Visualization of Exact Invariant Solutions Associated with Atmospheric Waves in a Thin Circular Layer

The purpose of the research was to investigate the exact solutions of nonlinear shallow water equations associated with planetary equatorial waves corresponding to the Cauchy-Poisson free boundary problem describing the nonstationary motion of an incompressible perfect fluid propagating around a solid circle. We consider water waves for which the ratio of the depth of fluid above the circular bottom to the radius of the circle is small (shallow water).

Advances in Studies on Nonlinear Atmospheric Waves

A review on the progress in the research of nonlinear atmospheric waves, especially the nonlinear Rossby waves is made in this paper. Many results reported here have been obtained in Peking University.

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.

ATMOSPHERIC WAVE AND ITS PHYSICAL ESSENCE AS REVEALED BY CHANGED CORRELATION COEFFICIENTS AND CORRELATION FIELD

Formal change is made of the correlation coefficient(COCOEF)expression,leading to a new formula consisting of Fourier spectral coefficients that indicates a direct connection between the new form and atmospheric dynamic equations,thus resulting in a dynamic equation represented by COCOEF,which is meaningful in exploring a large-scale dynamic process in terms of the correlation field because the connection revealed by the field can have dynamic explana- tion with the aid of the new formula.

THEORETICAL ANALYSIS OF ATMOSPHERIC WAVES IN EQUATORIAL ZONE

In the equatorial zone the dynamic equations of the atmospheric motion are written inthe β-plane.These equations are linearized according to the mean atmospheric conditions.Numerical method is used to obtain a characteristic wave solution. Results obtained showthat the easterly wind shear changes the phase speed of low frequency waves more strikinglythan that of high frequency waves. The structure of the characteristic disturbances is sim-ilar to that in middle latitudes only with some exceptions in the relationship of geopo-tential field with vorticity field.

Finding the Fibonacci Spiral Patterns in Atmospheric Equatorial Waves

The purpose of this paper is to analyze and visualize the exact invariant solution of the nonlinear simplified version of the shallow water equations which are being used to simulate equatorial atmospheric waves of planetary scales. The method of obtaining the exact solution is based on the Lie group invariance principle. It is shown that the obtained invariant solution has a Fibonacci spiral-like form and has two parameters k and t0. We have defined a new model hypermarameter Δkt = t – t0, where t is time. The question of particular interest is: can we tune the hypermarameter in order to match the exact solution to the actual Fibonacci spiral? It was discovered that the physically relevant part of the solution matches exactly the Fibonacci spiral.

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）.

A class of coupled nonlinear Schrdinger equations:Painlev'e property,exact solutions,and application to atmospheric gravity waves

The Painleve integrability and exact solutions to a coupled nonlinear Schrodinger （CNLS） equation applied in atmospheric dynamics are discussed. Some parametric restrictions of the CNLS equation are given to pass the Painleve test. Twenty periodic cnoidal wave solutions are obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions to the CNLS equation are used to explain the generation and propagation of atmospheric gravity waves.

INTERACTIONS OF ATMOSPHERIC SOLITARY WAVES OF DIFFERENT MODES

The interactions of atmospheric solitary waves with different modes are investigated by a perturbation method. The model considered in this paper consists of a lower layer with exponential density profile and an infinitely deep upper layer with constant density. The analysis show that the waves obey the Benjamin-Ono equation before and after interaction, and the main effect of the interaction is the phase shifts for each wave.

On a Class of Solitary Wave Solutions of Atmospheric Nonlinear Equations

In this paper, an attempt is made to study some interesting results of the coupled nonlinear equations in the atmosphere. By introducing a phase angle function ζ, it is shown that the atmospheric equations in the presence of specific forcing exhibit the exact and explicit solitary wave solutions under certain conditions.

The influence of pressure waves in tidal gravity records

For the reduction of atmospheric effects,observed gravity has initially been corrected by using the computed barometric admittance k of the in situ measured pressure,expressed in nms-2/hPa units and estimated by least squares method.However,the local pressure changes alone cannot account for the atmospheric mass attraction and loading when the coherent pressure field exceeds a specific size,i.e.,with increasing periodicities.To overcome this difficulty,it is necessary to compute the total atmospheric effect at each station using the global pressure field.However,the direct subtraction of the total gravity effect,provided by the models of pressure correction,is not yet satisfactory for S2 and other tidal components,such as K2 and P1,which include solar heating pressure tides.This paper identifies the origin of the problem and presents strategies to obtain a satisfactory solution.First,we set up a difference vector between the tidal factors of M2 and S2 after correction of the pressure and ocean tides effects.This vector,hereafter denoted as RES,presents the advantage of being practically insensitive to calibration errors.The minimum discrepancy between the tidal parameters of M2 and S2 corresponds to the minimum of the RES vector norm d.Secondly we adopt the hybrid pressure correction method,separating the local and the global pressure contribution of the models and replacing the local contribution by the pressure measured at the station multiplied by an admittance kATM.We tested this procedure on 8 stations from the IGETS superconducting gravimeters network(former GGP network).For stations at an altitude lower than 1000 m,the value of dopt is always smaller than0.0005.The discrepancy between the tidal parameters of the M2 and S2 waves is always lower than0.05% on the amplitude factors and 0.025° on the phases.For these stations,a correlation exists between the altitude and the value kopt.The results at the three Central European stations Conrad,Pecny and Vienna are in excellent agreement(0.05%) with the DDW99NH model for all the main tidal waves.

