The mechanism of volcanic eruptions (a steady state approach)

A theory of a volcanic eruption as a steady magma flow from a magma chamber to the surface is described. Magma is considered as a two-component two-phase medium and magma flow is steady, one-dimensional and isothermal. Mass and momentum exchange between condensed and gaseous phases is assumed to be in equilibrium with nucleation of bubbles as a fast process at small oversaturations. Three basic flow structures in a conduit are recognized and three resulting types of eruption are described. (1) In the discrete gas separation (DGS) flow, melt with discrete gas bubbles erupts. This type includes lava eruptions and Strombolian activity. (2) In the dispersion regime there is continuous eruption of a gas-pyroclastic suspension. Catastrophic explosive eruptions are included in this type. (3) Here a partly destroyed foam is erupted with permeable structure that allows gas escape. Near the surface this structure evolves with an increase in permeability and a decrease in the total porosity. This type corresponds to lava dome extrusions. A criterion dividing DGS flow from the other two regimes is obtained: Di=Uηn1/3a/c0, where U is the magma ascent velocity, η is magma viscosity, n is number of bubble nuclei in a unit mass of magma, a is the solubility coefficient for volatiles in magma and c0 is the volatile content. The boundary between the dispersion regime and the partly destroyed foam regime depends on U, c0 and particle size dp. For the dispersion regime the basic governing parameters are: magma chamber depth H, conduit conductivity σ=b2/η (b is the characteristic cross-dimension of the conduit), and excess pressure in the magma chamber. Instability of the dispersion regime is investigated numerically. The dependence of magma discharge rate on the governing parameters is described as a combination of equilibrium surfaces with cusp catastrophes. Magma chamber depth is a ‘splitting’ parameter in most cusps and controls the existence of unstable magma flow with sharp regime changes. Catastrophic rise of eruption intensity is possible if H<Hcr. The critical chamber depth Hcr depends approximately linearly on c0 and is about 15 km at c0=0.05. Some scenarios of eruption evolution are described in a steady state approximation, and the mechanism of catastrophic explosive eruptions is proposed. The theory is applied to well documented eruptions (Tolbachik, 1975–1976, and Mount St. Helens, 1980). The theory can also describe changes in a volcanic system, such as destruction of the conduit or chamber walls, destruction of the edifice, changes in magma composition, and caldera subsidence due to magma evacuation.