Solitary wave propagation in a fluid conduit within a viscous matrix

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Abstract
Conduits of low‐viscosity, buoyant fluid imbedded in a highly viscous matrix have been used to model the dynamics of magma transport in vertical dikes and within zones of partial melt. The theory predicts that disturbances can propagate along the conduit in the form of large‐amplitude waves. A set of experiments have been made to investigate the behavior of this system. Uniform, vertical conduits of low‐viscosity liquid (dilute aqueous solutions of ethyl alcohol and sucrose) were established in a column of high‐viscosity, high‐density matrix fluid (concentrated sucrose solution). Perturbations were introduced in the form of pulses of conduit liquid. Two classes of travelling disturbances were observed: slowly propagating, periodic wave trains, and fast propagating solitary waves. The slow, periodic waves form during the development of a conduit, behind an ascending diapir. The fast, solitary waves form in response to disturbances introduced into fully developed conduits. Both of these wave types are correctly predicted by the theory. Measurements were made of solitary wave propagation speed versus wave volume in two different conduit liquids over a wide range of background (undisturbed) conduit flux. Satisfactory agreement was found between the measured and the theoretical propagation speeds except in two limits. For very large wave volumes the observed propagation was always faster than expected. This deviation may be due to finite wave slope effects and to departures from Poiseuille flow in the conduit which are not included in the theory. For very thin conduits the observed propagation was generally slower than expected, an effect that can be attributed to mass diffusion between the conduit fluid and the matrix. Overall, our results indicate that the two‐fluid models of magma transport are adequate for describing the behavior of homogeneous, nondiffusive systems.

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