Growth Rate Of Waves Research Articles

Theoretical and computational study of instability in streaming negative ion plasma under static magnetic field

The instability and electrostatic wave modes generation in a cold negative ion plasma which streams across a static magnetic field has been analysed by fluid dynamical model and computer simulation technique. In the theoretical approach, we observed different kinds of acoustic modes and cyclotron modes at an oblique angle to the static magnetic field. At some critical wave number, the positive and negative ion acoustic modes split up into two, fast and slow waves. The value of critical wave numbers and wave growth rates depends on the plasma streaming velocity, electron concentration in the system, and magnetic field intensity. In the presence of high intense external magnetic fields, we observed a wave coupling between different electrostatic modes. With the help of computer simulation performed by the Particle In Cell method, we confirmed the presence of theoretically proposed wave modes and studied the evolution of instability in detail.

Variation of dayside chorus waves associated with solar wind dynamic pressure based on MMS observations

The whistler-mode chorus waves are one of the most important plasma waves in the Earth’s magnetosphere. Generally, the amplitude of whistler-mode chorus waves prefers to strengthen when the energetic fluxes of anisotropic electrons increase outside the plasmapause. This characteristic is commonly associated with the geomagnetic storms or substorms. However, the relationship between the solar wind dynamic pressure (Psw) and the long-time variation of chorus waves during the quiet period of the geomagnetic activity still needs more detailed investigations. In this paper, based on MMS observations, we present a chorus event just observed in the inner side of magnetopause without obvious geomagnetic storms or substroms. Interestingly, during this time interval, some Psw fluctuations were recorded. Both the amplitudes and frequencies of chorus waves changed as a response to the variation in Psw. It proved that the enhancement of Psw increases the energetic electrons fluxes, which provides free energies for the chorus amplification. Furthermore, the wave growth rates calculated using linear theory increases and the central frequency of the chorus waves shifts to a higher frequency when the Psw enhancement is greater, which are also consistent well with the observations. The results provide a direct evidence that the Psw play an important role in the long-time variation of whistler-mode chorus waves inside the magnetopause.

Measuring the Kelvin-Helmholtz instability, stabilized by a tangential magnetic field

In a flow channel we experimentally investigate the stability of the interface between a laminar flow of diamagnetic fluid, and a layer of ferrofluid, resting on top of it. This interface is locally perturbed by means of a bar oscillating with a driving frequency. Measuring the growth rate of the interfacial waves, we explore the stabilizing effect of a homogeneous magnetic field oriented in flow direction. A zero growth rate determines the critical flow velocity. The latter increases with the applied magnetic field and depends sensitively on the driving frequency. The results are described in part by an established, simple inviscid model.

Magnetic Rayleigh–Taylor instability at a contact discontinuity with an oblique magnetic field

Aims.We investigate the nature of the magnetic Rayleigh–Taylor instability at a density interface that is permeated by an oblique homogeneous magnetic field in an incompressible limit.Methods.Using the system of linearised ideal incompressible magnetohydrodynamics equations, we derive the dispersion relation for perturbations of the contact discontinuity by imposing the necessary continuity conditions at the interface. The imaginary part of the frequency describes the growth rate of waves due to instability. The growth rate of waves is studied by numerically solving the dispersion relation.Results.The critical wavenumber at which waves become unstable, which is present for a parallel magnetic field, disappears because the magnetic field is inclined. Instead, waves are shown to be unstable for all wavenumbers. Theoretical results are applied to diagnose the structure of the magnetic field in prominence threads. When we apply our theoretical results to observed waves in prominence plumes, we obtain a wide range of field inclination angles, from 0.5° up to 30°. These results highlight the diagnostic possibilities that our study offers.

Different responses of the Rayleigh–Taylor type and resistive drift wave instabilities to the velocity shear

The effects of velocity shear on the unstable modes driven by the effective gravity (Rayleigh–Taylor and interchange) and resistive drift wave instabilities for inhomogeneous equilibrium fluid/plasma density are analyzed for the localized eigenmode problems. It is shown that the effect of the velocity shear drastically depends on the type of instability. Whereas the velocity shear can significantly suppress both Rayleigh–Taylor and interchange instabilities, it has only a weak impact on the growth rate of the resistive drift wave. This is directly related to the physical nature of these instabilities. For the Rayleigh–Taylor and interchange instabilities, the shear flow tilts the eddies of the stream functions, while for the resistive drift wave instability the shear flow simply shifts the eddies in the radial direction with no tilting. However, for a large velocity shear, the eigenmode solutions for resistive drift waves cease to exist.

