Perspectives in Fluid Mechanics pp 143-207
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Sonic velocities of geologic fluids, such as volcanic magmas and geothermal fluids, can be as low as 1 m/s. Critical velocities in large rivers can be of the order of 1–10 m/s. Because velocities of fluids moving in these settings can exceed these characteristic velocities, sonic and supersonic gas flow and critical and supercritical shallow-water flow can occur. The importance of the low characteristic velocities of geologic fluids has not been widely recognized and, as a result, the importance of supercritical and supersonic flow in geological processes has generally been underestimated. The lateral blast at Mount St. Helens, Washington, propelled a gas heavily laden with dust into the atmosphere. Because of the low sound speed in this gas (about 100 m/s), the flow was internally supersonic. Old Faithful Geyser, Wyoming, is a converging-diverging nozzle in which liquid water refilling the conduit during the recharge cycle changes during eruption into a two-phase liquid-vapor mixture with a very low sound velocity. The high sound speed of liquid water determines the characteristics of harmonic tremor observed at the geyser during the recharge interval, whereas the low sound speed of the liquid-vapor mixture influences the fluid-flow characteristics of the eruption. At the rapids of the Colorado River in the Grand Canyon, Arizona, supercritical flow occurs where debris discharged from tributary canyons constricts the channel into the shape of a converging-diverging nozzle. The geometry of the channel in these regions can be used to interpret the flood history of the Colorado River over the past 103–105 years. The unity of fluid mechanics in these three natural phenomena is provided by the well-known analogy between gas flow and shallow-water flow in converging-diverging nozzles.
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