Hydrothermal Heat Output from a Convecting, Crystallizing, Replenished Sub-Axial Magma Chamber

Models of high-temperature seafloor hydrothermal systems require that heat is transferred from an underlying magma body across a conducting boundary layer to the hydrothermal system. Because magma is typically at or near its liquidus, heat transfer will result in crystallization and cooling of the magma itself. In previous models of magma cooling and crystallization, solidification was assumed to occur from the top downwards. Consequently, the conducting thermal boundary layer between the hydrothermal system and the magma body rapidly thickened, resulting in a concomitant decay in the hydrothermal heat output and vent temperature. We present a simple time-dependent model of heat transfer between a turbulently convecting crystallizing thin basaltic magma lens and the overlying hydrothermal circulation. Two different crystallization scenarios are considered--crystals in suspension and crystals settling. In either case, we assume that large-scale convection within the magma chamber is homogenous and can be parameterized by its Rayleigh and Nusselt numbers. Also, the effect of crystallinity-dependent magmatic viscosity is considered. The simulation results show that without magma replenishment, the heat output and the hydrothermal temperature decay markedly on a decadal time scale, though decay occurs more slowly for the crystal settling model. The rapid decay of heat transfer from a crystallizing magma lens leads us to consider the effects of magma replenishment. To investigate the heat output from a growing magma chamber, we consider replenishment at both a constant rate at an exponentially declining rate, respectively. Simulation results show that magma heat flux approaches a steady state on decadal time scales, provided the magma volume doubles during a replenishment episode of approximately 20 years duration.