Sorting and bed waves in unidirectional shallow-water flows

The stability of a uniform flow above an erodible bed composed of a bimodal mixture of sediments is investigated by means of linear analysis. Results show that, for any given set of the flow and sediment parameters, two distinct modes of instability arise, each one characterized by its own wave speed, growth rate and longitudinal wavelength, each one involving spatial variations of both grain size density and bed elevation. Although at a linear level no information on the amplitude of the perturbations is gathered, the analysis of the eigenvectors associated with the two modes of instability allows for an easy classification in terms of the relative amplitudes of the perturbations of bed elevation and size density. One eigenvalue is shown to be associated with the modifications of bed forms induced by the presence of the heterogeneous mixture, such as the local accumulation of finer and coarser material along the unit wavelength, the other with the formation of the low-amplitude sorting waves known as bedload sheets. In the present unidirectional shallow-water framework, only the sorting wave is found to be unstable, since dunes and antidunes, the relevant bed forms for this case, require a more refined rotational flow model in order to become unstable. On the other hand, the simple flow model adopted allows for the formulation of an algebraic eigenvalue problem that can be solved analytically, allowing for a deep insight into the mechanisms that drive both instabilities.

Effect of quadric shear basic zonal flows and topography on baroclinic instability

On the β plane approximation, the two-layer quasigeostrophic mode is used to study the baroclinic instability of the quadric shear basic zonal flows on a uniform bottom topography. The phase speed and growth rate of instability waves are functions of the shear zonal basic flows and bottom topographic slope. The study focus is on the effects of topography and the quadric shear basic zonal flows (the second derivative of basic zonal flows is not zero). The meridional slope destabilise (stabilise) zonal flows, it plays an unstable role in disturbance, moreover the effect of the second derivative of basic zonal flows is to accelerate the instability of disturbance. The zonal slope always destabilises the zonal basic flows through zonal and meridional wavenumber. Moreover, the effect of the second derivative of basic zonal flows is to accelerate the instability of disturbance.

Simulation-based study of wind—wave interactions under various sea conditions

Despite their importance in the ocean environment, the key physical processes in wind-wave interactions are poorly understood. Using a solver developed for undulatory boundaries, we perform numerical simulations of the wind-wave system under various sea conditions, including wind over monochromatic waves, early wind-wave generation, and wind over a broadband wave field. Our results show that the wave direction and wave age can significantly change the distribution of streamwise vorticity in the wind field. Different wave patterns are observed in the process of wind-wave generation. In a broadband wave field, the wave growth rate due to wind input is found to depend on the wave steepness.

Growth Rate of Gravity Wave Amplitudes Observed in Sodium Lidar Density Profiles and Nightglow Image Data

Amplitude growth rates of quasi-monochromatic gravity waves were estimated and compared from multiple instrument measurements carried out in Brazil. Gravity wave parameters, such as the wave amplitude and growth rate in distinct altitudes, were derived from sodium lidar density and nightglow all-sky images. Lidar observations were carried out in São Jose dos Campos (23 ∘ S, 46 ∘ W) from 1994 to 2004, while all-sky imagery of multiple airglow layers was conducted in Cachoeira Paulista (23 ∘ S, 45 ∘ W) from 1999–2000 and 2004–2005. We have found that most of the measured amplitude growth rates indicate dissipative behavior for gravity waves identified in both lidar profiles and airglow image datasets. Only a small fraction of the observed wave events (4% imager; 9% lidar) are nondissipative (freely propagating waves). Our findings also show that imager waves are strongly dissipated within the mesosphere and lower thermosphere region (MLT), decaying in amplitude in short distances (<12 km), while lidar waves tend to maintain a constant amplitude within that region. Part of the observed waves (16% imager; 36% lidar) showed unchanging amplitude with altitude (saturated waves). About 51.6% of the imager waves present strong attenuation (overdamped waves) in contrast with 9% of lidar waves. The general saturated or damped behavior is consistent with diffusive filtering processes imposing limits to amplitude growth rates of the observed gravity waves.

