  Transverse oscillations of coronal loops are often observed and have been
theoretically interpreted as kink magnetohydrodynamic (MHD) modes. Numerical
simulations by Terradas et al. (2008, ApJ 687, L115) suggest that shear flows
generated at the loop boundary during kink oscillations could give rise to a
Kelvin-Helmholtz instability (KHI). Here, we investigate the linear stage of
the KHI in a cylindrical magnetic flux tube in the presence of azimuthal shear
motions. We consider the basic, linearized MHD equations in the beta = 0
approximation, and apply them to a straight and homogeneous cylindrical flux
tube model embedded in a coronal environment. Azimuthal shear flows with a
sharp jump of the velocity at the cylinder boundary are included in the model.
We obtain an analytical expression for the dispersion relation of the unstable
MHD modes supported by the configuration, and compute analytical approximations
of the critical velocity shear and the KHI growth rate in the thin tube limit.
A parametric study of the KHI growth rates is performed by numerically solving
the full dispersion relation. We find that fluting-like modes can develop a KHI
in time-scales comparable to the period of kink oscillations of the flux tube.
The KHI growth rates increase with the value of the azimuthal wavenumber and
decrease with the longitudinal wavenumber. However, the presence of a small
azimuthal component of the magnetic field can suppress the KHI. Azimuthal
motions related to kink oscillations of untwisted coronal loops may trigger a
KHI, but this phenomenon has not been observed to date. We propose that the
azimuthal component of the magnetic field is responsible for suppressing the
KHI in a stable coronal loop. The required twist is small enough to prevent the
development of the pinch instability.

Solar and Stellar Astrophysics