  Over past ten years a variety of jet-like phenomena were detected in the
solar atmosphere, including plasma ejections over a range of coronal
temperatures being observed as extreme ultraviolet (EUV) and X-ray jets. We
study the possibility for the development of Kelvin--Helmholtz (KH) instability
of transverse magnetohydrodynamic (MHD) waves traveling along an EUV jet
situated on the west side of NOAA AR 10938 and observed by three instruments on
board Hinode on 2007 January 15/16 (Chifor et al., Astron. Astrophys.481, L57
(2008)). The jet was observed around LogT_e = 6.2 with up-flow velocities
exceeded 150 km/s. Using Fe XII lambda186 and lambda195 line ratios, the
measured densities were found to be above LogN_e = 11. We have modeled that EUV
jet as a vertically moving magnetic flux tube (untwisted and weakly twisted)
and have studied the propagation characteristics of the kink (m = 1) mode and
the higher m modes with azimuthal mode numbers m = 2, 3, 4. It turns out that
all these MHD waves can become unstable at flow velocities in the range of
112--114.8 km/s. The lowest critical jet velocity of 112 km/s is obtained when
modeling the jet as compressible plasma contained in an untwisted magnetic flux
tube. We have compared two analytically found criteria for predicting the
threshold Alfven Mach number for the onset of KH instability and have concluded
that one of them yields reliable values for the critical Alfven Mach number.
Our study of the nature of stable and unstable MHD modes propagating on the jet
shows that in a stable regime all the modes are pure surface waves, while the
unstable kink (m = 1) mode in untwisted compressible plasma flux tube becomes a
leaky wave. In the limit of incompressible media (for the jet and its
environment) all unstable modes are non-leaky surface waves.
