Gravity Wave Dispersion Research Articles

Calculating the acoustic and internal gravity wave dispersion relations in Venus's supercritical lower atmosphere

There is a growing interest in quantifying Venusian seismic events through their infrasonic signatures detected by balloon-borne sensors at ∼ 55 km altitude. The extreme pressure and temperature at Venus’s surface correspond to supercritical conditions in the planet’s deep atmosphere. Therefore, an appropriate real-gas equation of state (EoS) must be used to study the acoustic properties and thermodynamics in the Venusian lower atmosphere. In previous work, the Peng-Robinson (P-R) EoS was used to obtain the acoustic sound speed and attenuation coefficient in the lower atmosphere of Venus. Here, the P-R EoS is coupled with the fluid dynamics equations in order to derive the acoustic and internal gravity wave (IGW) dispersion equations. Results show that in Venus’s deep atmosphere, the acoustic cut-off frequency corresponds to a period of ∼480 s (0.0020 Hz), and the buoyancy frequency corresponds to a period of ∼600 s (0.0016 Hz). By comparison, the values in Earth’s lower atmosphere are ∼310 and ∼340 s, respectively. These differences in acoustic and IGW propagation characteristics will be useful in later efforts to discriminate between the various waves detected by high-altitude sensors.

On the time scales of spectral evolution of nonlinear waves

As presented in Annenkov & Shrira (Phys. Rev. Lett., vol. 102, 2009, 024502), when a surface gravity wave field is subjected to an abrupt perturbation of external forcing, its spectrum evolves on a ‘fast’ dynamic time scale of $O(\varepsilon ^{-2})$ , with $\varepsilon$ a measure of wave steepness. This observation poses a challenge to wave turbulence theory that predicts an evolution with a kinetic time scale of $O(\varepsilon ^{-4})$ . We revisit this unresolved problem by studying the same situation in the context of a one-dimensional Majda–McLaughlin–Tabak equation with gravity wave dispersion relation. Our results show that the kinetic and dynamic time scales can both be realised, with the former and latter occurring for weaker and stronger forcing perturbations, respectively. The transition between the two regimes corresponds to a critical forcing perturbation, with which the spectral evolution time scale drops to the same order as the linear wave period (of some representative mode). Such fast spectral evolution is mainly induced by a far-from-stationary state after a sufficiently strong forcing perturbation is applied. We further develop a set-based interaction analysis to show that the inertial-range modal evolution in the studied cases is dominated by their (mostly non-local) interactions with the low-wavenumber ‘condensate’ induced by the forcing perturbation. The results obtained in this work should be considered to provide significant insight into the original gravity wave problem.

Inferring neutral winds in the ionospheric transition region from atmospheric-gravity-wave traveling-ionospheric-disturbance (AGW-TID) observations with the EISCAT VHF radar and the Nordic Meteor Radar Cluster

Abstract. Atmospheric gravity waves and traveling ionospheric disturbances can be observed in the neutral atmosphere and the ionosphere at a wide range of spatial and temporal scales. Especially at medium scales, these oscillations are often not resolved in general circulation models and are parameterized. We show that ionospheric disturbances forced by upward-propagating atmospheric gravity waves can be simultaneously observed with the EISCAT very high frequency incoherent scatter radar and the Nordic Meteor Radar Cluster. From combined multi-static measurements, both vertical and horizontal wave parameters can be determined by applying a specially developed Fourier filter analysis method. This method is demonstrated using the example of a strongly pronounced wave mode that occurred during the EISCAT experiment on 7 July 2020. Leveraging the developed technique, we show that the wave characteristics of traveling ionospheric disturbances are notably impacted by the fall transition of the mesosphere and lower thermosphere. We also demonstrate the application of using the determined wave parameters to infer the thermospheric neutral wind velocities. Applying the dissipative anelastic gravity wave dispersion relation, we obtain vertical wind profiles in the lower thermosphere.

