Magneto-acoustic-gravity waves in the horizontal magnetic field

Abstract

In this paper we consider the propagation of magneto-acoustic-gravity waves in a compressible, conducting isothermal atmosphere permeated by a uniform horizontal magnetic field. The singular levels, arising in a horizontal magnetic field, are considered in their most general form. Exact analytical solutions for a number of particular cases of wave propagation are obtained. The wave transformation is analyzed for all these cases using the solutions obtained.

Based on the theory of wave propagation across a magnetic field, low-frequency wave trapping in a chromospheric resonator is explained, and some properties of running penumbral waves are discussed.     

Magnetic Rossby waves in a stably stratified layer near the surface of the Earth's outer core

Abstract

The stratification profile of the Earth's magnetofluid outer core is unknown, but there have been suggestions that its upper part may be stably stratified. Braginsky (1984) suggested that the magnetic analog of Rossby (planetary) waves in this stable layer (the ‘H’ layer) may be responsible for a portion of the short-period secular variation. In this study, we adopt a thin shell model to examine the dynamics of the H layer. The stable stratification justifies the thin-layer approximations, which greatly simplify the analysis. The governing equations are then the Laplace's tidal equations modified by the Lorentz force terms, and the magnetic induction equation. We linearize the Lorentz force in the Laplace's tidal equations and the advection term in the magnetic induction equation, assuming a zeroth order dipole field as representative of the magnetic field near the insulating core-mantle boundary. An analytical β-plane solution shows that a magnetic field can release the equatorial trapping that non-magnetic Rossby waves exhibit. A numerical solution to the full spherical equations confirms that a sufficiently strong magnetic field can break the equatorial waveguide. Both solutions are highly dissipative, which is a consequence of our necessary neglect of the induction term in comparison with the advection and diffusion terms in the magnetic induction equation in the thin-layer limit. However, were one to relax the thin-layer approximations and allow a radial dependence of the solutions, one would find magnetic Rossby waves less damped (through the inclusion of the induction term). For the magnetic field strength appropriate for the H layer, the real parts of the eigenfrequencies do not change appreciably from their non-magnetic values. We estimate a phase velocity of the lowest modes that is rather rapid compared with the core fluid speed typically presumed from the secular variation.     

High-latitude HF Doppler observations of ULF waves: 2. Waves with small spatial scale sizes

The DOPE (Doppler Pulsation Experiment) HF Doppler sounder located near Tromsø, Norway (geographic: 69.6°N 19.2°E; L = 6.3) is deployed to observe signatures, in the high-latitude ionosphere, of magnetospheric ULF waves. A type of wave has been identified which exhibits no simultaneous ground magnetic signature. They can be subdivided into two classes which occur in the dawn and dusk local time sectors respectively. They generally have frequencies greater than the resonance fundamentals of local field lines. It is suggested that these may be the signatures of high-m ULF waves where the ground magnetic signature has been strongly attenuated as a result of the scale size of the waves. The dawn population demonstrate similarities to a type of magnetospheric wave known as giant (Pg) pulsations which tend to be resonant at higher harmonics on magnetic field lines. In contrast, the waves occurring in the dusk sector are believed to be related to the storm-time Pc5s previously reported in VHF radar data. Dst measurements support these observations by indicating that the dawn and dusk classes of waves occur respectively during geomagnetically quiet and more active intervals.     

