Vertical structure of the head of a cylindrical mantle plume from a model of two-phase flow with melting

Within the mushroom-shaped head of a cylindrical mantle plume melting occurs, the melt segregates from the matrix, and the matrix deforms and spreads laterally. These processes have been studied with a model of two-phase flow with melting. After characteristics of the solution near the axis of symmetry of the plume were found, a set of asymptotic relations for the variables along the symmetry axis was derived from McKenzie's equations for conservation of mass, momentum and energy of a two-phase system. The distribution of porosity along the plume axis and the vertical and radial segregation velocity of the melt in the vicinity of the axis of symmetry were obtained as functions of depth. Our analytic results show that within the head of a cylindrical mantle plume the contribution of the deformation of the matrix to the total non-hydrostatic pressure gradient cannot be neglected, and melt convergence or divergence is controlled by the radial scale of the upward velocity profile at the depth of the beginning of melting.