Estimated Impacts of Climate Change on Eddy Meridional Moisture Transport in the Atmosphere

Research findings suggest that water (hydrological) cycle of the earth intensifies in response to climate change, since the amount of water that evaporates from the ocean and land to the atmosphere and the total water content in the air will increase with temperature. In addition, climate change affects the large-scale atmospheric circulation by, for example, altering the characteristics of extratropical transient eddies (cyclones), which play a dominant role in the meridional transport of heat, moisture, and momentum from tropical to polar latitudes. Thus, climate change also affects the planetary hydrological cycle by redistributing atmospheric moisture around the globe. Baroclinic instability, a specific type of dynamical instability of the zonal atmospheric flow, is the principal mechanism by which extratropical cyclones form and evolve. It is expected that, due to global warming, the two most fundamental dynamical quantities that control the development of baroclinic instability and the overall global atmospheric dynamics—the parameter of static stability and the meridional temperature gradient (MTG)—will undergo certain changes. As a result, climate change can affect the formation and evolution of transient extratropical eddies and, therefore, macro-exchange of heat and moisture between low and high latitudes and the global water cycle as a whole. In this paper, we explore the effect of changes in the static stability parameter and MTG caused by climate change on the annual-mean eddy meridional moisture flux (AMEMF), using the two classical atmospheric models: the mid-latitude f-plane model and the two-layer β-plane model. These models are represented in two versions: “dry,” which considers the static stability of dry air alone, and “moist,” in which effective static stability is considered as a combination of stability of dry and moist air together. Sensitivity functions were derived for these models that enable estimating the influence of infinitesimal perturbations in the parameter of static stability and MTG on the AMEMF and on large-scale eddy dynamics characterized by the growth rate of unstable baroclinic waves of various wavelengths. For the base climate change scenario, in which the surface temperature increases by 1 °C and warming of the upper troposphere outpaces warming of the lower troposphere by 2 °C (this scenario corresponds to the observed warming trend), the response of the mass-weighted vertically averaged annual mean MTG is -0.2 ℃ per 1000 km. The dry static stability increases insignificantly relative to the reference climate state, while on the other hand, the effective static stability decreases by more than 5.4%. Assuming that static stability of the atmosphere and the MTG are independent of each other (using One-factor-at-a-time approach), we estimate that the increase in AMEMF caused by change in MTG is about 4%. Change in dry static stability has little effect on AMEMF, while change in effective static stability leads to an increase in AMEMF of about 5%. Thus, neglecting atmospheric moisture in calculations of the atmospheric static stability leads to tangible differences between the results obtained using the dry and moist models. Moist models predict ~9% increase in AMEMF due to global warming. Dry models predict ~4% increase in AMEMF solely because of the change in MTG. For the base climate change scenario, the average temperature of the lower troposphere (up to ~4 km), in which the atmospheric moisture is concentrated, increases by ~1.5 ℃. This leads to an increase in specific humidity of about 10.5%. Thus, since both AMEMF and atmospheric water vapor content increase due to the influence of climate change, a rather noticeable restructuring of the global water cycle is expected.

Streaming instability of dust-acoustic mode with helical wavefronts

Making use of the kinetic approach for plasma species, the electrostatic twisted dust-acoustic (DA) waves are studied in a collisionless unmagnetized multi-component dusty plasma consisting of electrons, singly ionized positive ions and charged massive dust grains. The Vlasov-Poisson equations are coupled together to obtain a generalized response function by using the Laguerre-Gaussian (LG) perturbed electrostatic potential and distribution function in the paraxial limit. The dispersive properties and growth rate instability of twisted DA waves are examined with distinct OAM states in a multi-component dusty plasma. Various significant modifications associated with the real wave frequency and growth rate are shown with respect to twist parameter and dust concentration. It is examined that dust concentration enhances the growth rate of twisted DA waves, whereas an increase in twist parameter reduces the growth rate instability. The excitation of twisted DA mode is also found to enhance with streaming speed of inertialess electrons. Our results may be useful for particle transport and trapping phenomena due to wave excitation in laboratory dusty plasmas.

Ion and Electron Dynamics in the Presence of Mirror, Electromagnetic Ion Cyclotron, and Whistler Waves

Abstract The wave–particle cyclotron interaction is a basic process in collisionless plasmas, which results in the redistribution of the energy between plasma waves and charged particles. This paper presents an event observation in order to explore the dynamics of charged particles and plasma waves, i.e., mirror, electromagnetic ion cyclotron (EMIC), and whistler waves, in the Earth’s magnetosheath. It shows that when ions have a high-speed streaming velocity parallel to the magnetic field, EMIC waves arise. We also find that the frequency distribution of nearly parallel and nearly antiparallel whistler waves depends on the parallel streaming velocity of electrons. Based on the linear kinetic theory and the fitting plasma parameters, we show that the differential flows among ion components can enhance the ion cyclotron anisotropy instability that is even stronger than the mirror instability. The differential electron flows induce an asymmetry of the growth rate of counter-propagating whistler waves in the electron cyclotron anisotropy instability. On the other hand, the low-frequency EMIC and transverse electromagnetic waves modulate the ion pitch angle distribution. Moreover, when charged particles flow across the magnetic field, both low- and high-energy electrons are deeply trapped by mirror waves. These results illustrate new features of the observed plasma waves and charged particles in the Earth’s magnetosheath, which could inspire improvement of the wave models therein.