On the propagation of gravity waves in the lower solar atmosphere in different magnetic configurations

Gravity waves are generated by turbulent subsurface convection overshooting or penetrating locally into a stably stratified medium. While propagating energy upwards, their characteristic negative phase shift over height is a well-recognized observational signature. Since their first detailed observational detection and estimates of energy content, a number of studies have explored their propagation characteristics and interaction with magnetic fields and other waves modes in the solar atmosphere. Here, we present a study of the atmospheric gravity wave dispersion diagrams utilizing intensity observations that cover photospheric to chromospheric heights over different magnetic configurations of quiet-Sun (magnetic network regions), a plage, and a sunspot as well as velocity observations within the photospheric layer over a quiet and a sunspot region. In order to investigate the propagation characteristics, we construct two–height intensity - intensity and velocity- velocity cross-spectra and study phase and coherence signals in the wavenumber - frequency dispersion diagrams and their association with background magnetic fields. We find signatures of association between magnetic fields and much reduced coherence and phase shifts over height from intensity-intensity and velocity-velocity phase and coherence diagrams, both indicating suppression/scattering of gravity waves by the magnetic fields. Our results are consistent with the earlier numerical simulations, which indicate that gravity waves are suppressed or scattered and reflected back into the lower solar atmosphere in the presence of magnetic fields.

Characterization of Gravity Waves in Three Dimensions in the Daytime Thermosphere Using Combined Optical and Radio Measurements and Estimation of Horizontal Neutral Winds

AbstractGravity waves, which are considered omnipresent in the Earth's upper atmosphere, are generally investigated by monitoring the fluctuations in different atmospheric parameters. Here, we report the propagation characteristics of thermospheric gravity waves both in horizontal and vertical directions obtained using collocated optical and radio measurements from Ahmedabad, India for February 2021. The measurements of OI 630.0 nm dayglow emission rates over zenith are used to derive time periods of gravity waves. Wave number analyses of variations in the emission over a large field‐of‐view have been performed to derive gravity wave scale sizes and propagation characteristics in the horizontal direction. Time periods, horizontal scale sizes, and propagation directions are found to be in the range of 31–125 min, 78–243 km, and 203°–248° from east, respectively. Vertical wavelengths of the gravity waves are obtained from radio measurements and are in the range of 26–247 km. As the gravity wave characteristics are influenced by the ambient neutral winds, the measured gravity wave propagation characteristics in three dimensions have been used as inputs into the gravity wave dispersion relation to estimate the magnitudes of thermospheric horizontal neutral winds. These estimated daytime winds in the direction of wave propagation are found to be in the range of 1–105 ms−1, and they compare well with those measured independently from MIGHTI added HWM14 model‐derived winds. The daytime winds estimated by this approach are possibly the first of their kind as obtained from ground‐based measurements.

Imager observation of concentric mesospheric gravity waves over Srinagar, Jammu and Kashmir, India

Using the NARL airglow imager in the Indian subtropical station of Srinagar, Kashmir, India, we report the characteristics of the concentric deformed circular pattern of gravity waves detected at ∼85 km height. OH molecular emission intensities from the height of ∼85 km as observed by the imager in the wide band optical filter of centre wavelength of 840 nm show concentric deformed circular gravity waves drifting northwestward. Using Atmospheric Infrared Sounder (AIRS) image at the centre wavelength of 8.1 µm, deep convective activity around the imager site in the lower atmosphere is recognized as the source mechanism of the observed concentric gravity waves in the mesosphere. The determined phase speed, direction and period of these concentric gravity waves (CGWs) is ∼47 m/s, 150° north of east and ∼10 min (intrinsic period ∼8 min) respectively. At heights of ∼97 km [OI (1S)] and ∼250 km [OI (1D)], these concentric gravity waves are sporadically visible depending on the possible vertical movement of airglow layer height. The dissipated portions of these concentric gravity waves get converted into turbulence at these heights. Using anelastic gravity wave dispersion relation, decreasing horizontal wavelength from the centre of concentric gravity waves is explained. This result is novel in the sense that it disagrees with most of the earlier interpretations of such observations.

A new computational technique for the analytic treatment of time-fractional Emden–Fowler equations

This paper presents the study of fractional Emden–Fowler (FEF) equations by utilizinga new adequate procedure, specifically the q-homotopy analysis transform method (q-HATM). The EF equation has got greater significance in both physical and mathematical investigation of capillary and nonlinear dispersive gravity waves. The projected technique is tested by considering four illustrations of the time-fractional EF equations. The q-HATM furnish ℏ, known as an auxiliary parameter, by the support of ℏ we can modulate the various stages of convergence of the series solution. Additionally, to certify the resolution and accurateness of the proposed method we fitted the suitable numerical simulations. The redeem results guarantee that the proposed process is more convincing and scrutinizes the extremely nonlinear issues emerging in the field of science and engineering.

