MHD Wave Modes Resolved in Fine-Scale Chromospheric Magnetic Structures

Due to its complex and dynamic fine-scale structure, the chromosphere is a particularly challenging region of the Sun's atmosphere to understand. It is now widely accepted that to model chromospheric dynamics, even on a magnetohydrodynamic (MHD) scale, while also calculating spectral line emission, one must realistically include the effects of partial ionization and radiative transfer in a multi-fluid plasma under non-LTE conditions. Accurate quantification of MHD wave energetics must befounded on a precise identification of the actual wave mode being observed. This chapter focuses on MHD kink-mode identification, MHD sausage mode identification, and MHD torsional Alfvén wave identification. It then reviews progress in determining more accurate energy flux estimations of specific MHD wave modes observed in the chromosphere. The chapter finally examines how the discovery of these MHD wave modes has helped us advance the field of chromosphericmagnetoseismology.

Ultra-High-Resolution Observations of MHD Waves in Photospheric Magnetic Structures

This chapter reviews the recent observations of waves and oscillations manifesting in fine-scale magnetic structures in the solar photosphere, which are often interpreted as the "building blocks' of the magnetic Sun. The authors found, through phase relationships between the various waveforms, that small-scale magnetic bright points (MBPs) in the photosphere demonstrated signatures of specific magnetoacoustic waves, in particular the sausage and kink modes. Modern magnetohydrodynamic (MHD) simulations of the lower solar atmosphere clearly show how torsional motions can easily be induced in magnetic elements in the photosphere through the processes of vortical motions and/or buffeting by neighboring granules. The authors detected significant power associated with high-frequency horizontal motions, and suggested that these cases may be especially important in the creation of a turbulent environment that efficiently promotes Alfvén wave dissipation.

Inheritance of ductile and brittle structures in the development of large rock slope instabilities: Examples from western Norway

The high density of slope failures in western Norway is due to the steep relief and to the concentration of various structures that followed protracted ductile and brittle tectonics. On the 72 investigated rock slope instabilities, 13 were developed in soft weathered mafic and phyllitic allochthons. Only the intrinsic weakness of such rocks increases the susceptibility to gravitational deformation. In contrast, the gravitational structures in the hard gneisses reactivate prominent ductile or/and brittle fabrics. At 30 rockslides along cataclinal slopes, weak mafic layers of foliation are reactivated as basal planes. Slope-parallel steep foliation forms back-cracks of unstable columns. Folds are specifically present in the Storfjord area, together with a clustering of potential slope failures. Folding increases the probability of having favourably orientated planes with respect to the gravitational forces and the slope. High water pressure is believed to seasonally build up along the shallow-dipping Caledonian detachments and may contribute to destabilization of the rock slope upwards. Regional cataclastic faults localized the gravitational structures at 45 sites. The volume of the slope instabilities tends to increase with the amount of reactivated prominent structures and the spacing of the latter controls the size of instabilities.

Modélisation MHD tridimensionnelle de tubes de flux coronaux utilisant l'assimilation des donnés 4D-VAR

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Ferromagnetic instabilities in neutron matter at finite temperature with the Skyrme interaction

The properties of spin-polarized neutron matter are studied at both zero and finite temperature using Skyrme-type interactions. It is shown that the critical density at which ferromagnetism takes place decreases with temperature. This unexpected behavior is associated to an anomalous behavior of the entropy that becomes larger for the polarized phase than for the unpolarized one above a certain critical density. This fact is a consequence of the dependence of the entropy on the effective mass of the neutrons with different third spin component. A new constraint on the parameters of the effective Skyrme force is derived if this behavior is to be avoided.

On instabilities in data assimilation algorithms

Data assimilation algorithms are a crucial part of operational systems in numerical weather prediction, hydrology and climate science, but are also important for dynamical reconstruction in medical applications and quality control for manufacturing processes. Usually, a variety of diverse measurement data are employed to determine the state of the atmosphere or to a wider system including land and oceans. Modern data assimilation systems use more and more remote sensing data, in particular radiances measured by satellites, radar data and integrated water vapor measurements via GPS/GNSS signals. The inversion of some of these measurements are ill-posed in the classical sense, i.e. the inverse of the operator H which maps the state onto the data is unbounded. In this case, the use of such data can lead to significant instabilities of data assimilation algorithms. The goal of this work is to provide a rigorous mathematical analysis of the instability of well-known data assimilation methods. Here, we will restrict our attention to particular linear systems, in which the instability can be explicitly analyzed. We investigate the three-dimensional variational assimilation and four-dimensional variational assimilation. A theory for the instability is developed using the classical theory of ill-posed problems in a Banach space framework. Further, we demonstrate by numerical examples that instabilities can and will occur, including an example from dynamic magnetic tomography.

