Resonant absorption of standing MHD waves in coronal loops in the absence of directional symmetry: the effect of weak plasma flow

The oscillation properties of standing magnetohydrodynamic waves in coronal loops has been investigated. A coronal loop is modelled as a straight cylinder with purely axial magnetic field and field aligned plasma flow. The loop model includes an inhomogeneous transitional layer that causes the wave to be resonantly damped. Our aim is to obtain the solution describing a resonantly damped standing kink wave in a flowing loop with the directional symmetry of the loop being broken due to the presence of plasma flow. In the absence of damping the standing wave is a superposition of two waves propagating in the opposite directions that have the same frequency but different wavenumbers. However, the same approach cannot be used when there is damping because the decrements of the two propagating waves are different. We suggest that in the case of relatively weak flow, as is the case in coronal loops, the effect of flow on the decrements can be neglected. Then the decrements of the two waves are the same and the solution describing the damped standing kink wave is a superposition of two resonantly damped propagating waves.