EarthRef.org Reference Database (ERR) -- Bergman & Fearn 1994

Convection occurs in the ''mushy'' zone at the solid/liquid boundary of a non-eutectic melt freezing from below when the Rayleigh number Ram exceeds some critical value Ramc. Nonlinear processes can then lead to the rising fluid being concentrated in narrow ''chimneys.'' The focusing occurs because a fluid parcel rising in the mushy zone finds itself undersaturated in the solvent, resulting in encompassed dendrites remelting, and porosity, and hence permeability, increasing. This reduces the Darcy friction and increases the flow in an upwelling region, leading eventually to a solid-free chimney. A larger downwelling region of higher solid fraction becomes necessary to feed the chimney. Here, we are interested in applying these ideas to the Earth's core. Many discussions of compositional convection in the Earth's core tacitly assume that it will be in the form of chimney convection rising from the mushy zone at the inner-outer core boundary. We question this assumption here because the Chandrasekhar number Qm of flow through the dendrites may be large. Magnetic drag then supplants Darcy friction as the primary retarding force. Because the magnetic drag is independent of permeability and lengthscale, and thus porosity, the focusing mechanism that results in chimneys no longer operates. Although Ram is likely to remain highly super-critical, the nonlinear convection may assume a form different from chimney convection, in spite of lateral variations in permeability. Convection occurs in the ''mushy'' zone at the solid/liquid boundary of a non-eutectic melt freezing from below when the Rayleigh number Ram exceeds some critical value Ramc. Nonlinear processes can then lead to the rising fluid being concentrated in narrow ''chimneys.'' The focusing occurs because a fluid parcel rising in the mushy zone finds itself undersaturated in the solvent, resulting in encompassed dendrites remelting, and porosity, and hence permeability, increasing. This reduces the Darcy friction and increases the flow in an upwelling region, leading eventually to a solid-free chimney. A larger downwelling region of higher solid fraction becomes necessary to feed the chimney. Here, we are interested in applying these ideas to the Earth's core. Many discussions of compositional convection in the Earth's core tacitly assume that it will be in the form of chimney convection rising from the mushy zone at the inner-outer core boundary. We question this assumption here because the Chandrasekhar number Qm of flow through the dendrites may be large. Magnetic drag then supplants Darcy friction as the primary retarding force. Because the magnetic drag is independent of permeability and lengthscale, and thus porosity, the focusing mechanism that results in chimneys no longer operates. Although Ram is likely to remain highly super-critical, the nonlinear convection may assume a form different