Magneto-gravity Research Articles

Lagrangian approach to nonlinear waves in non-dispersive and dispersive rotating shallow water magnetohydrodynamics

A Lagrangian approach to both hydrostatic non-dispersive in the short-wave range and non-hydrostatic dispersive rotating shallow-water magnetohydrodynamics is developed, and used to analyse weakly and fully nonlinear waves described by the model. Hyperbolic structure in the non-dispersive case is displayed and Riemann invariants are constructed. Characteristic equations are used to establish criteria of breaking and formation of shocks by magneto-gravity waves, and conditions of the appearance of contact discontinuities in Alfvén waves. As in the case of non-magnetic rotating shallow water, rotation cannot prevent breaking. The Lagrangian equations of the model are reduced to a single partial differential ‘master’ equation, which is used to analyse the propagation of weakly nonlinear waves of both families, with or without weak rotation, and with or without weak short-wave dispersion. Corresponding modulation equations are constructed and their main properties sketched. The same master equation is used to obtain fully nonlinear finite-amplitude wave solutions in particular cases of no short-wave dispersion or no rotation.

Gravity waves in strong magnetic fields

ABSTRACT Strong magnetic fields in the cores of stars are expected to significantly modify the behaviour of gravity waves: this is likely the origin of suppressed dipole modes observed in many red giants. However, a detailed understanding of how such fields alter the spectrum and spatial structure of magnetogravity waves has been elusive. For a dipole field, we analytically characterize the horizontal eigenfunctions of magnetogravity modes, assuming that the wavevector is primarily radial. For axisymmetric modes (m = 0), the magnetogravity wave eigenfunctions become Hough functions, and they have a radial turning point for sufficiently strong magnetic fields. For non-axisymmetric modes (m ≠ 0), the interaction between the discrete g-mode spectrum and a continuum of Alfvén waves produces nearly discontinuous features in the fluid displacements at critical latitudes associated with a singularity in the fluid equations. We find that magnetogravity modes cannot propagate in regions with sufficiently strong magnetic fields, instead becoming evanescent. When encountering strong magnetic fields, ingoing gravity waves are likely refracted into outgoing slow magnetic waves. These outgoing waves approach infinite radial wavenumbers, which are likely to be damped efficiently. However, it may be possible for a small fraction of the wave power to escape the stellar core as pure Alfvén waves or magnetogravity waves confined to a very narrow equatorial band. The artificially sharp features in the Wentzel–Kramers–Brillouin-separated solutions suggest the need for global mode solutions which include small terms neglected in our analysis.

Magneto-gravity wave packet dynamics in strongly magnetized cores of evolved stars

ABSTRACT Magnetic fields are believed to be generated in the cores of massive main-sequence stars, and these may survive on to later stages of evolution. Observations of depressed dipole modes in red giant stars have been touted as evidence for these fields, but the predictions of existing magnetic theories have difficulty accommodating several aspects, including the need to return a fraction of wave energy from the core to the envelope, and the persistent gravity-like character of affected modes. In this work, we perform a Hamiltonian ray-tracing study investigating the dynamics of magneto-gravity waves in full spherical geometry, using realistic stellar models and magnetic field configurations. This technique applies in the limit where wavelengths are much shorter than scales of background variation. We conduct a comprehensive exploration of parameter space, examining the roles of wave frequency, spherical harmonic degree, wavevector polarization, incoming latitude, field strength, field radius, and evolutionary state. We demonstrate that even in the presence of a strong field, there exist trajectories where waves remain predominantly gravity-like in character, and these are able to undergo reflection out of the core, much like pure gravity waves. The remaining trajectories are ones where waves acquire significant Alfvén character, becoming trapped and eventually dissipated. Orientation effects, i.e. wavevector polarization and incoming latitude, are found to be crucial factors in determining the outcome (trapped versus reflected) of individual wave packets. The allowance for partial energy return from the core offers a solution to the conundrum faced by the magnetic hypothesis.

Distribution of magnetogravity waves during strong earthquakes (M > 6.5) preparation periods

Magnetogravity activity during the preparation of four strong (M > 6.5) earthquake with epicenters at medium (35–40° N) and low (10° S–10° N) latitudes is detected. For this purpose a comparison of simultaneous disturbances at dynamic spectra of ionospheric layers Es, E, F2 critical frequencies and geomagnetic field X, Y, Z components was performed. It was found that the greatest number of magnetogravity events noted in epicenters vicinity takes place at two days before the considered earthquakes. Evaluation of dynamic spectra intensity level which was obtained by data from magnetic stations located around the epicenter, allows to identify the magnetogravity waves (MGW) propagation direction with least damping. In most cases they coincide with geomagnetic field direction. Attention is paid to ionospheric wind influence for low-frequency MGW mode.