A framework to evaluate IMEX schemes for atmospheric models

Abstract. We present a new evaluation framework for implicit and explicit (IMEX) Runge–Kutta time-stepping schemes. The new framework uses a linearized nonhydrostatic system of normal modes. We utilize the framework to investigate the stability of IMEX methods and their dispersion and dissipation of gravity, Rossby, and acoustic waves. We test the new framework on a variety of IMEX schemes and use it to develop and analyze a set of second-order low-storage IMEX Runge–Kutta methods with a high Courant–Friedrichs–Lewy (CFL) number. We show that the new framework is more selective than the 2-D acoustic system previously used in the literature. Schemes that are stable for the 2-D acoustic system are not stable for the system of normal modes.

Application of the sampling moiré method to shallow open-channel flows with circular roughness elements

This research presents an application of the sampling moiré method, a novel technique originally developed for measuring slight deformation of a static object such as a plate, to fluctuating free water surface in rough open channel flows. The method was used to capture the two-dimensional water surface deformation at a high sampling rate by dyeing the color of water white. The target flow was a very shallow subcritical flow with a depth of 1.5 times the height of the roughness. As a result, a series of instantaneous water surface profiles with non-uniform rough planes were successfully measured at a sampling rate of 100 Hz.It has become clear that the effect of dispersive gravity waves traveling on the water surface is greater than that of non-dispersive waves driven by the turbulence, and that this feature becomes more pronounced as the Froude number increases in such shallow flow conditions. Furthermore, it was experimentally and theoretically verified that the intensity of water surface fluctuation increases with the square of the Froude number. The decomposition of surface fluctuations due to gravity waves and subsurface turbulence using the wavenumber frequency spectrum revealed that the effects of subsurface turbulence are about 20%. This is much less than the contribution from gravity waves in very shallow flows as in this experiment.

Suppression of Wind Ripples and Microwave Backscattering Due to Turbulence Generated by Breaking Surface Waves

The role of wave breaking in microwave backscattering from the sea surface is a problem of great importance for the development of theories and methods on ocean remote sensing, in particular for oil spill remote sensing. Recently it has been shown that microwave radar return is determined by both Bragg and non-Bragg (non-polarized) scattering mechanisms and some evidence has been given that the latter is associated with wave breaking, in particular, with strong breaking such as spilling or plunging. However, our understanding of mechanisms of the action of strong wave breaking on small-scale wind waves (ripples) and thus on the radar return is still insufficient. In this paper an effect of suppression of radar backscattering after strong wave breaking has been revealed experimentally and has been attributed to the wind ripple suppression due to turbulence generated by strong wave breaking. The experiments were carried out in a wind wave tank where a frequency modulated wave train of intense meter-decimeter-scale surface waves was generated by a mechanical wave maker. The wave train was compressed according to the gravity wave dispersion relation (“dispersive focusing”) into a short-wave packet at a given distance from the wave maker. Strong wave breaking with wave crest overturning (spilling) occurred for one or two highest waves in the packet. Short decimeter-centimeter-scale wind waves were generated at gentle winds, simultaneously with the long breaking waves. A Ka-band scatterometer was used to study microwave backscattering from the surface waves in the tank. The scatterometer looking at the area of wave breaking was mounted over the tank at a height of about 1 m above the mean water level, the incidence angle of the microwave radiation was about 50 degrees. It has been obtained that the radar return in the presence of short wind waves is characterized by the radar Doppler spectrum with a peak roughly centered in the vicinity of Bragg wave frequencies. The radar return was strongly enhanced in a wide frequency range of the radar Doppler spectrum when a packet of long breaking waves arrived at the area irradiated by the radar. After the passage of breaking waves, the radar return strongly dropped and then slowly recovered to the initial level. Measurements of velocities in the upper water layer have confirmed that the attenuation of radar backscattering after wave breaking is due to suppression of short wind waves by turbulence generated in the breaking zone. A physical analysis of the effect has been presented.

