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We have studied the nature of the magnetohydrodynamic (MHD) kink waves in magnetically twisted flux tubes in the presence of plasma flow. To do this, the eigenfunctions of the kink oscillations have been determined using the dispersion relation and the boundary conditions of the tube. Then the components of the magnetic-tension force and the gradient of the pressure force have been obtained to determine the nature of the waves. For the waves with positive azimuthal wavenumber, the magnetic twist and plasma flow have opposite effects on the ratio of restoring forces and the wave has a mixed nature. However, for the waves with negative azimuthal wavenumber the magnetic twist and plasma flow strengthen the effects of each other in increasing the ratio of the magnetic-tension force to the gradient of the pressure force, and they make the nature of the wave more Alfvenic. In the presence of both plasma flow and magnetic twist, in the case of the waves with negative azimuthal wavenumber, for some specific values of the tube parameters, the magnetic-tension force becomes the dominant restoring force both in the radial and azimuthal directions, and the wave can be considered as an Alfven wave in the internal region of the tube. However, in the case of the waves with positive azimuthal wavenumber, the nature of the wave remains mixed under all circumstances.

We consider a pressureless plasma in a thin magnetic-flux tube with a twisted magnetic field. We study the effect of twisted magnetic field on the nature of propagating kink waves. To do this, the restoring forces of oscillations in the linear ideal magnetohydrodynamics (MHD) were obtained. In the presence of a twisted magnetic field, the ratio of the magnetic-tension force to the gradient of the magnetic pressure increases for the mode with negative azimuthal wave number, but it decreases for the mode with positive azimuthal wave number. For the kink mode with positive azimuthal mode number, the ratio of the forces is more affected by the twisted magnetic field in dense loops. For the kink mode with negative azimuthal mode number, the perturbed magnetic pressure is negligible under some conditions. The magnetic twist increases (diminishes) the damping of the kink waves with positive (negative) azimuthal mode number due to resonant absorption. Our conclusion is that introducing a twisted magnetic field breaks the symmetry between the nature of the kink waves with positive and negative azimuthal wave number, and the wave can be a purely Alfvenic wave in the entire loop.

Transverse oscillations of a thin coronal loop in a zero-beta plasma in the presence of a twisted magnetic field and flow are investigated. The dispersion relation is obtained in the limit of weak twist. The twisted magnetic field modifies the phase difference and asymmetry of standing kink oscillations caused by the flow. Using data from observations the kink speed and flow speed have been determined. The presence of the twisted magnetic field can cause underestimation or overestimation of the flow speed in coronal loops depending on the direction of the flow and twisted magnetic field, but a twisted magnetic field has little effect on the estimated value of the kink speed.

The standing quasi modes in a cylindrical incompressible flux tube with magnetic twist that undergoes a radial density structuring is considered in ideal magnetohydrodynamics (MHD). The radial structuring is assumed to be a linearly varying density profile. Using the relevant connection formulae, the dispersion relation for the MHD waves is derived and solved numerically to obtain both the frequencies and damping rates of the fundamental and first-overtone modes of both the kink (m=1) and fluting (m=2,3) waves. It was found that a magnetic twist will increase the frequencies, damping rates and the ratio of the oscillation frequency to the damping rate of these modes. The period ratio P_1/P_2 of the fundamental and its first-overtone surface waves for kink (m=1) and fluting (m=2,3) modes is lower than 2 (the value for an untwisted loop) in the presence of twisted magnetic field. For the kink modes, particularly, the magnetic twists B_{\phi}/B_z=0.0065 and 0.0255 can achieve deviations from 2 of the same order of magnitude as in the observations. Furthermore, for the fundamental kink body waves, the frequency bandwidth increases with increasing the magnetic twist., Comment: 18 pages, 9 figures