Volcanic eruptions: Initial state of magma melt pulse unloading

In this paper we perform a linear stability analysis of the equilibrium solution of a suitable Korteweg model for a two-phase fluid modeling a magma transport in a volcanic conduit. By perturbing the fluid at rest and applying the principle of exchange of stabilities, we prove that at the onset of instability, a stationary cellular convection of bubbles prevails. This behavior could be a reasonable description of the transition from the two-phase system magma-dissolved gas in the chamber to the rising foam in the conduit, due to rapid decompression at the initial stage of a volcano's eruption. We analyze the disturbances in normal modes and show that the dimension of the cells, given by a suitable critical value of the wavelength, corresponds, consistently with the model, to the width of the Gaussian-shaped solitary wave solution found in the dynamical case. The implication of the model is to furnish the threshold value of the perturbations normal mode in order to trigger magma fragmentation, and as a consequence, we obtain the dimension value of the early cells of bubbles at the conduit's base. Copyright (C) EPLA, 2012