Estimating Horizontal Phase Speeds of a Traveling Ionospheric Disturbance From Digisonde Single Site Vertical Ionograms

AbstractHorizontal phase speeds for a medium‐scale traveling ionospheric disturbance (TID) are calculated from three different atmospheric gravity wave (AGW) dispersion relations using vertical phase speeds derived from vertical ionograms measured by a single ionosonde. Observed heights from a network of four ionosondes in southern New Mexico provide the measured phase velocities. Horizontal phase speeds calculated from the dispersion relations are compared to measured TID speeds as a function of altitude and show general agreement. However, the linear relationship between the vertical and calculated horizontal AGW speeds for this TID frequency and wavenumber range predicts larger variations than the observations. The inclusion of viscosity and thermal diffusion terms in the dispersion relations increases the agreement with measurements. This technique provides a new method of predicting horizontal TID phase speeds from measurements at a single ionosonde site.

Formation of Ionospheric Precursors of Earthquakes—Probable Mechanism and Its Substantiation

The purpose of this article is to attract the attention of the scientific community to atmospheric gravity waves (GWs) as the most likely mechanism for the transfer of energy from the surface layers of the atmosphere to space heights and describe the channel of seismic-ionospheric relations formed in this way. The article begins with a description and critical comparison of several basic mechanisms of action on the ionosphere from below: the propagation of electromagnetic radiation; the closure of the atmospheric currents through the ionosphere; the penetration of waves throughout the neutral atmosphere. A further part of the article is devoted to the analysis of theoretical and experimental information relating to the actual GWs. Simple analytical expressions are written that allow one to calculate the parameters of GWs in specific experimental situations. Specificity of GW dispersion properties and features of their propagation are analyzed on this mathematical basis, processes of amplitude amplification and dissipation of GWs with height are investigated, the mechanism of generation of ionosphere-magnetosphere current systems is described and their quantitative characteristics are determined. The experimental part presents an analysis of GWs global distribution in the thermosphere derived from the data of the instrument NACS (Neutral Atmosphere Composition Spectrometer) onboard the satellite DE-2 (NASA, 1981-1983). The statistical association of registered ionospheric disturbances with earthquakes is demonstrated. The results of DE-2 data processing are backed up by comparison with data from the DEMETER satellite (CNES, 2005-2010) whose purpose was to study the ionospheric effects of earthquakes. Specific features of GWs that characterize these waves as a factor of influence on the ionosphere from below are indicated.

Experimental study of dispersion and modulational instability of surface gravity waves on constant vorticity currents

This paper examines experimentally the dispersion and stability of weakly nonlinear waves on opposing linearly vertically sheared current profiles (with constant vorticity). Measurements are compared against predictions from the unidirectional constant vorticity nonlinear Schrodinger equation (the vor-NLSE) derived by Thomas et al. (Phys. Fluids, vol. 24, no. 12, 2012, 127102). The shear rate is negative in opposing currents when the magnitude of the current in the laboratory reference frame is negative (i.e. opposing the direction of wave propagation) and reduces with depth, as is most commonly encountered in nature. Compared to a uniform current with the same surface velocity, negative shear has the effect of increasing wavelength and enhancing stability. In experiments with a regular low-steepness wave, the dispersion relationship between wavelength and frequency is examined on five opposing current profiles with shear rates from to . For all current profiles, the linear constant vorticity dispersion relation predicts the wavenumber to within the confidence bounds associated with estimates of shear rate and surface current velocity. The effect of shear on modulational instability was determined by the spectral evolution of a carrier wave seeded with spectral sidebands on opposing current profiles with shear rates between and . Numerical solutions of the vor-NLSE are consistently found to predict sideband growth to within two standard deviations across repeated experiments, performing considerably better than its uniform-current NLSE counterpart. Similarly, the amplification of experimental wave envelopes is predicted well by numerical solutions of the vor-NLSE, and significantly over-predicted by the uniform-current NLSE.

