Baines, P. G., and Sparks, R. S. J. Dynamics of giant volcanic ash clouds from supervolcanic eruptions.The point of the paper, more or less, is that based on a simple physical model and some (reasonable) assumptions about the eruption flow volume and a few other parameters, you can calculate an eruption size threshold at which Coriolis forces begin to have significant effects on the development of a plume.
Geophysical Research Letters (2005): 32: L24808.
The largest explosive volcanic eruptions that have occurred on Earth generated giant ash clouds from rising plumes that spread in the stratosphere around a height of neutral buoyancy, with estimated supply rates that are in the range 1011 to 1013 m3/s. These giant ash clouds are controlled by a balance between gravity and Coriolis forces, forming spinning bodies of nearly fixed proportions after a few hours and are initially insensitive to stratospheric winds. In contrast, volcanic plumes from eruptions with small to intermediate magnitude spread as inertial intrusions under the influence of stratospheric winds, with the Earth's rotation being unimportant. In the largest eruptions the giant spinning ash clouds typically develop diameters greater than 600 km and up to 6000 km in the most powerful super-eruptions, thus explaining why areas of continental size can be covered with volcanic ash. The radial expansion and spinning velocities are calculated at tens of metres per second and increase with eruption intensity. Higher spreading velocities carry larger ash grain sizes to a given radius, so that grain size at a given distance from the source increases with eruption intensity, consistent with geological observations.
Very large magnitude explosive eruptions have the potential for global catastrophe. Such eruptions can cover continental scale areas with volcanic ash and may cause severe environmental effects in the years and possibly decades that follow. Here we consider explosive eruptions of magnitude M = 6.5 and above, where M = Log10 m – 7 and m is the mass of magma erupted in kg. Such eruptions range from the largest magnitude eruptions of the last century, such as Mount Pinatubo in 1991 (M ~ 6.5), to the largest explosive eruptions known, such as the eruption of Toba, Sumatra at 71 kya (M ~ 9). Explosive eruptions with M > 8 are commonly described as “super-eruptions”. Here we establish that the spreading of such clouds is controlled by the Earth's rotation. The giant ash clouds can have very large horizontal dimensions, with spreading and spinning velocities exceeding typical stratospheric wind speeds. The model can explain why continents can be covered with volcanic ash, and why the grain size of the ash tends to be much coarser than in smaller magnitude explosive eruptions . . .If you would like a copy of this paper PDF, let me know. A Google Scholar search for "volcanic" and "Coriolis" will turn up other papers too.
. . . The calculations confirm that only explosive eruptions of magnitude 6.5 and above develop giant clouds a few thousand kilometres in diameter where rotational effects dominate. Mount Pinatubo in 1991 falls at the lower end of this magnitude range. The cloud for Pinatubo (magma flux ~ 7 × 104 m3/s and stratospheric flow rate ~ 5 × 1010 m3/s) behaved like a gravity-driven intrusion during its initial expansion , reaching a diameter of 1200 km after 4 × 104 seconds. Rotational waves were observed at a diameter of 800 km in qualitative agreement with our model . . . Above a magnitude of 6.5 the clouds have dimensions from several hundred kilometres to a few thousand kilometres in the largest magnitude cases. Beyond the threshold diameter the radial expansion speeds are commonly larger than typical stratospheric wind speeds but reduce to low values as the spin velocities increase with size; the cloud dimensions become constrained by the Earth's rotation . . .
. . . Hence a dynamic model of ash clouds from very large magnitude eruptions shows that rotational effects become dominant for eruptions that have magnitude much greater than about M ~ 6.5. The clouds expand to diameters of hundreds to thousands of kilometres in time scales of order of a day, and rotate in an anti-cyclonic manner much like a rigid body. The size of a giant cloud is limited by its volume and cyclostrophic balance, which helps to maintain its integrity against a mean stratospheric wind. This explains how these giant ash clouds can cover continent-sized areas and deposit ash over them, as has been observed from geological evidence of previous eruptions . . .
...the clouds expand to diameters of hundreds to thousands of kilometres in time scales of order of a day, and rotate in an anti-cyclonic manner much like a rigid body.I would point out that the research I linked to is more recent than that paper, but there could be something we're missing.
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posted by dinger at 3:51 PM on March 29