Analytical study of atmospheric internal waves model with fractional approach

This study looks at the mathematical model of internal atmospheric waves,often known as gravity waves,occurring inside a fluid rather than on the surface.Under the shallow-fluid assumption,internal atmospheric waves may be described by a nonlinear partial differential equation system.The shallow flow model’s primary concept is that the waves are spread out across a large horizontal area before rising vertically.The Fractional Reduced Differential Transform Method(FRDTM)is applied to provide approximate solutions for any given model.This aids in the modelling of the global atmosphere,which has applications in weather and climate forecasting.For the integer-order value(α=1),the FRDTM solution is compared to the precise solution,EADM,and HAM to assess the correctness and efficacy of the proposed technique.

Under the surface:Pressure-induced planetary-scale waves,volcanic lightning,and gaseous clouds caused by the submarine eruption of Hunga Tonga-Hunga Ha'apai volcano

We present a narrative of the eruptive events culminating in the cataclysmic January 15, 2022 eruption of Hunga Tonga-Hunga Ha’apai Volcano by synthesizing diverse preliminary seismic, volcanological, sound wave, and lightning data available within the first few weeks after the eruption occurred. The first hour of eruptive activity produced fast-propagating tsunami waves, long-period seismic waves, loud audible sound waves, infrasonic waves, exceptionally intense volcanic lightning and an unsteady volcanic plume that transiently reached-at 58km-the Earth’s mesosphere. Energetic seismic signals were recorded worldwide and the globally stacked seismogram showed episodic seismic events within the most intense periods of phreatoplinian activity, and they correlated well with the infrasound pressure waveform recorded in Fiji. Gravity wave signals were strong enough to be observed over the entire planet in just the first few hours, with some circling the Earth multiple times subsequently. These large-amplitude, long-wavelength atmospheric disturbances come from the Earth’s atmosphere being forced by the magmatic mixture of tephra, melt and gasses emitted by the unsteady but quasicontinuous eruption from 0402±1–1800 UTC on January 15, 2022. Atmospheric forcing lasted much longer than rupturing from large earthquakes recorded on modern instruments, producing a type of shock wave that originated from the interaction between compressed air and ambient(wavy) sea surface. This scenario differs from conventional ideas of earthquake slip, landslides, or caldera collapse-generated tsunami waves because of the enormous(~1000x) volumetric change due to the supercritical nature of volatiles associated with the hot,volatile-rich phreatoplinian plume. The time series of plume altitude can be translated to volumetric discharge and mass flow rate. For an eruption duration of ~12 h, the eruptive volume and mass are estimated at 1.9 km^(3) and~2 900 Tg, respectively, corresponding to a VEI of 5–6 for this event. The high frequency and intensity of lightning was enhanced by the production of fine ash due to magma-seawater interaction with concomitant high charge per unit mass and the high pre-eruptive concentration of dissolved volatiles. Analysis of lightning flash frequencies provides a rapid metric for plume activity and eruption magnitude. Many aspects of this eruption await further investigation by multidisciplinary teams. It represents a unique opportunity for fundamental research regarding the complex, non-linear behavior of high energetic volcanic eruptions and attendant phenomena, with critical implications for hazard mitigation, volcano forecasting, and first-response efforts in future disasters.

Contaminated Effect of Geomagnetic Storms on Pre-Seismic Atmospheric and Ionospheric Anomalies during Imphal Earthquake

Study of seismo-ionospheric coupling mechanism demands the quiet geomagnetic condition to eliminate any kind of contamination in the lower atmospheric and ionospheric parameters. In this manuscript, we present the effect of back to back two geomagnetic storms before a strong earthquake happened in Imphal, India on January 4, 2016 (M = 6.7). We studied the lower ionospheric irregularities for the duration of 31 days by computing the nighttime fluctuations in Very Low Frequency (VLF) radio signal received transmitter JJI (22.2 kHz) in Japan at Ionospheric and Earthquake Research Centre & Optical Observatory (IERCOO), Sitapur, India. We also studied the presence of Atmospheric Gravity Wave (AGW) in nighttime VLF signal in lower ionospheric heights and the same computed that from SABER/TIMED satellite. Two geomagnetic storms occurred on December 21, and 31, 2015. By the conventional analysis, we found that there is a significant decrease in nighttime trend and an increase in nighttime fluctuations around 15 days before the earthquake and just on the first storm and thus the pre-seismic effects on VLF signal gets contaminated due to the presence of storms. The wave-like structure in VLF fluctuations shows significant increase in intensity by using Fourier and Wavelet analysis before the earthquake. By analysis of SABER data, we found significant enhancement in AGW around 10 days before the earthquake. As the wavelike structures are coming from neutral acoustics reasons from pressure or temperature variations, this paper exhibits a significant example of contamination in ionospheric parameters due to geomagnetic storm where the acoustics parameters remain un-contaminated.

