The role of turbulence in explosive magma-water mixing

Juvenile tephra from explosive hydromagmatic eruptions differs from that of dry magmatic eruptions by its fine average grain size and highly variable vesicularity. These characteristics are generally interpreted to indicate that fragmentation, which occurs in dry magmas by bubble growth, is supplemented in hydromagmatic eruptions by quench-fracturing. Quench fragmentation is thought to accelerate heat transfer to water, driving violent steam expansion and increasing eruptive violence. Although some observed hydromagmatic events (e.g. at Surtsey) are indeed violent, others (e.g. quiescent entry of lava into the ocean at Kilauea) are not. We suggest that the violence of magma-water mixing and the grain size and dispersal of hydromagmatic tephras are controlled largely by the turbulence of magma-water mixing. At Surtsey, fine-grained, widely dispersed hydromagmatic tephras were produced primarily during continuous uprush events in which turbulent jets of magma and gas passed through shallow water (Thorarinsson, 1967). During Kilauea's current eruption, videos show generation of fine-grained tephras when turbulent jets of magma, steam, and seawater exited through skylights at the coastline. Turbulence intensity, or the fraction of total jet kinetic energy contained in fine-scale turbulent velocity oscillations, has long been known to control the scale of atomization in spray nozzles and the rate of heat transfer and chemical reaction in fuel injectors. We hypothesize that turbulence intensity also influences grain size and heat transfer rate in magma-water mixing, though such processes are complicated by boiling (in water) and quench fracturing (in magma). We are testing this hypothesis in experiments involving turbulent injection of water (a magma analog) into liquid nitrogen (a water analog). We also suggest that turbulent mixing influences relative proportions of magma and water in hydromagmatic eruptions. Empirical studies indicate that pressure-neutral turbulent jets ingest a mass of ambient fluid equal to the jet fluid by the time the jet has traveled several vent diameters from the orifice. In subaqueous magmatic jets, such a magma-water mass ratio of 1 would result in incomplete water vaporization and wet, sloppy deposits. Magma-water ratios of 3-5, which result in complete vaporization and maximal mechanical energy release, require a water depth that is roughly equal to or less than the vent diameter. In such shallow conditions, water would be entrained only in a narrow boundary layer at the jet margin by the time the jet exited the water body; additional mixing would take place in the atmosphere. These inferences are consistent with observations of continuous-uprush jets at Surtsey, which were surrounded by steam clouds for hundreds of meters above the water surface, but whose cores glowed red at night (Thorarinsson, 1967).