Coupled Kelvin-wave and mirage-wave instabilities in semigeostrophic dynamics

A weak instability mode, associated with phase-locked counterpropagating coastal Kelvin waves in horizontal anticyclonic shear, is found in the semigeostrophic (SG) equations for stratified flow in a channel. This SG instability mode approximates a similar mode found in the Euler equations in the limit in which particle-trajectory slopes are much smaller than f/N, where f is the Coriolis frequency and N > f the buoyancy frequency. Though weak under normal parameter conditions, this instability mode is of theoretical interest because its existence accounts for the failure of an Arnol’d-type stability theorem for the SG equations. In the opposite limit, in which the particle motion is purely vertical, the Euler equations allow only buoyancy oscillations with no horizontal coupling. The SG equations, on the other hand, allow a physically spurious coastal “mirage wave,” so called because its velocity field vanishes despite a nonvanishing disturbance pressure field. Counterpropagating pairs of these waves can phase-lock to form a spurious “mirage-wave instability.” Closer examination shows that the mirage wave arises from failure of the SG approximations to be self-consistent for trajectory slopes f/N.

Rigorous bounds on the nonlinear saturation of instabilities to parallel shear flows

A novel method is presented for obtaining rigorous upper bounds on the finite-amplitude growth of instabilities to parallel shear flows on the beta-plane. The method relies on the existence of finite-amplitude Liapunov (normed) stability theorems, due to Arnol'd, which are nonlinear generalizations of the classical stability theorems of Rayleigh and Fjørtoft. Briefly, the idea is to use the finite-amplitude stability theorems to constrain the evolution of unstable flows in terms of their proximity to a stable flow. Two classes of general bounds are derived, and various examples are considered. It is also shown that, for a certain kind of forced-dissipative problem with dissipation proportional to vorticity, the finite-amplitude stability theorems (which were originally derived for inviscid, unforced flow) remain valid (though they are no longer strictly Liapunov); the saturation bounds therefore continue to hold under these conditions.

Nonlinear stability and the saturation of instabilities to axisymmetric vortices

Nonlinear stability theorems are presented for axisymmetric vortices under the restriction that the disturbance is independent of either the azimuthal or the axial coordinate. These stability theorems are then used, in both cases, to derive rigorous upper bounds on the saturation amplitudes of instabilities. Explicit examples of such bounds are worked out for some canonical profiles. The results establish a minimum order for the dependence of saturation amplitude on supercriticality, and are thereby suggestive as to the nature of the bifurcation at the stability threshold.

Ideal internal kink modes in a differentially rotating cylindrical plasma

The Velikhov effect leading to magnetorotational instability (MRI) is incorporated into the theory of ideal internal kink modes in a differentially rotating cylindrical plasma column. It is shown that this effect can play a stabilizing role for suitably organized plasma rotation profiles, leading to suppression of MHD (magnetohydrodynamic) instabilities in magnetic confinement systems. The role of this effect in the problem of the Suydam and the m = 1 internal kink modes is elucidated, where m is the poloidal mode number.

Contributions to the theory of magnetorotational instability and waves in a rotating plasma

The one-fluid magnetohydrodynamic (MHD) theory of magnetorotational instability (MRI) in an ideal plasma is presented. The theory predicts the possibility of MRI for arbitrary 0, where 0 is the ratio of the plasma pressure to the magnetic field pressure. The kinetic theory of MRI in a collisionless plasma is developed. It is demonstrated that as in the ideal MHD, MRI can occur in such a plasma for arbitrary P. The mechanism of MRI is discussed; it is shown that the instability appears because of a perturbed parallel electric field. The electrodynamic description of MRI is formulated under the assumption that the dispersion relation is expressed in terms of the permittivity tensor; general properties of this tensor are analyzed. It is shown to be separated into the nonrotational and rotational parts. With this in mind, the first step for incorporation of MRI into the general theory of plasma instabilities is taken. The rotation effects on Alfven waves are considered.

Instabilities in thermal gravity with a cosmological constant

It is shown that in quantum gravity at finite temperature, the effective potential evaluated in the tadpole approximation can have a local minimum below a certain critical temperature. However, when the leading higher order thermal loop corrections are included, one finds that no static solution exists at high temperature. (C) 2008 Elsevier B.V. All rights reserved.

Short-wave instabilities in the Benjamin-Bona-Mahoney-Peregrine equation: theory and numerics

In this paper we discuss the nonlinear propagation of waves of short wavelength in dispersive systems. We propose a family of equations that is likely to describe the asymptotic behaviour of a large class of systems. We then restrict our attention to the analysis of the simplest nonlinear short-wave dynamics given by U-0 xi tau, = U-0 - 3(U-0)(2). We integrate numerically this equation for periodic and non-periodic boundary conditions, and we find that short waves may exist only if the amplitude of the initial profile is not too large.

The application of interpolating MLS approximations to the analysis of MHD flows

The element-free Galerkin method (EFGM) is a very attractive technique for solutions of partial differential equations, since it makes use of nodal point configurations which do not require a mesh. Therefore, it differs from FEM-like approaches by avoiding the need of meshing, a very demanding task for complicated geometry problems. However, the imposition of boundary conditions is not straightforward, since the EFGM is based on moving-least-squares (MLS) approximations which are not necessarily interpolants. This feature requires, for instance, the introduction of modified functionals with additional unknown parameters such as Lagrange multipliers, a serious drawback which leads to poor conditionings of the matrix equations. In this paper, an interpolatory formulation for MLS approximants is presented: it allows the direct introduction of boundary conditions, reducing the processing time and improving the condition numbers. The formulation is applied to the study of two-dimensional magnetohydrodynamic flow problems, and the computed results confirm the accuracy and correctness of the proposed formulation. (C) 2002 Elsevier B.V. All rights reserved.