319 research outputs found
Kelvin-Helmholtz instability in coronal magnetic flux tubes due to azimuthal shear flows
Transverse oscillations of coronal loops are often observed and have been
theoretically interpreted as kink magnetohydrodynamic (MHD) modes. Numerical
simulations by Terradas et al. (2008, ApJ 687, L115) suggest that shear flows
generated at the loop boundary during kink oscillations could give rise to a
Kelvin-Helmholtz instability (KHI). Here, we investigate the linear stage of
the KHI in a cylindrical magnetic flux tube in the presence of azimuthal shear
motions. We consider the basic, linearized MHD equations in the beta = 0
approximation, and apply them to a straight and homogeneous cylindrical flux
tube model embedded in a coronal environment. Azimuthal shear flows with a
sharp jump of the velocity at the cylinder boundary are included in the model.
We obtain an analytical expression for the dispersion relation of the unstable
MHD modes supported by the configuration, and compute analytical approximations
of the critical velocity shear and the KHI growth rate in the thin tube limit.
A parametric study of the KHI growth rates is performed by numerically solving
the full dispersion relation. We find that fluting-like modes can develop a KHI
in time-scales comparable to the period of kink oscillations of the flux tube.
The KHI growth rates increase with the value of the azimuthal wavenumber and
decrease with the longitudinal wavenumber. However, the presence of a small
azimuthal component of the magnetic field can suppress the KHI. Azimuthal
motions related to kink oscillations of untwisted coronal loops may trigger a
KHI, but this phenomenon has not been observed to date. We propose that the
azimuthal component of the magnetic field is responsible for suppressing the
KHI in a stable coronal loop. The required twist is small enough to prevent the
development of the pinch instability.Comment: Submitted in Ap
Nonlinear Instability of kink oscillations due to shear motions
First results from a high-resolution three-dimensional nonlinear numerical
study of the kink oscillation are presented. We show in detail the development
of a shear instability in an untwisted line-tied magnetic flux tube. The
instability produces significant deformations of the tube boundary. An extended
transition layer may naturally evolve as a result of the shear instability at a
sharp transition between the flux tube and the external medium. We also discuss
the possible effects of the instability on the process of resonant absorption
when an inhomogeneous layer is included in the model. One of the implications
of these results is that the azimuthal component of the magnetic field of a
stable flux tube in the solar corona, needed to prevent the shear instability,
is probably constrained to be in a very specific range
Three-Dimensional Propagation of Magnetohydrodynamic Waves in Solar Coronal Arcades
We numerically investigate the excitation and temporal evolution of
oscillations in a two-dimensional coronal arcade by including the
three-dimensional propagation of perturbations. The time evolution of
impulsively generated perturbations is studied by solving the linear, ideal
magnetohydrodynamic (MHD) equations in the zero-beta approximation. As we
neglect gas pressure the slow mode is absent and therefore only coupled MHD
fast and Alfven modes remain. Two types of numerical experiments are performed.
First, the resonant wave energy transfer between a fast normal mode of the
system and local Alfven waves is analyzed. It is seen how, because of resonant
coupling, the fast wave with global character transfers its energy to Alfvenic
oscillations localized around a particular magnetic surface within the arcade,
thus producing the damping of the initial fast MHD mode. Second, the time
evolution of a localized impulsive excitation, trying to mimic a nearby coronal
disturbance, is considered. In this case, the generated fast wavefront leaves
its energy on several magnetic surfaces within the arcade. The system is
therefore able to trap energy in the form of Alfvenic oscillations, even in the
absence of a density enhancement such as that of a coronal loop. These local
oscillations are subsequently phase-mixed to smaller spatial scales. The amount
of wave energy trapped by the system via wave energy conversion strongly
depends on the wavelength of perturbations in the perpendicular direction, but
is almost independent from the ratio of the magnetic to density scale heights.Comment: 27 pages, 11 figure
The effect of the solar corona on the attenuation of small-amplitude prominence oscillations. I. Longitudinal magnetic field
Context. One of the typical features shown by observations of solar
prominence oscillations is that they are damped in time and that the values of
the damping times are usually between one and three times the corresponding
oscillatory period. However, the mechanism responsible for the attenuation is
still not well-known. Aims. Thermal conduction, optically thin or thick
radiation and heating are taken into account in the energy equation, and their
role on the attenuation of prominence oscillations is evaluated. Methods. The
dispersion relation for linear non-adiabatic magnetoacoustic waves is derived
considering an equilibrium made of a prominence plasma slab embedded in an
unbounded corona. The magnetic field is orientated along the direction parallel
to the slab axis and has the same strength in all regions. By solving the
dispersion relation for a fixed wavenumber, a complex oscillatory frequency is
obtained, and the period and the damping time are computed. Results. The effect
of conduction and radiation losses is different for each magnetoacoustic mode
and depends on the wavenumber. In the observed range of wavelengths the
internal slow mode is attenuated by radiation from the prominence plasma, the
fast mode by the combination of prominence radiation and coronal conduction and
the external slow mode by coronal conduction. The consideration of the external
corona is of paramount importance in the case of the fast and external slow
modes, whereas it does not affect the internal slow modes at all. Conclusions.
Non-adiabatic effects are efficient damping mechanisms for magnetoacoustic
modes, and the values of the obtained damping times are compatible with those
observed.Comment: Accepted in A&
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