海浪引起的地磁场波动的观测与初步分析

近岸海浪是影响近岸水域环境状态的重要环节.海洋近岸波的波动性质和变化规律的研究对于海岸防护、近岸航运、军事活动等具有重要意义.感应磁场波动可为探测海洋近岸波的非线性过程提供一种有效手段.本文首次对海洋近岸波引起的感应磁场进行了频谱指数分析,获得了能量注入和耗散过程对应的谱段.2016年5月15日—6月30日在昌黎海岸(东经119.3,北纬39.7°)利用KDM-2型磁通门磁力仪对海洋近岸波引起的磁场变化进行了测量,数据分辨率为0.01 nT/(HZ)~(1/2),时间采样率为1 Hz和128 Hz.观测数据显示,在距海岸线2 m远处,清晰地观测到了海洋近岸波引起的磁场波动,在0.001~10.0 Hz频段的波动最大振幅约为1 nT.波动的小波频谱呈现出多次谐波结构,符合海洋近岸波的谐波特征.傅里叶频谱显示不同频段谱的斜率不同,反映了海洋近岸波发展与耗散的非线性物理过程,进一步开展长期观测和统计分析有助于深入了解海洋中的电动力学过程.     

A mechanism for angular momentum mixing

Abstract

If a contained homogeneous, rotating fluid is forced near to a resonance for elastoid-inertia waves, strong vortices are observed to form. Numerical experiments reported here lend support to the explanation that these are due to a redistribution of the angular momentum by the waves. If the waves grow until the Angular momentum gradient is overturned somewhere, turbulent mixing there make the redistribution irreversible, resulting in a vortex. The process is analogous to the formation of steps in a stratified fluid by breaking internal waves.     

Observations of Pc 3–4 and Pi 2 geomagnetic pulsations in the low-latitude ionosphere

Day-time Pc 3–4 (≃5–60 mHz) and night-time Pi 2 (≃5–20 mHz) ULF waves propagating down through the ionosphere can cause oscillations in the Doppler shift of HF radio transmissions that are correlated with the magnetic pulsations recorded on the ground. In order to examine properties of these correlated signals, we conducted a joint HF Doppler/magnetometer experiment for two six-month intervals at a location near L = 1.8. The magnetic pulsations were best correlated with ionospheric oscillations from near the F region peak. The Doppler oscillations were in phase at two different altitudes, and their amplitude increased in proportion to the radio sounding frequency. The same results were obtained for the O- and X-mode radio signals. A surprising finding was a constant phase difference between the pulsations in the ionosphere and on the ground for all frequencies below the local field line resonance frequency, independent of season or local time. These observations have been compared with theoretical predictions of the amplitude and phase of ionospheric Doppler oscillations driven by downgoing Alfvén mode waves. Our results agree with these predictions at or very near the field line resonance frequency but not at other frequencies. We conclude that the majority of the observations, which are for pulsations below the resonant frequency, are associated with downgoing fast mode waves, and models of the wave-ionosphere interaction need to be modified accordingly.     

The rapid dissipation of magnetic fields in highly conducting fluids

Abstract

This paper treats the dynamical conditions that obtain when long straight parallel twisted flux tubes in a highly conducting fluid are packed together in a broad array. It is shown that there is generally no hydrostatic equilibrium. In place of equilibrium there is a dynamical nonequilibrium, leading to neutral point reconnection and progressive coalescence of neighboring tubes (with the same sense of twisting), forming tubes of larger diameter and reduced twist. The magnetic energy in the twisting of each tube declines toward zero, dissipated into small-scale motions of the fluid and thence into heat.

The physical implications are numerous. For instance, it has been suggested that the subsurface magnetic field of the sun is composed of close-packed twisted flux tubes. Any such structures are short lived, at best.

The footpoints of the filamentary magnetic fields above bipolar magnetic regions on the sun are continually shuffled and rotated by the convection, so that the fields are composed of twisted rubes. The twisting and mutual wrapping is converted directly into fluid motion and heat by the dynamical nonequilibrium, so that the work done by the convection of the footpoints goes directly into heating the corona above. This theoretical result is the final step, then, in understanding the assertion by Rosner, Tucker, and Valana, and others, that the observed structure of the visible corona implies that it is heated principally by direct dissipation of the supporting magnetic field. It is the dynamical nonequilibrium that causes the dissipation, in spite of the high electrical conductivity. It would appear that any bipolar magnetic field extending upward from a dense convective layer into a tenuous atmosphere automatically produces heating, and a corona of some sort, in the sun or any other convective star.     

