An axisymmetric model of the Mush-Chimney system

We develop a model of the mush-chimney system based on the assumption that the order of magnitude of the vertical velocity component in the chimney is much greater than the speed of upward advance of the mush, and making use of the fact that the radius of chimney is much less than the (dimensionless) thickness of the mush. We determine the fluid flow structure in the chimney by utilizing the knowledge of the mass fraction of light constituent, the vertical velocity component, and the pressure that are obtained from the mush. We find a relation between a parameter measuring the ratio of viscous and buoyancy forces in the chimney and the vertical velocity component on the top of the mush, and estimate numerically the value of this velocity.