Disturbances of the upper atmosphere and ionosphere caused by acoustic-gravity wave sources in the lower atmosphere

The results of observations of acoustic-gravity waves in the troposphere and the ionosphere at middle latitudes during periods of passage of the solar terminator are presented. Tropospheric observations were performed using a lidar. The frequency characteristics of variations of the tropospheric parameters are determined based on observations of the intensity of the scattered lidar signal. The characteristics of variations of the total electron content (TEC) in the atmosphere are determined from data collected by GPS navigation satellites. An analysis of the observational data showed that the spectrum of variations of the atmospheric and ionospheric parameters is indicative of acoustic-gravity waves (AGW) propagating from the lower atmosphere. Modeling studies of the vertical propagation of AGW from the Earth’s surface showed that such waves quickly (within ~15 min) reach altitudes of the upper atmosphere (~300 km). The refraction and dissipation of waves in the upper atmosphere produces perturbations of the background state of the atmosphere and gives rise to the waveguide propagation of infrasonic wave components. The observed manifestations of TEC disturbances caused by AGW propagating from the lower atmosphere can be explained by the diurnal variation of the altitude of the ionosphere and the waveguide propagation of infrasonic waves.     

Reflectionless propagation of acoustic waves through the Earth’s atmosphere

The vertical propagation of acoustic waves in the inhomogeneous compressible atmosphere has been studied in the framework of the linear theory of ideal hydrodynamics. It has been shown that the initial equations under certain conditions can be reduced to the Klein-Gordon equation with constant coefficients. Its solutions describe traveling waves with a variable amplitude and wavenumber that are not reflected in the atmosphere despite its strong inhomogeneity. The wave energy flux at such reflectionless profiles holds, providing the possibility of the energy transfer to high altitudes. It has been shown that the Standard Earth Atmosphere is approximated well by four reflectionless profiles with small jumps in the gradient of the speed of sound. It is found that the Earth’s atmosphere is almost transparent in a wide frequency range; this feature explains the observation data and conclusions made on the basis of numerical solutions in the framework of the initial equations.     

Simulation of Internal Gravity Wave Propagation Due to Sudden Stratospheric Warming

The results of modeling the effect of stratospheric internal gravity waves (IGWs) excited in the region of sudden stratospheric warming (SSP) on the state of the upper atmosphere are presented. The numerical experiment used a two-dimensional model of atmospheric wave propagation including the dissipative and nonlinear processes accompanying the wave propagation. As a perturbation source, perturbations of temperature and density in a localized region at stratospheric altitudes during the SSW were considered. The amplitude and frequency of the perturbation source were evaluated from the results of observations and IGW theory. The results of numerical calculations showed that the heat source localized in the stratosphere excites IGWs with periods of up to several hours, which reach the thermospheric altitudes within a few hours. The maximum relative perturbations created by these waves relative to the unperturbed conditions were noted at altitudes of 100–200 km and at distances of up to ~1000 km from the source center.     

Atmospheric Turbulence and Internal Gravity Waves Examined by the Method of Artificial Periodic Irregularities

A method for studying the Earth’s ionosphere at altitudes of the mesosphere and lower thermosphere based on creating artificial periodic irregularities in the ionospheric plasma by means of powerful radio waves is breafly described. Methods for determining the temperature and density of the neutral component and the velocity of vertical and turbulent motions by measuring the characteristics of the signal backscattered by the irregularities are described. The results of experiments performed on a SURA heating facility aimed at a comprehensive investigation of the natural processes occurring in the Earth’s lower ionosphere due to the propagation of atmospheric waves and turbulent phenomena are examined. Based on measurements of the amplitude and phase of the signal scattered by periodic irregularities, the most important characteristics of the neutral and plasma components of the Earth’s atmosphere at altitudes of the mesosphere and lower thermosphere are determined. Further research on the subject is discussed.     

