Can Hall effect trigger Kelvin–Helmholtz instability in sub-Alfvénic flows?

Abstract

In the Hall magnetohydrodynamics, the onset condition of the Kelvin–Helmholtz instability is solely determined by the Hall effect and is independent of the nature of shear flows. In addition, the physical mechanism behind the super- and sub-Alfvénic flows becoming unstable is quite different: the high-frequency right circularly polarized whistler becomes unstable in the super-Alfvénic flows whereas low-frequency, left circularly polarized ion-cyclotron wave becomes unstable in the presence of sub-Alfvénic shear flows. The growth rate of the Kelvin–Helmholtz instability in the super-Alfvénic case is higher than the corresponding ideal magnetohydrodynamic rate. In the sub-Alfvénic case, the Hall effect opens up a new, hitherto inaccessible (to the magnetohydrodynamics) channel through which the partially or fully ionized fluid can become Kelvin–Helmholtz unstable. The instability growth rate in this case is smaller than the super-Alfvénic case owing to the smaller free shear energy content of the flow. When the Hall term is somewhat smaller than the advection term in the induction equation, the Hall effect is also responsible for the appearance of a new overstable mode whose growth rate is smaller than the purely growing Kelvin–Helmholtz mode. On the other hand, when the Hall diffusion dominates the advection term, the growth rate of the instability depends only on the Alfvén –Mach number and is independent of the Hall diffusion coefficient. Further, the growth rate in this case linearly increases with the Alfvén frequency with smaller slope for sub-Alfvénic flows.