  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 Alfvenic flows becoming unstable is quite different: the high frequency
right circularly polarized whistler becomes unstable in the super Alfvenic
flows whereas low frequency, left circularly polarized ion-cyclotron wave
becomes unstable in the presence of sub Alfvenic shear flows. The growth rate
of the Kelvin Helmholtz instability in the super Alfvenic case is higher than
the corresponding ideal magnetohydrodynamic rate. In the sub Alfvenic 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 Alfvenic 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 Alfven
Mach number and is independent of the Hall diffusion coefficient. Further, the
growth rate in this case linearly increase with the Alfven frequency with
smaller slope for sub Alfvenic flows.
