Nonlinear wave-mechanical effects in Korteweg fluid magma transport

Institute of Systems Science, Durban University of Technology - P.O. Box 1334, Durban 4000, South Africa

Received: 20 February 2018
Accepted: 29 May 2018

Abstract

Statistical mechanics arguments and Madelung hydrodynamical presentation are applied to the transport of magma in volcanic conduits. An effective wave equation with logarithmic nonlinearity becomes apparent in systems of this kind, which describes the flow of a two-phase barotropic Korteweg fluid with capillarity, and allows multiple eigensolutions thus leading to wave-mechanical effects. We study spontaneous symmetry breaking in the erupting lava which flows up the conduit, so that fluid fragmentation and nucleation of density inhomogeneities occur; therefore, changing temperature can trigger a transition between the “magma-dissolved gas” fluid and magmatic foam phases. This phase structure is studied by both analytical and numerical methods. In the fluid phase, cell-like inhomogeneities occur which are described by solitary wave solutions with a Gaussian density profile; we derive the many-body interaction potential for these inhomogeneities. For the foam phase, we demonstrate the existence of topological kink solitons which describe bubble-type inhomogeneities; their stability is ensured by the conservation of a topological charge.