The weak taylor state in an αω-dynamo

Abstract

A spherical αω-dynamo is studied for small values of the viscous coupling parameter ε ～ v^1/2, paying attention particularly to large dynamo numbers. The present study is a follow-up of the work by Hollerbach et al. (1992) with their choice of α-effect and Archimedean wind including also the constraint of magnetic field symmetry (or antisymmetry) due to equatorial plane. The magnetic field scaled by ε^1/2 is independent of ε in the solutions for dynamo numbers smaller than a certain value of D _b (the Ekman state) which are represented by dynamo waves running from pole to equator or vice-versa. However, for dynamo numbers larger than D _b the solution bifurcates and subsequently becomes dependent on ε. The bifurcation is a consequence of a crucial role of the meridional convection in the mechanism of magnetic field generation. Calculations suggest that the bifurcation appears near dynamo number about 33500 and the solutions for larger dynamo numbers and ε = 0 become unstable and fail, while the solutions for small but non-zero ε are characterized by cylindrical layers of local maximum of magnetic field and sharp changes of geostrophic velocity. Our theoretical analysis allows us to conclude that our solution does not take the form of the usual Taylor state, where the Taylor constraint should be satisfied due to the special structure of magnetic field. We rather obtained the solution in the form of a “weak” Taylor state, where the Taylor constraint is satisfied partly due to the amplitude of the magnetic field and partly due to its structure. Calculations suggest that the roles of amplitude and structure are roughly fifty-fifty in our “weak” Taylor state solution and thus they can be called a Semi-Taylor state. Simple estimates show that also Ekman state solutions can be applicable in the geodynamo context.     

α-effect due to wave reflection from the core mantle boundary

Abstract

Latitude behavior of the boundary α-effect based on reflection of hydromagnetic waves from the Core-Mantle Boundary (CMB) studied earlier by Anufriev (1991), is discussed. Its form given in Figure 2 is in good agreement with that used in model-Z of Braginsky. We want to emphasize the following main features of our α-effect which resemble those of Braginsky: concentration near the boundary, sign-changing of α in the layer and geometrical behavior. The last includes the vanishing of α near the poles and the equator which is characteristic for Braginsky's α-effect. It is also shown that for Magnetic Reynolds Number of order 100 the amplitude of the α-effect and the thickness of the α-layer is of the order of those used in model-Z.     

Theory of azimuthally small-scale hydromagnetic waves in the axisymmetric magnetosphere with finite plasma pressure

The structure of monochromatic MHD-waves with large azimuthal wave number m 1 in a two-dimensional model of the magnetosphere has been investigated. A joint action of the field line curvature, finite plasma pressure, and transversal equilibrium current leads to the phenomenon that waves, standing along the field lines, are travelling across the magnetic shells. The wave propagation region, the transparency region, is bounded by the poloidal magnetic surface on one side and by the resonance surface on the other. In their meaning these surfaces correspond to the usual and singular turning points in the WKB-approximation, respectively. The wave is excited near the poloidal surface and propagates toward the resonance surface where it is totally absorbed due to the ionospheric dissipation. There are two transparency regions in a finite-beta magnetosphere, one of them corresponds to the Alfvén mode and the other to the slow magneto-sound mode.     

Onset of an energy cascade and nonperiodic behaviour in the nonlinear propagation of MHD waves in the solar atmosphere

Abstract

We study the nonlinear stability of MHD waves propagating in a two-dimensional, compressible, highly magnetized, viscous plasma. These waves are driven by a weak, shear body force which could be imposed by large scale internal fluctuations present in the solar atmosphere.

The effects of anisotropic viscosity (leading to a cubic damping) and of the nonlinear coupling of the Alfven and the magnetoacoustic waves are analysed using Galerkin and multiple-scale analysis: the MHD equations are reduced to a set of nonlinear ordinary differential equations which is then suitably truncated to give a model dynamical system, representing the interaction of two complex Galerkin modes.

