Magmons: Solitary Waves Arising in the Buoyant Ascent of Magma by Porous Flow through a Viscously Deformable Matrix

The dynamics of partially molten regions of the Earth's mantle are studied using a combination of theoretical, experimental, and numerical techniques. The physical model is based on experimental observations of partially molten ultramafic rocks and incorporates two elements: buoyancy-driven porous flow of magma through a viscously deformable matrix, and buoyancy-driven circulation of the whole rock. The first element of this model is analogous to buoyancy-driven pipe flow of a liquid through a denser and more viscous wall fluid. Laboratory experiments on this system illustrate the phenomenon of solitary waves. These are waves of larger pipe radius that ascend a uniform pipe of smaller radius. The waves are very nearly conserved in collisions. These, and the corresponding waves of higher porosity that arise in one-dimensional porous flow, are characterized further by analysis and numerical experiments. The full system, incorporating circulation in a multidimensional porous medium, also displays solitary waves governed by the same basic processes as the one-dimensional waves. Analysis and numerical experiments show that the multidimensional waves have a circular or spherical form. A possible natural manifestation of this fluid dynamical phenomenon is in igneous processes. Magmons, as the waves are called in that setting, probably have wavelengths of kilometers and velocities of centimeters per year. Magma ascent in magmons may account for episodicity in igneous emplacement. Also, a magmon can collect and mobilize a small degree of partial melt without disturbing its geochemical signature. In a partially molten region the characteristic wavelength of magmons will always be superimposed on that of large scale variations in porosity.