The dynamics of shear Alfvénic disturbances in the vicinity of two-dimensional magnetic null X-points is studied. The study complements recent work on compressional Alfvénic disturbances near X-points. For disturbances not straddling the separatrix, it is found that the shear Alfvén wave phase mixes rapidly. The damping rate, however, is not as large as [ln (1/η)]–2, as was found for magnetosonic disturbances (η is the resistivity). For low-frequency forced motions straddling the separatrix, sheet currents are formed at the separatrix and the current layer width is found to scale as η1/2. This results in a volumetric ohmic heating rate which also scales as η1/2.
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