On Deriving Gravity Wave Characteristics in the Daytime Upper Atmosphere Using Radio Technique

AbstractThe importance of neutral wave dynamics in the understanding of the upper atmospheric processes is well known. Conventionally, optical methods are used to derive information on the neutral wave dynamics by obtaining gravity wave (GW) characteristics. Optical measurement techniques use airglow emissions as tracers to obtain such information that correspond to altitudes from where the emissions emanate. However, in this paper, we describe a method using radio wave measurement technique (digisonde) to obtain information on the neutral GW behavior. It involves monitoring of variations in the heights of isoelectron densities as a function of time, and their phase shifts, if any, to derive vertical propagation speeds and scale sizes of GWs. The daytime values of GW time periods, vertical phase speeds, and vertical scale sizes obtained for the duration of 16–21 May 2015 are in the range of 1.47 ± 0.05 to 2.64 ± 0.07 hr, 30.06 ± 4.35 to 45.69 ± 11.84 m/s, and 183.21 ± 39.23 to 393.07 ± 66.38 km, respectively. Further, we have used the GW dispersion relation to make a first‐order estimation of the horizontal scale sizes. This method of deriving neutral GW characteristics through radio measurement technique is effective for the daytime conditions and opens up new possibilities of investigations of the wave dynamical behavior in the upper atmosphere during all weather conditions.

Estimating the influence of precipitation variability by considering effect of middle atmosphere parameters on lower atmosphere over upper Blue Nile basin in Ethiopia

Precipitation over upper Blue Nile basin (UBNB) exhibits complex variability because of topographical features and the variability in tropopause temperature. The factors affecting its temporal and spatial distribution are not well known over the UBNB. Since precipitation is influenced by middle and lower atmosphere parameters such as greenhouse gases (carbon dioxide and methane), ozone concentration, incident solar radiation, gravity wave dispersion, cloud cover, and temperature. There is no study conducted to estimate precipitation variability using these parameters. In this study, we investigated the influence of precipitation variability by considering the effect of the middle atmosphere on lower atmospheres over UBNB in Ethiopia. Most of the data sets used in this study are derived from the European Centre for Medium-range Weather Forecast (ECMWF), in situ measurements and the Global monitoring division of National Oceanic and Atmospheric Administration. The results indicate that the correlation between ECMWF and in situ precipitation and temperature data is 0.82 and 0.32, respectively. The maximum ozone concentration is found during the summer season (6.2 × 10−3 kg m−2). In this season, precipitation and cloud cover has positive correlations and both are negative correlations with temperature and incident solar radiation. The observed positive trend in temperature is associated with the enhancement of greenhouse gases. Cloud cover and ozone is quite useful for reduced incident solar radiation. Ozone is increased with temperature for all seasons except winter. Gravity wave dispersion affects the spatial distributions of temperature. Finally, we conclude that precipitation is directly influenced by temperature and incident solar radiation and indirectly affected by gravity waves, ozone concentration, and greenhouse gases. To draw a better conclusion, further study is needed with water vapor nuclei on precipitation variability in addition to middle atmospheric parameters.

Atmospheric gravity wave ray tracing: Ordinary and extraordinary waves

Calculation of internal gravity-wave ray paths in the atmosphere using a general three-dimensional ray tracing computer program is discussed. To initialize a ray-path calculation, it is necessary to specify the initial values for the components of the wave vector at the source so that the dispersion relation is satisfied. For acoustic waves, or for gravity waves in the absence of wind, there is no ambiguity in determining the magnitude of the wave vector once the frequency and direction of propagation (wave-normal direction) have been specified. For gravity waves with wind, however, it is necessary to solve a quartic equation to specify the magnitude of the wavenumber. Two of the roots of the quartic reduce to the usual solutions in the absence of wind, and we designate these roots as ‘ordinary waves.’ The two new roots (whose values approach infinity as the wind speed approaches zero), we designate as ‘extraordinary waves.’ A section contrasts the properties of the different gravity wave types.Comparison with some previously published examples of ray-path calculations of gravity waves shows that those previous examples were actually extraordinary waves, but their significance was not recognized at that time.In the absence of wind, gravity waves are restricted to a fan of propagation directions centered about horizontal propagation, but asymptotic gravity waves (in the Bousinesq approximation) have a fixed propagation direction for a given frequency. In the presence of a horizontal wind, however, the wave-normal direction is restricted to a fan of directions in the upwind direction, but not in the downwind direction. The ray direction for upwind propagation has no restrictions. A short review of gravity wave theory and the gravity wave dispersion relation is included.

