Growth and saturation of the 
Kelvin–Helmholtz instability with parallel 
and antiparallel magnetic fields

Keppens, Rony; Tóth, G.; Westermann, Rüdiger; Goedbloed, J. P.

doi:10.1017/s0022377898007223

Cited by 128 publications

(151 citation statements)

References 18 publications

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“…For strong initial fields, corresponding to an initial Alfvén number A = 5, we observe in accordance with Keppens et al (1999) a destabilization of the shear layer with respect to the non-magnetic case.…”

Section: Anti-parallel Initial Fieldssupporting

confidence: 85%

“…A magnetic field is known to reduce the growth rate and potentially, i.e., for A < 2, even to suppress the instability (Chandrasekhar 1961;Miura & Pritchett 1982;Keppens et al 1999). However, less is known about the saturation level and the dynamic back-reaction, in particular for weak initial fields.…”

Section: Discussionmentioning

confidence: 99%

“…To demonstrate this we recalculated some of the models studied by Keppens et al (1999) (models grw-n in Table A.1). The growth rates for these models are either given in Keppens et al (1999), or can be obtained from the figures of Miura & Pritchett (1982). The models have a uniform background density ρ 0 = 1, and a uniform background pressure P 0 .…”

Section: Linear Growthmentioning

confidence: 99%

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Local simulations of the magnetized Kelvin-Helmholtz instability in neutron-star mergers

Obergaulinger¹,

Aloy

Müller³

2010

A&A

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Context. Global magnetohydrodynamic simulations show the growth of Kelvin-Helmholtz instabilities at the contact surface of two merging neutron stars. That region has been identified as the site of efficient amplification of magnetic fields. However, these global simulations, due to numerical limitations, were unable to determine the saturation level of the field strength, and thus the possible back-reaction of the magnetic field onto the flow. Aims. We investigate the amplification of initially weak magnetic fields in Kelvin-Helmholtz unstable shear flows, and the backreaction of the field onto the flow. Methods. We use a high-resolution finite-volume ideal MHD code to perform 2D and 3D local simulations of hydromagnetic shear flows, both for idealized systems and simplified models of merger flows. Results. In 2D, the magnetic field is amplified on time scales of less than 0.01 ms until it reaches locally equipartition with the kinetic energy. Subsequently, it saturates due to resistive instabilities that disrupt the Kelvin-Helmholtz unstable vortex and decelerate the shear flow on a secular time scale. We determine scaling laws of the field amplification with the initial field strength and the grid resolution. In 3D, the hydromagnetic mechanism seen in 2D may be dominated by purely hydrodynamic instabilities leading to less filed amplification. We find maximum magnetic fields ∼10 16 G locally, and rms maxima within the box ∼10 15 G. However, due to the fast decay of the shear flow such strong fields exist only for a short period (<0.1 ms). In the saturated state of most models, the magnetic field is mainly oriented parallel to the shear flow for rather strong initial fields, while weaker initial fields tend to lead to a more balanced distribution of the field energy among the components. In all models the flow shows small-scale features. The magnetic field is at most in energetic equipartition with the decaying shear flow. Conclusions. The magnetic field may be amplified efficiently to very high field strengths, the maximum field energy reaching values of the order of the kinetic energy associated with the velocity components transverse to the interface between the two neutron stars. However, the dynamic impact of the field onto the flow is limited to the shear layer, and it may not be adequate to produce outflows, because the time during which the magnetic field stays close to its maximum value is short compared to the time scale for launching an outflow (i.e., a few milliseconds).

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Section: Anti-parallel Initial Fieldssupporting

confidence: 85%

Section: Discussionmentioning

confidence: 99%

Section: Linear Growthmentioning

confidence: 99%

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Local simulations of the magnetized Kelvin-Helmholtz instability in neutron-star mergers

Obergaulinger¹,

Aloy

Müller³

2010

A&A

View full text Add to dashboard Cite

show abstract

“…Depending on the direction of the magnetic field with respect to the shear flow, a magnetic field might (de)stabilize KH instabilities (Miura & Pritchett 1982;Keppens et al 1999). Miura & Pritchett (1982) found that in a sheared magnetohydrodynamical flow in a compressible plasma, modes with kΔ < 2 are unstable, with Δ the scale length of the shear layer and k the wavenumber.…”