Electron acceleration at comet 67P/Churyumov-Gerasimenko

We report the observation by the Ion and Electron Sensor (IES) of energetic (>1 keV) electrons in the plasma environment of comet 67P Churyumov-Gerasimenko (67P). Most of the electrons in the cometary coma are expected to be of solar wind, photoionization, or electron impact origin and are therefore not expected to exceed some hundreds of eV in energy. During the Vega flybys of comet Halley, 1 keV electrons were also observed, and these are explained as having been accelerated by lower hybrid (LH) waves resulting from the two-stream instability involving the solar wind and pickup-ion flows. These waves resonate with the cyclotron motion of the ions and the longitudinal motion of electrons and are on the order of several Hz, at least in the case of 67P. We postulate that the energetic electrons we have observed intermittently during December 2015 through January 2016 are also the result of such a process and that Landau damping causes the acceleration and subsequent abrupt decrease in this energy (also seen at Halley). We show from this study an event on 19 January 2016 when IES simultaneously observed accelerated electrons, solar wind protons, water ions, and LH waves. A dispersion analysis shows that the ion–ion two-stream instability has positive growth rates for such waves during the observation period.

The Wave Energy Up Conversion of Plasma Wave in Inhomogeneous Ionosphereic Plasma

Different types of instabilities are observed in the thermodynamically nonequilibrium Earth's ionosphere. Effective energy exchange process among waves may takes place through nonlinear interaction modes because of availability of free energy. We consider gradients in density and magnetic field is present in the system which support drift wave turbulence. In this study we concern on the wave energy up conversion of electrostatic nonresonant lower hybrid wave through plasma maser instability in the mid-altitude ionospheric region. We have formulated the growth rate of lower hybrid wave by Vlasov-Poisson mathematical frame and estimated its value by observational data.

Thermal fluctuations in capillary thinning of thin liquid films

Thermal fluctuations have been shown to influence the thinning dynamics of planar thin liquid films, bringing predicted rupture times closer to experiments. Most liquid films in nature and industry are, however, non-planar. Thinning of such films not just results from the interplay between stabilizing surface tension forces and destabilizing van der Waals forces, but also from drainage due to curvature differences. This work explores the influence of thermal fluctuations on the dynamics of thin non-planar films subjected to drainage, with their dynamics governed by two parameters: the strength of thermal fluctuations, $\unicode[STIX]{x1D703}$, and the strength of drainage, $\unicode[STIX]{x1D705}$. For strong drainage ($\unicode[STIX]{x1D705}\gg \unicode[STIX]{x1D705}_{tr}$), we find that the film ruptures due to the formation of a local depression called a dimple that appears at the connection between the curved and flat parts of the film. For this dimple-dominated regime, the rupture time, $t_{r}$, solely depends on $\unicode[STIX]{x1D705}$, according to the earlier reported scaling, $t_{r}\sim \unicode[STIX]{x1D705}^{-10/7}$. By contrast, for weak drainage ($\unicode[STIX]{x1D705}\ll \unicode[STIX]{x1D705}_{tr}$), the film ruptures at a random location due to the spontaneous growth of fluctuations originating from thermal fluctuations. In this fluctuations-dominated regime, the rupture time solely depends on $\unicode[STIX]{x1D703}$ as $t_{r}\sim -(1/\unicode[STIX]{x1D714}_{max})\ln (\sqrt{2\unicode[STIX]{x1D703}})^{\unicode[STIX]{x1D6FC}}$, with $\unicode[STIX]{x1D6FC}=1.15$. This scaling is rationalized using linear stability theory, which yields $\unicode[STIX]{x1D714}_{max}$ as the growth rate of the fastest-growing wave and $\unicode[STIX]{x1D6FC}=1$. These insights on if, when and how thermal fluctuations play a role are instrumental in predicting the dynamics and rupture time of non-flat draining thin films.