Comparison of 2D triangular C-grid shallow water models

An ideal two-dimensional (2D) shallow water model should be able to simulate correctly various types of waves including pure gravity and inertia-gravity waves. In this paper, two different triangular C-grid methods are considered, and their dispersion of pure gravity waves, frequencies of inertia-gravity waves and geostrophic balance solutions are investigated. The proposed C-grid methods employ different spatial discretization schemes for coupling shallow water equations together with the various reconstruction techniques for tangential velocity estimation. The proposed reconstruction technique for the second method, which is analogous to a hexagonal C-grid scheme, is shown to be energy conservative and satisfies the geostrophic balance exactly while it supports the unphysical geostrophic modes for hexagonal C-grid. Because of the importance of the application of 2D shallow water models on fully unstructured grids, particular attention is also given to various types of isosceles triangles that may appear in such grids. For the gravity waves, the results of the phase speed ratio of the computed phase speeds over the analytical one are shown and compared. The non-dimensional frequencies of various modes for inertia-gravity waves are also investigated and compared in terms of being monotonic and isotropic respect to the continuous solution. The analyses demonstrate some advantages of the first method in phase speed behaviour for gravity waves and monotonicity of inertia-gravity dispersion. The results of the dispersion analysis are verified through a number of numerical tests. The first method, which is shown to have a better performance, examined through more numerical tests in presence of various source terms and results confirm its capability.

Concentric traveling ionospheric disturbances triggered by the launch of a SpaceX Falcon 9 rocket

AbstractWe report the first observation of concentric traveling ionospheric disturbances (CTIDs) triggered by the launch of a SpaceX Falcon 9 rocket on 17 January 2016. The rocket‐triggered ionospheric disturbances show shock acoustic wave signature in the time rate change (time derivative) of total electron content (TEC), followed by CTIDs in the 8–15 min band‐pass filtering of TEC. The CTIDs propagated northward with phase velocity of 241–617 m/s and reached distances more than 1000 km away from the source on the rocket trajectory. The wave characteristics of CTIDs with periods of 10.5–12.7 min and wavelength ~ 200–400 km agree well with the gravity wave dispersion relation. The optimal wave source searching and gravity wave ray tracing technique suggested that the CTIDs have multiple sources which are originated from ~38–120 km altitude before and after the ignition of the second‐stage rocket, ~200 s after the rocket was launched.

On dispersion of directional surface gravity waves

Using a nonlinear evolution equation we examine the dependence of the dispersion of directional surface gravity waves on the Benjamin–Feir index (BFI) and crest length. A parameter for describing the deviation between the dispersion of simulated waves and the theoretical linear dispersion relation is proposed. We find that for short crests the magnitude of the deviation parameter is low while for long crests the magnitude is high and depends on the BFI. In the present paper we also consider laboratory data of directional waves from the Marine Research Institute of the Netherlands (MARIN). The MARIN data confirm the simulations for three cases of BFI and crest length.

An investigation into the dispersion of ocean surface waves in sea ice

This investigation considers theoretical models and empirical studies related to the dispersion of ocean surface gravity waves propagating in ice covered seas. In theory, wave dispersion is related to the mechanical nature of the ice. The change of normalized wavenumber is shown for four different dispersion models: the mass-loading model, an elastic plate model, an elastic plate model extended to include dissipation, and a viscous-layer model. For each dispersion model, model parameters are varied showing the dependence of deviation from open water dispersion on ice thickness, elasticity, and viscosity. In all cases, the deviation of wavenumber from the open water relation is more pronounced for higher frequencies. The effect of mass loading, a component of all dispersion models, tends to shorten the wavelength. The Voigt model of dissipation in an elastic plate model does not change the wavelength. Elasticity in the elastic plate model and viscosity in the viscous-layer model tend to increase the wavelength. The net effect, lengthening or shortening, is a function of the particular combination of ice parameters and wave frequency. Empirical results were compiled and interpreted in the context of these theoretical models of dispersion. A synopsis of previous measurements is as follows: observations in a loose pancake ice in the marginal ice zone, often, though not always, showed shortened wavelengths. Both lengthening and shortening have been observed in compact pancakes and pancakes in brash ice. Quantitative matches to the flexural-gravity model have been found in Arctic interior pack ice and sheets of fast ice.