The secondary instability initiated by the three-dimensional nonlinear evolution of the Kelvin-Helmholtz instability

[1] Three-dimensional magnetohydrodynamic simulations of the Kelvin-Helmholtz instability (KHI) are conducted. The resultant three-dimensional evolution of the KHI possesses new signatures that cannot be obtained in two-dimensional evolutions. It is shown that the vortex core is susceptible to the three-dimensional secondary instability. In the early nonlinear stage, after a vortex fully develops, the three-dimensional secondary instability starts growing inside the vortex core. The newly generated components of the magnetic field lead the two-dimensional vortex motion to a highly structured one in the three-dimensional space. To understand its nature, we model a one-dimensional axisymmetric vortex core, where the centrifugal force is balanced with the gradient of the total pressure, and examine the linear response to the perturbed fields. The obtained dispersion relation shows that the eigenmode peaks off the vortex center, the linear growth rate of the unstable mode is order of the rotation period, and it only slightly changes with varying beta while its wavelength gets longer as b decreases. These results suggest that a simple two-dimensional KHI evolution cannot be applied to the magnetospheric boundary and the three-dimensional evolution may owe a wave excitation and thus the energy transport along the closed magnetic field lines to the ionosphere.