  Observations show various jets in the solar atmosphere with significant
rotational motions, which may undergo instabilities leading to heat ambient
plasma. We study the Kelvin-Helmholtz (KH) instability of twisted and rotating
jets caused by the velocity jumps near the jet surface. We derive a dispersion
equation with appropriate boundary condition for total pressure (including
centrifugal force of tube rotation), which governs the dynamics of
incompressible jets. Then, we obtain analytical instability criteria of
Kelvin-Helmholtz instability in various cases, which were verified by numerical
solutions to the dispersion equation. We find that twisted and rotating jets
are unstable to KH instability when the kinetic energy of rotation is more than
the magnetic energy of the twist. Our analysis shows that the azimuthal
magnetic field of 1-5 G can stabilize observed rotations in
spicule/macrospicules and X-ray/EUV jets. On the other hand, non-twisted jets
are always unstable to KH instability. In this case, the instability growth
time is several seconds for spicule/macrospicules and few minutes (or less) for
EUV/X-ray jets. We also find that standing kink and torsional Alfven waves are
always unstable near the antinodes due to the jump of azimuthal velocity at the
surface, while the propagating waves are generally stable. KH vortices may lead
to enhanced turbulence development and heating of surrounding plasma, therefore
rotating jets may provide energy for chromospheric and coronal heating.
