  Solar wind plasma is supposed to be structured in magnetic flux tubes carried
from the solar surface. Tangential velocity discontinuity near the boundaries
of individual tubes may result in Kelvin-Helmholtz instability, which may
contribute into the solar wind turbulence. While the axial magnetic field may
stabilize the instability, a small twist in the magnetic field may allow to
sub-Alfvenic motions to be unstable. We aim to study the Kelvin-Helmholtz
instability of twisted magnetic flux tube in the solar wind with different
configurations of external magnetic field. We use magnetohydrodynamic equations
in the cylindrical geometry and derive the dispersion equations governing the
dynamics of twisted magnetic flux tube moving along its axis in the cases of
untwisted and twisted external fields. Then we solve the dispersion equations
analytically and numerically and found thresholds for Kelvin-Helmholtz
instability in both cases of external field. Both analytical and numerical
solutions show that the Kelvin-Helmholtz instability is suppressed in the
twisted tube by external axial magnetic field for sub-Alfvenic motions.
However, even small twist in the external magnetic field allows the
Kelvin-Helmholtz instability to be developed for any sub-Alfvenic motions. The
unstable harmonics correspond to vortices with high azimuthal mode numbers,
which are carried by the flow. Twisted magnetic flux tubes can be unstable to
Kelvin-Helmholtz instability when they move with small speed relative to main
solar wind stream, then the Kelvin-Helmholtz vortices may significantly
contribute into the solar wind turbulence.
