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Observations show the ubiquitous presence of propagating magnetohydrodynamic(MHD) kink waves in the solar atmosphere. Waves and flows are often observedsimultaneously. Due to plasma inhomogeneity in the perpendicular direction tothe magnetic field, kink waves are spatially damped by resonant absorption. Thepresence of flow may affect the wave spatial damping. Here, we investigate theeffect of longitudinal background flow on the propagation and spatial dampingof resonant kink waves in transversely nonuniform magnetic flux tubes. Wecombine approximate analytical theory with numerical investigation. Theanalytical theory uses the thin tube (TT) and thin boundary (TB) approximationsto obtain expressions for the wavelength and the damping length. Numerically,we verify the previously obtained analytical expressions by means of the fullsolution of the resistive MHD eigenvalue problem beyond the TT and TBapproximations. We find that the backward and forward propagating waves havedifferent wavelengths and are damped on length scales that are inverselyproportional to the frequency as in the static case. However, the factor ofproportionality depends on the characteristics of the flow, so that the dampinglength differs from its static analogue. For slow, sub-Alfvenic flows thebackward propagating wave gets damped on a shorter length scale than in theabsence of flow, while for the forward propagating wave the damping length islonger. The different properties of the waves depending on their direction ofpropagation with respect to the background flow may be detected by theobservations and may be relevant for seismological applications.

Spatial Damping of Propagating Kink Waves Due to Resonant Absorption: Effect of Background Flow