Tearing instability, Kelvin‐Helmholtz instability, and magnetic reconnection

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Abstract
Two closely related macroscopic instabilities at the magnetospheric boundary layer are the tearing instability and the Kelvin‐Helmholtz (KH) instability. It has been suggested that a coupling of these modes may lead to larger reconnection rates and thus may explain magnetic flux transfer events at the dayside magnetopause. In the framework of two‐dimensional compressible MHD simulations we study the linear and nonlinear evolution of these instabilities. When the velocity of shear flow is below the Alfvén speed, it is verified that the tearing mode is stabilized by the flow shear and the reconnection rate is reduced. For super‐Alfvénic shear velocities the tearing mode ceases its growth, and the KH instability develops consistently with analytical results. A reasonably low resistivity has no significant influence on the growth of the KH mode. Only for nonlinear amplitudes of the KH mode is reconnection driven by the KH vortices. Thus our results do not confirm a linear interaction between the KH and the tearing mode in terms of vortex‐induced reconnection in two dimensions. Particularly, a reasonably small resistivity does not lower the threshold velocity for the KH instability to a level at which it could be excited for typical magnetopause conditions. Therefore the evolution of the KH mode (and vortex‐induced reconnection) with k vectors aligned with a southward interplanetary magnetic field component appears rather unrealistic for the subsolar magnetopause where the magnetosheath flow is slow.