For propagation oblique to the background magnetic field, analytical integration shows that the low-wavenumber mode is physically unstable. For propagation parallel to the background magnetic field the high-wavenumber wave can undergo saddlenode bifurcations, in way that is similar to the van der Pol oscillator; these bifurcations lead to the appearance of a hysteresis cycle.

A numerical integration of the dynamical system shows that a sequence of Hopf bifurcations takes place as the Reynolds number is increased, up to the onset of nonperiodic behaviour. It also shows that energy can be transferred from the low- wavenumber to the high-wavenumber mode.     

Turning surface behaviour for internal waves subject to general gravitational fields

Abstract

It is shown that the turning surfaces associated with internal waves in a uniformly rotating, density stratified, Boussinesq fluid in the presence of an arbitrary gravitational field are regular points for the governing eigenvalue differential equation. The results are illustrated for two particular examples that have geophysical and astrophysical significance, namely radially directed spherical gravity, and the gravitational field in a rapidly rotating cylinder.     

Thermal Generation of Alfvén Waves in Oscillatory Magnetoconvection: Diffusively Modified Modes

Thermal instabilities in the form of oscillatory magnetoconvection representing diffusively modified Alfvén waves in an electrically-conducting Bénard fluid layer of rigid walls in the presence of a vertical magnetic field are investigated. Emphasis of the article is on the transition from a nearly undamped Alfvén wave to diffusively modified Alfvén waves, and on the effect of physically realisable magnetic field boundary conditions on magnetoconvection. It is found that the extra magnetic dissipation in the magnetic Hartmann boundary layers can enhance oscillatory magnetoconvection in the form of strongly modified Alfvén waves. Oscillatory magnetoconvection produced solely by the Alfvén wave mechanism can be the most unstable mode even in the presence of a strong viscous effect. This article also represents the first study on the effect of an electrically conducting wall on magnetoconvection which is associated with a nonlinear eigenvalue problem. We find that the electrically perfectly conducting condition does not yield a good approximation for magnetoconvection with an electrically highly conducting wall. The size of oscillation frequency with an electrically highly conducting wall can be more than a factor of 2 larger than that obtained using the perfectly conducting condition.     

The generation of baroclinic rossby waves by meridional oscillations of a zonal wind stress

Abstract

This paper investigates the generation of linear baroclinic Rossby waves by meridional oscillations of a climatological zonal wind stress in a reduced gravity ocean bounded by an eastern coastline. Using a power series technique an analytical solution is derived for the interfacial displacement. It is found that for a given period of oscillation of the zonal winds, a finite number of propagating Rossby waves will be generated with frequencies equal to a harmonic of the forcing frequency. The number of propagating modes increases with increasing period of the wind stress. In addition to the propagating waves the complete solution for the interfacial displacement consists of a rapidly convergent infinite sum of evanescent terms. The displacement field is calculated for atmospheric forcing parameters typical of those found at mid-latitudes. Further, it is shown that a near resonant response can be generated using atmospheric parameter values typical of those found over the North Pacific.     

The existence of internal solitary waves in a two-fluid system near the KdV limit

Abstract

Two fluid layers of constant density lying one over the other on top of a rigid horizontal lower boundary with either a free upper surface or a rigid upper boundary can support solitary waves. The existence of a unique branch of such waves emanating from the horizontal flow at a critical speed U _? is demonstrated in both cases by use of the Nash—Moser implicit function theorem. These results complement the global results of Amick and Turner (1986) and are analogous to the work of Friedrichs and Hyers (1954) and Beale (1977) for surface waves. It is also noted that the most obvious variational principle which characterizes these waves as constrained extremals (Benjamin, 1984) is of indefinite type, having a Hessian with infinitely many positive and infinitely many negative eigenvalues.     

