wave motion.

Application of higher-order KdV-mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere

Higher-order Korteweg-de Vries （KdV）-modified KdV （mKdV） equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV-mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.

Investigating the Dominant Source for the Generation of Gravity Waves during Indian Summer Monsoon Using Ground-based Measurements

Over the tropics, convection, wind shear （i.e., vertical and horizontal shear of wind and/or geostrophic adjustment comprising spontaneous imbalance in jet streams） and topography are the major sources for the generation of gravity waves. During the summer monsoon season （June August） over the Indian subcontinent, convection and wind shear coexist. To determine the dominant source of gravity waves during monsoon season, an experiment was conducted using mesosphere-stratosphere-troposphere （MST） radar situated at Gadanki （13.5°N, 79.2°E）, a tropical observatory in the southern part of the Indian subcontinent. MST radar was operated continuously for 72 h to capture high-frequency gravity waves. During this time, a radiosonde was released every 6 h in addition to the regular launch （once daily to study low-frequency gravity waves） throughout the season. These two data sets were utilized effectively to characterize the jet stream and the associated gravity waves. Data available from collocated instruments along with satellite-based brightness temperature （TBB） data were utilized to characterize the convection in and around Gadanki. Despite the presence of two major sources of gravity wave generation （i.e., convection and wind shear） during the monsoon season, wind shear （both vertical shear and geostrophic adjustment） contributed the most to the generation of gravity waves on various scales.

The Spatial and Temporal Variability of Global Stratospheric GravityWaves and Their Activity during Sudden StratosphericWarming Revealed by COSMIC Measurements

This study investigates the spatial and temporal variability of global stratospheric gravity waves(GWs) and the characteristics of GW activity during sudden stratospheric warming(SSW) using the GPS radio occultation measurements from the COSMIC mission during September 2006 to May 2013. Corresponding to the COSMIC RO observational window and analysis method,GW potential energy(Ep) with vertical scales no shorter than ～2 km is resolved. It is found that the distributions of GW Ep over 20-30 km and 30-38 km show similar spatial and seasonal variations. The variations of GW Ep with altitude and latitude along the westerly wind are identified in different seasons over 60°-80°W. In the middle and high latitudes,seasonal cycles are distinct in the time-latitude and time-altitude distributions of GW activities,which show larger Ep in winters when westerly wind dominates and smaller Ep in summers when easterly wind dominates. The influence of quasi-biennial oscillation on GW activity is recognized in the tropics. GW Ep enhances closely following the occurrence of minor SSW events; while during major events, GW Ep may not enhance, and sometimes may even weaken,in the regions where reversals of zonal wind occur, probably caused by the filtering impact of the 0 ms^(-1) wind level on the GWs.

Global static stability and its relation to gravity waves in the middle atmosphere

The global atmospheric static stability(N2)in the middle atmosphere and its relation to gravity waves(GWs)were investigated by using the temperature profiles measured by the Sounding of the Atmosphere using Broadband Emission Radiometry(SABER)instrument from 2002 to 2018.At low latitudes,a layer with enhanced N2 occurs at an altitude of^20 km and exhibits annual oscillations caused by tropopause inversion layers.Above an altitude of^70 km,enhanced N2 exhibits semiannual oscillations at low latitudes caused by the mesosphere inversion layers and annual oscillations at high latitudes resulting from the downward shift of the summer mesopause.The correlation coefficients between N2 and GW amplitudes can be larger than 0.8 at latitudes poleward of^40°N/S.This observation provides factual evidence that a large N2 supports large-amplitude GWs and indicates that N2 plays a dominant role in maintaining GWs at least at high latitudes of the middle atmosphere.This evidence also partially explains the previous results regarding the phase changes of annual oscillations of GWs at high latitudes.

Frictionless Surface Gravity Waves

A physical explanation is given for the observations that ocean surface gravity waves can travel up to half way around the world from generation in a wind storm to dissipation on shore. Inherent in these waves is an orbital fluid particle motion, known from laboratory experiments, that has no friction according to the Navier-Stokes equations. The prediction is based on application of Bernoulli’s law to all the closed orbital paths of the fluid particles and the cross-stream force balance on the particles between a pressure gradient and the centrifugal force in each orbital loop.

Atmospheric frontal gravity waves observed in satellite SAR images of the Bohai Sea and Huanghai Sea

In the satellite synthetic aperture radar（SAR） images of the Bohai Sea and Huanghai Sea,the authors observe sea surface imprints of wave-like patterns with an average wavelength of 3.8 km.Comparing SAR observations with sea surface wind fields and surface weather maps,the authors find that the occurrence of the wave-like phenomena is associated with the passing of atmospheric front.The authors define the waves as atmospheric frontal gravity waves.The dynamical parameters of the wave packets are derived from statistics of 9 satellite SAR images obtained from 2002 to 2008.A two-dimensional linear physical wave model is used to analyze the generation mechanism of the waves.The atmospheric frontal wave induced wind variation across the frontal wave packet is compared with wind retrievals from the SAR images.The CMOD-5（C-band scatterometer ocean geophysical model function） is used for SAR wind retrievals VV（transmitted vertical and received vertical） for ENVISAT and HH（transmitted horizontally and received horizontally） for RADARSAT-1.A reasonable agreement between the analytical solution and the SAR observation is reached.This new SAR frontal wave observation adds to the school of SAR observations of sea surface imprints of AGWs including island lee waves,coastal lee waves,and upstream Atmospheric Gravity Waves（AGW）.

Case study on stratospheric and mesospheric concentric gravity waves generated by deep convection

Concentric gravity waves(CGWs)in the middle and upper atmosphere show wave-coupling processes between the lower atmosphere and the middle and upper atmosphere.In this research,we analyzed a case of CGWs detected simultaneously by the AIRS(Atmospheric Infrared Sounder)and the VIIRS/DNB(Day/Night Band of the Visible Infrared Imager Radiometer Suite)in the stratosphere and mesosphere.Results showed that gravity waves(GWs)were generated by the collocated Hurricane Bejisa on the island of Mauritius.The AIRS data showed arc-like phase fronts of GWs with horizontal wavelengths of 190 and 150 km at 21:08 coordinated universal time(UTC)on 1 January 2014 and at 10:00 UTC on 2 January 2014,whereas the DNB observed arced GWs with horizontal wavelengths of 60 and 150 km in the same geographic regions at 22:24 UTC.The characteristics of CGW parameters in the stratosphere(~40 km)and the mesosphere(~87 km),such as the vertical wavelength,intrinsic frequency,and intrinsic horizontal phase speed,were first derived together with the background winds from ERA5 reanalysis data and Horizontal Wind Model data through the dispersion relationship of GWs and the wind-filtering theory.