Frequency characteristics of the troposphere and ionosphere variations in periods of solar terminator passage

An analysis of the results of lidar observations in the lower atmosphere and observations of the total electron content in the ionosphere (TEC) in Kaliningrad (53°N, 22°E) during the period of solar terminator passage is presented. The observations at troposphere altitudes were performed with a two-wavelength atmospheric lidar (532 and 1064 nm). The ionospheric TEC was determined using signals from GLO-NASS navigation satellites. The observations in the lower atmosphere were performed in February and March 2012, starting ～1 h before sunrise and ending ～1–2 h after sunrise, whereas ionospheric observations were performed continuously throughout the day. Analysis of the spectrum of the observed parameters showed that, during solar terminator passage, the lower atmosphere and ionosphere parameters vary with periods of 4–6 min. Variations of the parameters in the atmosphere with these periods are associated with the propagation of acoustic-gravity waves (AGW). Analysis of the experimental results shows that AGW arise in the lower atmosphere and propagate vertically to ionospheric altitudes. It is assumed that AGW with these periods can be efficiently excited in the lower atmosphere and play an important role in the dynamic interactions between the lower and upper atmosphere.     

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.     

Investigation of acoustic gravity waves in the upper atmosphere by the artificial periodic inhomogeneities method at Nizhny Novgorod

We present the results of observation of acoustic gravity waves in the height range 60–120 km. AGW were studied by means of plasma velocity measurements. The observations, based upon use of a newly-developed diagnostic technique, were carried out during September 1990–May 1991. The method uses the artificial periodic inhomogeneities (API) which occur in the ionosphere illuminated by high- power HF radio waves. This method, based upon measurements of phases of waves back scattered from API, has a time resolution sufficient to observe short-term variations in the atmosphere. Seasonal variations of daily averaged vertical velocities were obtained. Above the turbopause height upward vertical motions dominated. Wave-like oscillations in the vertical velocity, which are most probably caused by AGW, occurred.Published from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 3, pp. 329–334, March, 1996.     

Resonant excitation of rossby waves in the equatorial waveguide and their nonlinear evolution

Nonlinear interactions between the baroclinic Rossby waves trapped in the equatorial waveguide and the barotropic Rossby waves freely propagating across the equator are studied within the two-layer model of the atmosphere, or the ocean. It is shown that a barotropic wave can resonantly excite a pair of baroclinic waves with amplitudes much greater than its proper amplitude. The envelopes of the baroclinic waves obey Ginzburg-Landau-type equations and exhibit nonlinear saturation and formation of characteristic "domain-wall" and "dark-soliton" defects.     

Simulation of the coupling of the upper and lower atmosphere

The coupling of the upper and lower atmosphere and the problem of developing a unified numerical model of the Earth’s gaseous envelope is considered. The existing models of the upper and lower atmosphere are analyzed and specific models for use as parts of a future metamodels of Earth’s atmosphere are selected. A general algorithm for combining these models is proposed.     

General solution of the modified Korteweg-de-Vries equation in the lattice hydrodynamic model

Traffic congestion is related to various density waves, which might be described by the nonlinear wave equations, such as the Burgers, Korteweg-de-Vries (KdV) and modified Korteweg-de-Vries (mKdV) equations. In this paper, the mKdV equations of four different versions of lattice hydrodynamic models, which describe the kink--antikink soliton waves are derived by nonlinear analysis. Furthermore, the general solution is given, which is applied to solving a new model --- the lattice hydrodynamic model with bidirectional pedestrian flow. The result shows that this general solution is consistent with that given by previous work.     

A free-surface hydrodynamic model for density-stratified flow in the weakly to strongly non-hydrostatic regime