Wavelike perturbations in Titan’s ionosphere and their compositional variation:A preliminary survey of Cassini Ion Neutral Mass Spectrometer measurements

Wavelike perturbations in the ionosphere of Titan,the largest satellite of Saturn,are explored based on the Cassini Ion Neutral Mass Spectrometer(INMS)measurements.Strong wavelike perturbations are identified for more than twenty ion species,from simple ones such as N^(+)and CH_(4)^(+)to complex ones such as C_(2)H_(3)CNH^(+)and C_(4)H_(7)^(+).Simultaneous wavelike perturbations in background N_(2),indicative of atmospheric gravity waves,are also observed,motivating us to speculate that the INMS-derived ion perturbations are wave-driven.The amplitudes of the ion perturbations are found to be larger than that of the N_(2)perturbations.Clear compositional variation is revealed by the data:heavier ion species exhibit greater amplitudes.Such observations might be understood based on considerations either of force balance or chemical loss in Titan’s ionosphere.

Radiation of Ultra Low Frequency Electromagnetic Waves from Atmosphere under the Influence of Strong Shock Waves

We present preliminary results from the experimental investigation of the response of the atmosphere due to the impact of powerful shock waves. The response is evidenced as ultra low frequency electromagnetic wave radiation at frequency of 2-5 kHz and in duration of 3 7s. We hypothesize that this radiation appears due to the following process： the shock wave ionizes the neutral particles in the air and these charged and neutral particles continue their vertical motion, which forms in the trail of the shock wave. Such motion can cause the cyclotron-like radiation measured.

The Solitary Wave of Barotropic Atmosphere on a Sphere

In this paper, we have investigated large scale disturbance in barotropic atmosphere on a sphere. It demonstrates that: considering nonlinear effects of interaction between waves in barotropic vorticity equation, the wave packet of the disturbance is governed by the famous equation-nonlinear Schrodinger equation. For the solitary wave, two factors are very important: one is spherical effect of the disturbance and the other is meridional shear of blocking high. In comparison with the results of local Cartesian coordinates, the former factor is the individuality of spherical soliton.

A robust fuzzy-fractional approach for the atmospheric internal wave model

The study of internal atmospheric waves,also known as gravity waves,which are detectable inside the fluid rather than at the fluid surface,is presented in this work.We have used the time-fractional and fuzzy-fractional techniques to solve the differential equation system representing the atmospheric inter-nal waves model.The q-Homotopy analysis Shehu transform technique(q-HAShTM)is used to solve the model.The method helps find convergent solutions since it helps solve nonlinearity,and the fractional derivative can be easily computed using the Shehu transform.Finally,the obtained solution is compared for the particular case ofα=1 with the HAM solution to explain the method’s accuracy.

Symmetry Analysis of Nonlinear Incompressible Non-Hydrostatic Boussinesq Equations

The symmetries of the （2＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq （INHB） equations, which describe the atmospheric gravity waves （GWs）, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. Calculation shows the INHB equations are invariant under some Galilean transformations, scaling transformations, and space-time translations. The symmetry reduction equations and similar solutions of the INHB equations are proposed.

Role of Atlantic Multidecadal Oscillation(AMO) in winter intraseasonal variability over Ural

The modulation of winter intraseasonal variability(ISV)by the Atlantic Multidecadal Oscillation(AMO)is investigated through three sets of reanalysis data and numerical experiments with the NCEP’s atmospheric general circulation model(AGCM).Results show that the positive phase of the AMO tends to intensify ISV activity over the northern Atlantic and shift ISV activity over the Ural Mountains toward the south,causing weakened ISV activity at 200 hPa in the north to the Urals and intensified activity in the south.The modulation of ISV activity by the AMO over the Urals is then explored through comparison of the composite evolution of anomalous ISV cases for the different AMO phases.Fewer ISV cases are found in the AMO positive phase than the negative phase,but no substantial difference in the temporal evolution of anomalous ISV events between the two opposing phases of the AMO.Thus,the AMO exerts its modulation through influencing the occurrence frequency of ISV events,rather than their development or evolution processes.A similar result is seen in the AGCM sensitivity experiments.