Section: Discussionmentioning

confidence: 99%

“…For the transverse case (B 0 ⊥ u 0 ), only the fast magnetosonic mode is destabilized, but if k · B 0 0, the instability contains Alfvén-mode and slow-mode components as well. Keppens et al (1999) studied the case of an initial magnetic field aligned with the shear flow. In the case the initial magnetic field is unidirectional everywhere (uniform case), the growth of KH instabilities is compressed, while a reversed field (i.e.…”

Section: Discussionmentioning

confidence: 99%

The enigmatic nature of the circumstellar envelope and bow shock surrounding Betelgeuse as revealed byHerschel

Decin

Cox

Royer

et al. 2012

A&A

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Context. The interaction between stellar winds and the interstellar medium (ISM) can create complex bow shocks. The photometers on board the Herschel Space Observatory are ideally suited to studying the morphologies of these bow shocks. Aims. We aim to study the circumstellar environment and wind-ISM interaction of the nearest red supergiant, Betelgeuse. Methods. Herschel PACS images at 70, 100, and 160 μm and SPIRE images at 250, 350, and 500 μm were obtained by scanning the region around Betelgeuse. These data were complemented with ultraviolet GALEX data, near-infrared WISE data, and radio 21 cm GALFA-HI data. The observational properties of the bow shock structure were deduced from the data and compared with hydrodynamical simulations. Results. The infrared Herschel images of the environment around Betelgeuse are spectacular, showing the occurrence of multiple arcs at ∼6-7 from the central target and the presence of a linear bar at ∼9 . Remarkably, no large-scale instabilities are seen in the outer arcs and linear bar. The dust temperature in the outer arcs varies between 40 and 140 K, with the linear bar having the same colour temperature as the arcs. The inner envelope shows clear evidence of a non-homogeneous clumpy structure (beyond 15 ), probably related to the giant convection cells of the outer atmosphere. The non-homogeneous distribution of the material even persists until the collision with the ISM. A strong variation in brightness of the inner clumps at a radius of ∼2 suggests a drastic change in mean gas and dust density ∼32 000 yr ago. Using hydrodynamical simulations, we try to explain the observed morphology of the bow shock around Betelgeuse. Conclusions. Different hypotheses, based on observational and theoretical constraints, are formulated to explain the origin of the multiple arcs and the linear bar and the fact that no large-scale instabilities are visible in the bow shock region. We infer that the two main ingredients for explaining these phenomena are a non-homogeneous mass-loss process and the influence of the Galactic magnetic field. The hydrodynamical simulations show that a warm interstellar medium, reflecting a warm neutral or partially ionized medium, or a higher temperature in the shocked wind also prevent the growth of strong instabilities. The linear bar is probably an interstellar structure illuminated by Betelgeuse itself.

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Sodium Ion Dynamics in the Magnetospheric Flanks of Mercury

Aizawa

Delcourt

Terada

2018

Geophysical Research Letters

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We investigate the transport of planetary ions in the magnetospheric flanks of Mercury. In situ measurements from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft show evidences of Kelvin‐Helmholtz instability development in this region of space, due to the velocity shear between the downtail streaming flow of solar wind originating protons in the magnetosheath and the magnetospheric populations. Ions that originate from the planet exosphere and that gain access to this region of space may be transported across the magnetopause along meandering orbits. We examine this transport using single‐particle trajectory calculations in model Magnetohydrodynamics simulations of the Kelvin‐Helmholtz instability. We show that heavy ions of planetary origin such as Na+ may experience prominent nonadiabatic energization as they E × B drift across large‐scale rolled up vortices. This energization is controlled by the characteristics of the electric field burst encountered along the particle path, the net energy change realized corresponding to the maximum E × B drift energy. This nonadiabatic energization also is responsible for prominent scattering of the particles toward the direction perpendicular to the magnetic field.

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Growth and saturation of the Kelvin–Helmholtz instability with parallel and antiparallel magnetic fields

Cited by 128 publications

References 18 publications

Local simulations of the magnetized Kelvin-Helmholtz instability in neutron-star mergers

Local simulations of the magnetized Kelvin-Helmholtz instability in neutron-star mergers

The enigmatic nature of the circumstellar envelope and bow shock surrounding Betelgeuse as revealed byHerschel

Sodium Ion Dynamics in the Magnetospheric Flanks of Mercury

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