Spectral characteristics of magnetogravity waves generated by high-energy mass source in the equatorial region of the atmosphere, Part I

Spectral characteristics of magnetogravity waves generated by high-energy mass source in the equatorial region of the atmosphere, Part I

Spectral characteristics of magnetogravity waves generated by high energy mass source in the equatorial region of the atmosphere, Part II

The possibility of magnetogravity wave (MGW) propagation in the equatorial ionosphere taking into account the finite conductivity is analyzed. The dispersion relation shows the existence of two propagating MGW modes in ionospheric layer F2: high-frequency (HF MGW) and low frequency (LF MGW). The dispersion relations for them are executed and the characteristic frequencies and propagation velocities are determined. In this part of research the spectral features of disturbances in components of environment displacement for HF MGW, generated by a mass source, is carried out. The results are applied to estimate the values of density, pressure and magnetic field spectral components of magnetogravity disturbances caused by horizontal meteor sweep. They may be useful in the analysis of ionospheric disturbances excited by high energy geophysical sources.

Instability of subharmonic resonances in magnetogravity shear waves

We study analytically the instability of the subharmonic resonances in magnetogravity waves excited by a (vertical) time-periodic shear for an inviscid and nondiffusive unbounded conducting fluid. Due to the fact that the magnetic potential induction is a Lagrangian invariant for magnetohydrodynamic Euler-Boussinesq equations, we show that plane-wave disturbances are governed by a four-dimensional Floquet system in which appears, among others, the parameter ɛ representing the ratio of the periodic shear amplitude to the vertical Brunt-Väisälä frequency N(3). For sufficiently small ɛ and when the magnetic field is horizontal, we perform an asymptotic analysis of the Floquet system following the method of Lebovitz and Zweibel [Astrophys. J. 609, 301 (2004)]. We determine the width and the maximal growth rate of the instability bands associated with subharmonic resonances. We show that the instability of subharmonic resonance occurring in gravity shear waves has a maximal growth rate of the form Δ(m)=(3√[3]/16)ɛ. This instability persists in the presence of magnetic fields, but its growth rate decreases as the magnetic strength increases. We also find a second instability involving a mixing of hydrodynamic and magnetic modes that occurs for all magnetic field strengths. We also elucidate the similarity between the effect of a vertical magnetic field and the effect of a vertical Coriolis force on the gravity shear waves considering axisymmetric disturbances. For both cases, plane waves are governed by a Hill equation, and, when ɛ is sufficiently small, the subharmonic instability band is determined by a Mathieu equation. We find that, when the Coriolis parameter (or the magnetic strength) exceeds N(3)/2, the instability of the subharmonic resonance vanishes.

Magnetogravity waves in the ionosphere under conditions of finite conductivity

We obtain dispersion relations for magnetogravity waves in the ionosphere with allowance for the combined influence of magnetic field, gravity, and finite conductivity within the framework of the hydrodynamic approximation. The required conditions are fulfilled in the ionosphere at altitudes over or about 250 km. The auroral electrojet is considered as a source of magnetogravity waves which are frequently observed as traveling ionospheric disturbances. The contribution of magnetogravity waves to the ionospheric disturbances is determined on the basis of analyzing the data from the vertical sounding of the ionospheric F2 layer and the geomagnetic disturbances along the chosen magnetic meridian and on its sides. The features of the obtained dynamic spectra of magnetogravity waves agree with the characteristic frequencies and velocities determined by the calculated dispersion curves. As a result, we confirm the fact that magnetogravity waves stipulate some traveling ionospheric disturbances and can be used for diagnostics of the ionospheric parameters.

Mode conversion of radiatively damped magnetogravity waves in the solar chromosphere

Modelling of adiabatic gravity wave propagation in the solar atmosphere showed that mode conversion to field guided acoustic waves or Alfv\'en waves was possible in the presence of highly inclined magnetic fields. This work aims to extend the previous adiabatic study, exploring the consequences of radiative damping on the propagation and mode conversion of gravity waves in the solar atmosphere. We model gravity waves in a VAL-C atmosphere, subject to a uniform, and arbitrarily orientated magnetic field, using the Newton cooling approximation for radiatively damped propagation. The results indicate that the mode conversion pathways identified in the adiabatic study are maintained in the presence of damping. The wave energy fluxes are highly sensitive to the form of the height dependence of the radiative damping time. While simulations starting from 0.2 Mm result in modest flux attenuation compared to the adiabatic results, short damping times expected in the low photosphere effectively suppress gravity waves in simulations starting at the base of the photosphere. It is difficult to reconcile our results and observations of propagating gravity waves with significant energy flux at photospheric heights unless they are generated in situ, and even then, why they are observed to be propagating as low as 70 km where gravity waves should be radiatively overdamped.