A non-hydrostatic density-stratified hydrodynamic model with a free surface has been developed from the vorticity equations rather than the usual momentum equations. This approach has enabled the model to be obtained in two different forms, weakly non-hydrostatic and fully non-hydrostatic, with the computationally efficient weakly non-hydrostatic form applicable to motions having horizontal scales greater than the local water depth. The hydrodynamic model in both its weakly and fully non-hydrostatic forms is validated numerically using exact nonlinear non-hydrostatic solutions given by the Dubriel–Jacotin–Long equation for periodic internal gravity waves, internal solitary waves, and flow over a ridge. The numerical code is developed based on a semi-Lagrangian scheme and higher order finite-difference spatial differentiation and interpolation. To demonstrate the applicability of the model to coastal ocean situations, the problem of tidal generation of internal solitary waves at a shelf-break is considered. Simulations carried out with the model obtain the evolution of solitary wave generation and propagation consistent with past results. Moreover, the weakly non-hydrostatic simulation is shown to compare favorably with the fully non-hydrostatic simulation. The capability of the present model to simulate efficiently relatively large scale non-hydrostatic motions suggests that the weakly non-hydrostatic form of the model may be suitable for application in a large-area domain while the computationally intensive fully non-hydrostatic form of the model may be used in an embedded sub-domain where higher resolution is needed.     

Nonlinear electrostatic surface waves in a semi-infinite plasma

The nonlinear equations which govern the filamentation of a large-amplitude high-frequency electrostatic surface wave are studied considering solutions in the form of stationary traveling waves. It is shown that solitary surface waves exist at certain amplitude and phase conditions.     

Weakly nonlinear non-Boussinesq internal gravity wavepackets

Internal gravity wavepackets induce a horizontal mean flow that interacts nonlinearly with the waves if they are of moderately large amplitude. In this work, a new theoretical derivation for the wave-induced mean flow of internal gravity waves is presented. Using this we examine the weakly nonlinear evolution of internal wavepackets in two dimensions. By restricting the two-dimensional waves to be horizontally periodic and vertically localized, we derive the nonlinear Schrödinger equation describing the vertical and temporal evolution of the amplitude envelope of non-Boussinesq waves. The results are compared with fully nonlinear numerical simulations restricted to two dimensions. The initially small-amplitude wavepacket grows to become weakly nonlinear as it propagates upward due to non-Boussinesq effects. In comparison with the results of fully nonlinear numerical simulations, the nonlinear Schrödinger equation is found to capture the dominant initial behaviour of the waves, indicating that the interaction of the waves with the induced horizontal mean flow is the dominant mechanism for weakly nonlinear evolution. In particular, due to modulational stability, hydrostatic waves propagate well above the level at which linear theory predicts they should overturn, whereas strongly non-hydrostatic waves, which are modulationally unstable, break below the overturning level predicted by linear theory.     

Quasi-stationary nonlinear waves in nuclear matter close to pion condensation

The nuclear hydrodynamic model is extended to include the fluctuating spin-isospin density and its interaction with the nuclear matter density. Using the TDHF equations, it is shown that the dynamics of these densities interacting with the pion field can be expressed in terms of the generalized pressures derivable from the generalized nuclear matter equation of state. A phenomenological Skyrme interaction model is used to obtain these pressures. A theory of pion-like spin-isospin quasi-stationary nonlinear waves is formulated from the generalized hydroequations describing the dynamics of a coupled pion nuclear matter system. In the lowest order of nonlinearity, it is proved that the amplitude of the spin-isospin sound wave satisfies a nonlinear Schrödinger equation. The solution of these equations is the amplitude modulated pion-like solitary waves in nuclear matter. When this matter is near the pion condensate, the speed of these nonlinear waves is much smaller than that of the ordinary sound waves. An implication of the solitary waves excited in such nuclear matter produced in heavy ion collisions is discussed. The characteristic signature of breaking of such waves, produced in a heavy ion central collision, is the emission of a delayed component of correlated nucleons (possibly also with a pion) peaked in the forward direction. It may be that the lighter nuclei³He and³H are produced through such a mechanism.     

Nonlinear stage of the Benjamin-Feir instability: three-dimensional coherent structures and rogue waves

A specific, genuinely three-dimensional mechanism of rogue wave formation, in a late stage of the modulational instability of a perturbed Stokes deep-water wave, is recognized through numerical experiments. The simulations are based on fully nonlinear equations describing weakly three-dimensional potential flows of an ideal fluid with a free surface in terms of conformal variables. Spontaneous formation of zigzag patterns for wave amplitude is observed in a nonlinear stage of the instability. If initial wave steepness is sufficiently high (ka>0.06), these coherent structures produce rogue waves. The most tall waves appear in turns of the zigzags. For ka<0.06, the structures decay typically without formation of steep waves.     

