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Numerically computed logarithm of the growth rate in K space for (a) α + = 1/11 and M A = 0.02 and (b) α + = 2/5 and M A = 0.02. In each panel the green dashed line marks the critical wavenumber for the growth of the KH instability in the asymptotic limit. The solid red line give the fastest growing parametric mode in the asymptotic limit, with the dashed red lines marking the band of approximate resonance. The vertical dashed blue lines show the position of K x,KINK and the horizontal dashed blue lines show the position of K y,D. The top right quadrant, which is most relevant for instability in a solar setting, is dominated by parametric modes.

Numerically computed logarithm of the growth rate in K space for (a) α + = 1/11 and M A = 0.02 and (b) α + = 2/5 and M A = 0.02. In each panel the green dashed line marks the critical wavenumber for the growth of the KH instability in the asymptotic limit. The solid red line give the fastest growing parametric mode in the asymptotic limit, with the dashed red lines marking the band of approximate resonance. The vertical dashed blue lines show the position of K x,KINK and the horizontal dashed blue lines show the position of K y,D. The top right quadrant, which is most relevant for instability in a solar setting, is dominated by parametric modes.

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The Kelvin-Helmholtz instability has been proposed as a mechanism to extract energy from magnetohydrodynamic (MHD) kink waves in flux tubes, and to drive dissipation of this wave energy through turbulence. It is therefore a potentially important process in heating the solar corona. However, it is unclear how the instability is influenced by the osc...

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Context 1
... an instability, either KH or parametric, with Fig. (4) the growth rate is in the range σ = |iω| ∼ 1 to 10 × ω 0 . Taking a characteristic oscillation period of a kink wave in the corona to be 300 s, then the time scale for the instability is approximately 30 to 300 s. Note that these parametric modes are associated with positions in K-space above the dashed green lines in Fig. (4). For ...
Context 2
... or parametric, with Fig. (4) the growth rate is in the range σ = |iω| ∼ 1 to 10 × ω 0 . Taking a characteristic oscillation period of a kink wave in the corona to be 300 s, then the time scale for the instability is approximately 30 to 300 s. Note that these parametric modes are associated with positions in K-space above the dashed green lines in Fig. (4). For perturbations below that line (i.e. regions that would be stable for a non-oscillatory shear flow) the growth rate will be σ ≤ ω 0 , and so these perturbations can grow (with high wave number along the magnetic field) at time scales longer than 300 s and as such can still occur on dynamically important times scales. Prominence ...
Context 3
... an instability, either KH or parametric, with Fig. (4) the growth rate is in the range σ = |iω| ∼ 1 to 10 × ω 0 . Taking a characteristic oscillation period of a kink wave in the corona to be 300 s, then the time scale for the instability is approximately 30 to 300 s. Note that these parametric modes are associated with positions in K-space above the dashed green lines in Fig. (4). For ...
Context 4
... or parametric, with Fig. (4) the growth rate is in the range σ = |iω| ∼ 1 to 10 × ω 0 . Taking a characteristic oscillation period of a kink wave in the corona to be 300 s, then the time scale for the instability is approximately 30 to 300 s. Note that these parametric modes are associated with positions in K-space above the dashed green lines in Fig. (4). For perturbations below that line (i.e. regions that would be stable for a non-oscillatory shear flow) the growth rate will be σ ≤ ω 0 , and so these perturbations can grow (with high wave number along the magnetic field) at time scales longer than 300 s and as such can still occur on dy- namically important times scales. Prominence ...

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Article
Full-text available
The Kelvin–Helmholtz instability has been proposed as a mechanism to extract energy from magnetohydrodynamic (MHD) kink waves in flux tubes, and to drive dissipation of this wave energy through turbulence. It is therefore a potentially important process in heating the solar corona. However, it is unclear how the instability is influenced by the osc...