Numerical simulation of propagation of the MHD waves in sunspots

AbstractWe present results of numerical 3D simulation of propagation of MHD waves in sunspots. We used two self consistent magnetohydrostatic background models of sunspots. There are two main differences between these models: (i) the topology of the magnetic field and (ii) dependence of the horizontal profile of the sound speed on depth. The model with convex shape of the magnetic field lines near the photosphere has non-zero horizorntal perturbations of the sound speed up to the depth of 7.5 Mm (deep model). In the model with concave shape of the magnetic field lines near the photosphere Δ c/c is close to zero everywhere below 2 Mm (shallow model). Strong Alfven wave is generated at the wave source location in the deep model. This wave is almost unnoticeable in the shallow model. Using filtering technique we separated magnetoacoustic and magnetogravity waves. It is shown, that inside the sunspot magnetoacoustic and magnetogravity waves are not spatially separated unlike the case of the horizontally uniform background model. The sunspot causes anisotropy of the amplitude distribution along the wavefront and changes the shape of the wavefront. The amplitude of the waves is reduced inside the sunspot. This effect is stronger for the magnetogravity waves than for magnetoacoustic waves. The shape of the wavefront of the magnetogravity waves is distorted stronger as well. The deep model causes bigger anisotropy for both mgnetoacoustic and magneto gravity waves than the shallow model.

Detection of magneto-gravity waves in the ionosphere by analysis of the maximum observable frequencies on oblique-sounding paths

The existence of magneto-gravity waves stipulated by the substorm activity can lead to the occurrence of traveling ionospheric disturbances, whose velocity exceeds the sound speed. For detection of magneto-gravity waves, we used experimental data on propagation of decameter radio waves on the midlatitude and subauroral oblique sounding paths Inskip–Rostov-on-Don, Cyprus–Rostovon-Don, Irkutsk–Rostov-on-Don, and Norilsk–Rostov-on-Don in December 2006 and March 2007 under conditions of weak geomagnetic disturbance. Time delays between the AE indices of polar electrojets and the maximum observable frequencies for the considered paths were established by calculation of linear correlations. These delays correspond to the times required for transport of gravity disturbances from the auroral region to the reflection points of radio waves on respective paths. Among the obtained time shifts, we mention the 5–10-min ones which correspond to increased velocity of the disturbances compared with the usual velocities of acoustic-gravity waves for the paths under study. Such cases can be related to the transport of magneto-gravity waves. Study of the spectral composition of the AE-index disturbances and recorded maximum observable frequencies shows consistency of their spectral features in the cases of increased correlation for small time delays. It is also found that the spectral features of the AE-index disturbances coincide with the spectral features of the disturbances of the horizontal component of the geomagnetic field on ground-based magnetic stations. According to calculated dispersion curves, the frequencies of magneto-gravity waves were estimated, and they turned out to be equal to ω ≈ (1–2) ・ 10−4 Hz.

To “Magneto-gravity response function and its application to the Daito Ridge,” Yoshio Ueda, Ryuji Kubota, and Jiro Segawa, GEOPHYSICS, 67, 110–116Magneto-gravity response function and its application to the Daito Ridge

To “Magneto-gravity response function and its application to the Daito Ridge,” Yoshio Ueda, Ryuji Kubota, and Jiro Segawa, GEOPHYSICS, 67, 110–116Magneto-gravity response function and its application to the Daito Ridge

Hydromagnetic edge waves and instability in reduction cells

To clarify the function of gravity in the shallow-water theory of the interfacial instability in aluminium reduction cells, we analyse the existing long-wave theory of the instability in the limit of vanishing gravitational acceleration , gravity is essential to the long-wave instability because a correlation imposed by the magneto-gravity waves is essential for the disturbance to extract power from the mean state.

Resonant origin for density fluctuations deep within the Sun: helioseismology and magneto-gravity waves

We analyse helioseismic waves near the solar equator in the presence of magnetic fields deep within the solar radiative zone. We find that reasonable magnetic fields can significantly alter the shapes of the wave profiles for helioseismic g-modes. They can do so because the existence of density gradients allows g-modes to excite Alfvén waves resonantly, causing mode energy to be funnelled along magnetic field lines, away from the solar equatorial plane. The resulting waveforms show comparatively sharp spikes in the density profile at radii these resonances take place. We estimate how big these waves might be in the Sun, and perform a first search for observable consequences. We find the density excursions at the resonances to be too narrow to be ruled out by present-day analyses of p-wave helioseismic spectra, even if their amplitudes were to be larger than a few per cent. (In contrast, it has been shown by Burgess et al. that such density excursions could affect solar neutrino fluxes in an important way.) Because solar p-waves are not strongly influenced by radiative-zone magnetic fields, standard analyses of helioseismic data should not be significantly altered. The influence of the magnetic field on the g-mode frequency spectrum could be used to probe sufficiently large radiative-zone magnetic fields, should solar g-modes ever be definitively observed. Our results would have stronger implications if overstable solar g-modes should prove to have very large amplitudes, as has sometimes been argued.