Electromagnetic backscattering from freak waves in(1+1)-dimensional deep-water

To study the electromagnetic (EM) backscatter characteristics of freak waves at moderate incidence angles, we establish an EM backscattering model for freak waves in (1+1)-dimensional deep water. The nonlinear interaction between freak waves and Bragg short waves is considered to be the basic hydrodynamic spectra modulation mechanism in the model. Numerical results suggest that the EM backscattering intensities of freak waves are less than those from the background sea surface at moderate incidence angles. The normalised radar cross sections (NRCSs) from freak waves are highly polarisation dependent, even at low incidence angles, which is different from the situation for normal sea waves; moreover, the NRCS of freak waves is more polarisation dependent than the background sea surface. NRCS discrepancies between freak waves and the background sea surface with using horizontal transmitting horizomtal (HH) polarisation are larger than those with using vertical transmitting vertical (VV) polarisation, at moderate incident angles. NRCS discrepancies between freak waves and background sea surface decreases with the increase of incidence angle, in both HH and VV polarisation radars. As an application, in the synthetic-aperture radar (SAR) imaging of freak waves, we suggest that freak waves should have extremely low backscatter NRCSs for the freak wave facet with the strongest slope. Compared with the background sea surface, the freak waves should be darker in HH polarisation echo images than in VV echo images, in SAR images. Freak waves can be more easily detected from the background sea surface in HH polarisation images than in VV polarisation images. The possibility of detection of freak waves at low incidence angles is much higher than at high incidence angles.     

An iterative method to solve a regularized model for strongly nonlinear long internal waves

We present a simple iterative scheme to solve numerically a regularized internal wave model describing the large amplitude motion of the interface between two layers of different densities. Compared with the original strongly nonlinear internal wave model of Miyata [10] and Choi and Camassa [2], the regularized model adopted here suppresses shear instability associated with a velocity jump across the interface, but the coupling between the upper and lower layers is more complicated so that an additional system of coupled linear equations must be solved at every time step after a set of nonlinear evolution equations are integrated in time. Therefore, an efficient numerical scheme is desirable. In our iterative scheme, the linear system is decoupled and simple linear operators with constant coefficients are required to be inverted. Through linear analysis, it is shown that the scheme converges fast with an optimum choice of iteration parameters. After demonstrating its effectiveness for a model problem, the iterative scheme is applied to solve the regularized internal wave model using a pseudo-spectral method for the propagation of a single internal solitary wave and the head-on collision between two solitary waves of different wave amplitudes.     

土卫六探测器高超声速化学非平衡特性数值计算

为了研究土卫六探测器在地球大气和土卫六大气中飞行时气动热环境的差异,采用数值模拟的方法分别对地球大气成分和土卫六大气成分下探测器前方流场内气动热环境进行了研究,得到如下结论:与地球大气条件相比,土卫六大气条件下探测器表面的热流密度较高,其峰值可达到地球大气条件的1倍以上.探测器表面的热流密度先随着高度的减小而增加,而后...     

Estimation methodology for amplitude of second-order harmonic in nonlinear surface acoustic wave measured by optical diffraction method

An estimation methodology for amplitude from the fundamental to fourth-order harmonic composed of nonlinear surface acoustic waves on a LiNbO₃ substrate with a 128° Y-X propagation axis was demonstrated. First, equations for estimation of amplitudes from diffracted light intensity were shown and then numerical simulations of main factors were carried out. Normalized diffraction light intensities due to components of nonlinear surface acoustic waves were measured and their amplitudes were obtained from measured values. Finally, the amplitude of the second harmonic propagating on a gold thin film of about 50 nm thickness was estimated. It was found that the amplitude of the second harmonic increased continuously from 0.8 to 2.0 Å with propagation distance in the thin film.