Experimental results on the tidal resonance effect of the liquid core

Abstract

Molodenskii's theory on the resonance effect of the liquid core predicts anomalous amplitudes in the diurnal spectrum for earth tide registrations of gravity and tilt. A two years recording of an Askania gravimeter at Kiel University has been analysed using three different numerical methods: harmonic analysis (least squares method), gliding harmonic analysis, and Fourier spectral analysis. Because of difficulties in resolving tidal waves near the resonance frequency, efforts were made towards improving the Fourier spectral analysis by successive subtraction of high amplitudes in the Fourier spectrum. The resonance of the liquid core has been observed with a high degree of confidence thereby supporting Molodenskii's model calculations.     

Convective dynamos with intermediate and strong fields

Abstract

The weak-field Benard-type dynamo treated by Soward is considered here at higher levels of the induced magnetic field. Two sources of instability are found to occur in the intermediate field regime M ～ T ^1/12, where M and T are the Hartmann and Taylor numbers. On the time scale of magnetic diffusion, solutions may blow up in finite time owing to destabilization of the convection by the magnetic field. On a faster time scale a dynamic instability related to MAC-wave instability can also occur. It is therefore concluded that the asymptotic structure of this dynamo is unstable to virtual increases in the magnetic field energy.

In an attempt to model stabilization of the dynamo in a strong-field regime we consider two approximations. In the first, a truncated expansion in three-dimensional plane waves is studied numerically. A second approach utilizes an ad hoc set of ordinary differential equations which contains many of the features of convection dynamos at all field energies. Both of these models exhibit temporal intermittency of the dynamo effect.     

Construction of fast dynamos using unsteady flows and maps in three dimensions

Abstract

Unsteady fast dynamos are constructed using a sequence of rapid movements separated by periods of diffusion of the magnetic field. Motivated by the physical mechanism described by Ze'dovich and by Soward, we examine the effect of single-mode Beltrami waves applied sequentially, and show that they can be approximated by a simple “stretch-fold-shear” (SFS) map of the unit cube onto itself. In the SFS map, the field points in a fixed direction and diffusion is easily computed. The numerical results indicate that fast dynamo action occurs for sufficiently large shear, and that the process is primarily a coherent feature of the larger magnetic scales. Similar results are obtained for smooth flows. Some preliminary analysis of the SFS map using a decomposition method is described.     

Periodic and aperiodic dynamo waves

Abstract

In order to show that aperiodic magnetic cycles, with Maunder minima, can occur naturally in nonlinear hydromagnetic dynamos, we have investigated a simple nonlinear model of an oscillatory stellar dynamo. The parametrized mean field equations in plane geometry have a Hopf bifurcation when the dynamo number D=1, leading to Parker's dynamo waves. Including the nonlinear interaction between the magnetic field and the velocity shear results in a system of seven coupled nonlinear differential equations. For D>1 there is an exact nonlinear solution, corresponding to periodic dynamo waves. In the regime described by a fifth order system of equations this solution remains stable for all D and the velocity shear is progressively reduced by the Lorentz force. In a regime described by a sixth order system, the solution becomes unstable and successive transitions lead to chaotic behaviour. Oscillations are aperiodic and modulated to give episodes of reduced activity.     

A steady state of the disc dynamo

Abstract

We discuss the steady states of the αω-dynamo in a thin disc which arise due to α-quenching. Two asymptotic regimes are considered, one for the dynamo numberD near the generation thresholdD ₀, and the other for |D| ? 1. Asymptotic solutions for |D—D ₀| ? |D ₀| have a rather universal character provided only that the bifurcation is supercritical. For |D| ? 1 the asymptotic solution crucially depends on whether or not the mean helicity α, as a function ofB, has a positive root (hereB is the mean magnetic field). When such a root exists, the field value in the major portion of the disc is O(l), while near the disc surface thin boundary layers appear where the field rapidly decreases to zero (if the disc is surrounded by vacuum). Otherwise, when α = O(|B|^?s) for |B| → ∞, we demonstrate that |B| = O(|D|^1/s ) and the solution is free of boundary layers. The results obtained here admit direct comparison with observations of magnetic fields in spiral galaxies, so that an appropriate model of nonlinear galactic dynamos hopefully could be specified.