Phase mixing of a three dimensional magnetohydrodynamic pulse

Phase mixing of a three dimensional magnetohydrodynamic (MHD) pulse is studied in the compressive, three-dimensional (without an ignorable coordinate) regime. It is shown that the efficiency of decay of an Alfvénic part of a compressible MHD pulse is related linearly to the degree of localization of the pulse in the homogeneous transverse direction. In the developed stage of phase mixing (for large times), coupling to its compressive part does not alter the power-law decay of an Alfvénic part of a compressible MHD pulse. The same applies to the dependence upon the resistivity of the Alfvénic part of the pulse. All this implies that the dynamics of Alfvén waves can still be qualitatively understood in terms of the previous 2.5D models. Thus, the phase mixing remains a relevant paradigm for the coronal heating applications in the realistic 3D geometry and compressive plasma.