Effect of heat and mass transfer on the instability of an annular liquid sheet

A temporal linear instability analysis has been conducted to investigate the effect of heat and mass transfer on the instability of an annular liquid sheet axially moving in the gas medium. The dispersion relation is obtained and solved numerically. Energy budget is calculated to provide physical insights of various instability driving mechanisms. The results show that heat and mass transfer promotes the wave growth rate mainly at small wave numbers. In contrast to the case without heat and mass transfer, the wave growth rate with strong heat and mass transfer peaks at zero wave number. Liquid viscosity is found to have a minimal stabilizing effect on the sheet instability. Regardless of the heat and mass transfer, increasing liquid Weber number suppresses the sheet instability below a crossover point of wave number at 1.15, and promotes the sheet instability above the crossover point. In the presence of strong heat and mass transfer, increasing gas-to-liquid density ratio reduces the wave growth rate at small wave numbers below 0.28, and beyond which increases the wave growth rate. Reducing sheet thickness promotes the sheet instability for all wave numbers. The energy budgets show that the inner gas disturbance is most responsible for promoting the wave growth rate at large liquid Weber numbers; and the inner interface dominates the outer one in destabilizing the annular liquid sheet.

Growth Rates of the Electrostatic Waves in Radio Zebra Models

Abstract Zebras were observed not only in the solar radio emission but also in radio emissions of Jupiter and the Crab Nebula pulsar. In their models, growth rates of the electrostatic waves play an important role. Considering the plasma composed from the thermal background plasma and hot and rare component with the Dory–Guest–Harris distribution, we compute the growth rates γ and dispersion branches of the electrostatic waves in the ω − k ⊥ domain. We show complexity of the electrostatic wave branches in the upper-hybrid band. In order to compare the results, which we obtained using the kinetic theory and particle-in-cell (PIC) simulations, we define and compute the integrated growth rate Γ, where the “characteristic width” of dispersion branches was considered. We found a very good agreement between the integrated growth rates and those from PIC simulations. For maximal and minimal Γ we showed locations of dispersion branches in the ω − k ⊥ domain. We found that Γ has a maximum when the dispersion branches not only cross the region with high growth rates γ, but when the dispersion branches in this region are sufficiently long and wide. We also mentioned the effects of changes in the background plasma and hot component temperatures.

Whistler instability based on observed flat-top two-component electron distributions in the Earth's magnetosphere

ABSTRACT One of the fundamental features of space plasmas is the observation of non-Maxwellian particle velocity distributions. In the present study, we observe electron velocity distributions in the Earth's magnetosphere at times when the electron density is low, typical of cusp values, and when it is enhanced as a result of disturbances by the solar wind. We find that electron distributions are flat-topped and have two populations: one cold and one hot. We fit the observed electron distributions by a generalized $( {r,q} )$ distribution, and derive and plot expressions for the real frequency and growth rate using fitted and observed parameters. We show that enhancement in the density of hot electrons enhances the growth rate of whistler waves, which play an important role in energy transport in the Earth's magnetosphere.

Wind–wave coupling study using LES of wind and phase-resolved simulation of nonlinear waves

We present a study on the interaction between wind and water waves with a broad-band spectrum using wave-phase-resolved simulation with long-term wave field evolution. The wind turbulence is computed using large-eddy simulation and the wave field is simulated using a high-order spectral method. Numerical experiments are carried out for turbulent wind blowing over a wave field initialised using the Joint North Sea Wave Project spectrum, with various wind speeds considered. The results show that the waves, together with the mean wind flow and large turbulent eddies, have a significant impact on the wavenumber–frequency spectrum of the wind turbulence. It is found that the shear stress contributed by sweep events in turbulent wind is greatly enhanced as a result of the waves. The dependence of the wave growth rate on the wave age is consistent with the results in the literature. The probability density function and high-order statistics of the wave surface elevation deviate from the Gaussian distribution, manifesting the nonlinearity of the wave field. The shape of the change in the spectrum of wind-waves resembles that of the nonlinear wave–wave interactions, indicating the dominant role played by the nonlinear interactions in the evolution of the wave spectrum. The frequency downshift phenomenon is captured in our simulations wherein the wind-forced wave field evolves for$O(3000)$peak wave periods. Using the numerical result, we compute the universal constant in a wave-growth law proposed in the literature, and substantiate the scaling of wind–wave growth based on intrinsic wave properties.

Influence of non-spherical dust grains on the growing of astrophysical dusty plasma waves with (r, q) distribution function

The influence of dust rotation on the growing of dust-ion acoustic surface waves is investigated in a sharply bounded astrophysical dusty plasma containing the non-spherical dust grains and non-thermal electrons whose velocity distribution function takes the form of the generalized (r, q) distribution function, where r and q are the two spectral indices for the generalized distribution function. We assume that the angular frequency of the rotating non-spherical dust grains is close to the wave frequency to derive the resonant growth rate of the surface wave. The result shows that the surface wave becomes more unstable as the rotation frequency is increasing. If the rotation frequency is too low, the instability disappears in the domain of high wave numbers. We also have found that growth rate decreases as the moment of inertia of the rotating dust grains increases in astrophysical non-thermal plasmas.