The decompression of volcanic jets in a crater during explosive volcanic eruptions

During explosive volcanic eruptions, fragmented silicic magma and volatiles exit the vent with pressures typically in the range 10–100 atm and at the speed of sound of the mixture. We show that for magmatic volatile contents no in the range 0.03 < no < 0.06 this has the approximate value (0.95 ± 0.05)(noRT)12, where R is the gas constant and T is the eruption temperature. This speed is nearly independent of the vent pressure and vent radius. By assuming there is negligible mixing with the air, we have modelled the decompression of such jets following eruption from the vent. For free decompression into the atmosphere the velocity of the decompressed jet has the approximate value (1.85 ± 0.05)(noRT)12; this is nearly independent of the eruption rate. For decompression into a crater the process is more complex. At low eruption rates with low vent pressure, the material becomes underpressured as it rises in the crater. A shock then forms in the crater. This recompresses the magma-volatile mixture, which then issues from the crater as a relatively slow subsonic jet at atmospheric pressure. As the eruption rate increases, such shocks move towards the top of the crater, and ultimately cannot form in the crater. Instead, the material issues from the crater as a high-speed supersonic jet. The upward thrust provided by the crater walls on this high-pressure jet then increases the upward velocity above that of a freely decompressing jet. The presence of a crater may therfore cause collapse in relatively small eruptions, whereas it may promote formation of buoyant eruption columns at higher eruption rates. If a crater grows through erosion during an eruption, column collapse will typically ensue even if the mass flux remains steady.