Dispersive shallow water magnetohydrodynamics

Shallow water magnetohydrodynamics (SWMHD) is a recently proposed model for a thin layer of incompressible, electrically conducting fluid. The velocity and magnetic field are taken to be nearly two dimensional, with approximate magnetohydrostatic balance in the perpendicular direction, leading to a reduced two-dimensional model. The SWMHD equations have been found previously to admit unphysical cusp-like singularities in finite amplitude magnetogravity waves. This paper extends the Hamiltonian formulation of SWMHD to construct a dispersively regularized system, analogous to the Green–Naghdi equations of hydrodynamics, that supports smooth solitary waves and cnoidal wave trains, and shares the potential vorticity conservation properties of SWMHD.

“Shallow-Water” Magnetohydrodynamic Waves in the Solar Tachocline

This Letter discusses waves in a rotating magnetized fluid layer, governed by shallow-water magnetohydrodynamics. Such waves likely exist in the solar tachocline, and we focus on this application. A dispersion relation is derived, giving two branches of waves: Alfven and magnetogravity. In general, finite Alfven and magnetogravity waves can propagate without change of shape. However, if the Coriolis force is absent, as on the equator of the tachocline, finite magnetogravity waves steepen and develop singularities in a time τs. It is shown that τs increases monotonically with the ambient magnetic field strength.

Nonlinear magnetogravity waves in a low‐β plasma

We derive a set of nonlinear equations for magnetogravity waves based on a reduced set of fluid variables. The equations describe the self‐consistent time evolution of the density perturbation and the velocity and magnetic vector potential component in the direction along the horizontal background magnetic field. These reduced equations take account of the propagation of Alfvén waves along the background field, of gravity waves perpendicular to the background field and their mutual nonlinear interaction. The Strauss‐Boussinesq approximations are shown to be applicable if the vertical gravitational scale height H is much larger than the typical vertical wavelength λz under consideration and if the aspect ratio of the fluctuation wavelengths parallel to the background magnetic field to the perpendicular wavelengths is even larger than H0/λz. As an application of these equations, we investigate some typical nonlinear phenomena. A stability analysis of plane harmonic waves suggests that as a result of the parametric decay instability the energy of buoyancy fluctuations is eventually converted into magnetic fluctuation energy of Alfvén waves with large vertical wave number. Furthermore it is shown that modonlike, horizontally extended traveling vortices are a nontrivial solution to the Boussinesq‐Strauss equations. The vortex axis of these modons is inclined with respect to the background magnetic field and in a stably stratified plasma, a necessary condition for the existence of these solutions is an apparent phase velocity along the background magnetic field smaller than the Alfvén velocity.

Wave transformation at the cusp resonance in a finite conductivity isothermal atmosphere permeated by a nearly horizontal magnetic field

The paper considers wave transformation in the vicinity of the cusp resonance in an isothermic finite conductivity medium with a nearly horizontal magnetic field. It is shown that absorption of magnetogravity waves takes place when the inclination angle of the magnetic field is smaller than the critical angle. When the inclination angle is large then the critical magnetogravity waves are transformed into slow magnetoacoustic waves.

Resonant absorption of internal gravity waves in stellar atmospheres

An equation describing wave propagation in an incompressible medium of finite conductivity with a uniform tilted magnetic field has been derived. It is shown that magneto-gravity waves are absorbed in the vicinity of the cusp resonant level if the angle of inclination of the magnetic field is smaller than the critical and are transformed into nondamping Alfvenp-waves if the angle of inclination of the magnetic field is larger than the critical. An evaluation of the critical angle is given on the basis of simple physics.

Photoelectric observations of chromospheric sunspot oscillations. II - Propagation characteristics

Measurements of oscillations in umbrae and penumbrae using the line pairs (Ca II lambda8498--lambda8542) and (Fe I lambda5434--Ca II lambda8498)= are presented for seven sunspots and 11 observing runs. In the umbral chromosphere, the observations reported here, taken with other measurements of umbral oscillations, suggest that the oscillations are upward propagating acoustic (or slow mode) disturbances, and that they become nonlinear and develop into shock waves in the upper layers. They cause a significant increase in the radiative output of the umbral chromosphere, indicating the possibility of nonthermal heating at these levels. On the basis of this picture, umbral chromosphere, indicating the possibility of nonthermal heating at these levels. On the basis of this picture, umbral chromospheres have a greater physical extent in height than predicted by umbral models with coronal pressures greater than those found in the quiet Sun. Oscillations are present in the outer regions of penumbrae with frequencies and phase relationships that suggest the possibility of magneto-gravity waves.