Equilibrium magnetic field with (solid curves) and shear flow profiles with (dashed curves).
Dependence of the linear growth rate on the flow amplitude for m = 1 mode.
Contour plots of the magnetic flux for undistorted (a) and distorted (b) island structure. The markers X and O stand for the X-point and O-point of the magnetic islands. (a) and (b) .
Evolution of the potential energy for , , and .
Linear growth rates (a) and real frequencies (b) of the eigen modes as a function of the flow amplitude. Zoomed views for the region are shown in (c) and (d). The parameters are the same as in Fig. 2 . The dotted-dashed lines are straight lines for reference.
Contour plots of the island structures (upper panel) and the perturbed magnetic fluxes (middle panel) as well as the eigen functions of m = 1 mode (lower panel) for the two DTMs corresponding to the cases A–E marked in Fig. 5 for different flow amplitudes.
Radial profiles of the phase angle of perturbed magnetic flux for different flow amplitudes , , and . (a) even DTM, (b) odd DTM. The dotted-dashed lines are straight lines for reference.
Difference between the phase angles at two sides out of the current sheets, , as a function of flow amplitude.
Growth rates as a function of for the even and odd DTMs with equilibrium flow profile and .
Time evolution of the potential energy of the DTMs with different initial perturbations: (a) only the eigen function with or , (b)mixed eigen function of the both. The analytical expression of Eq. (14) is also plotted for comparison.
Radial structures of the perturbed currents ( ) and the Alfvén resonance condition of the DTM with negative frequency for different flow amplitudes (a) , (b) , and (c) .
Plasma flow patterns (arrows) overlapped by the island structure (curves) for different flow amplitudes (a) , (b) , and (c) corresponding to the cases in Fig. 11 .
Real part of the instability parameter, , for the STM-type DTM as a function of flow amplitude in the region .
Growth rates (a) and real frequencies (b) of the DTMs with the equilibrium flow profile .
Comparison of the growth rates of the KHI for different models. Case 1: the ideal piecewise continuous profile of shear flow (solid). Case 2: asymptotic limit ( ) of Eq. (5) with constant B 0 (long dashed). Case 3: with double current sheet configuration (dotted-dashed). Case 4: with constant B 0 (short dashed).
Eigen functions of the KHIs under double current sheet configuration (case 3, thick curves) and constant magnetic field (case 4, thin curves) with .
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