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I understand that volcanic ash plumes can only rise to great heights (e.g. 50km) with the help of some other processes, as the velocity of the material ejected isn't great enough to send it high into the atmosphere.

I don't understand how exactly these processes take place. I think that cooler, atmospheric gases are entrained towards the hotter, denser volcanic plume, then become heated and incorporated into the ash plume, causing it to become buoyant and to expand.

What causes the cool, atmospheric gas to move towards the plume? Is it due to the temperature differences between the plume and the atmosphere, or some kind of pressure difference?

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    $\begingroup$ I am thinking it is just conservation of mass? As the volcanic ash rises the "missing" mass has to be replaced by neighboring atmospheric gases. $\endgroup$ – Isopycnal Oscillation Mar 2 '15 at 19:18
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This answer seeks to just answer about ambient air entrainment, as per the question (not eruptive plume height, as suggested in the comments) which is a separate question.

According to the book, Modeling Volcanic Processes: The Physics and Mathematics of Volcanism, (Fagents et al, 2012, p. 155-156), your assumption (2nd paragraph) is on the right track, particularly for energetic eruptions (e.g. Plinian).

When the plume initially erupts, it possesses significant momentum, with a greater density and are influenced by pressures considerably greater than the ambient atmosphere. However, once in the atmosphere, the plume undergoes rapid decompression and expands, ascending as a turbulent flow in the convective ascent region (an example is shown below).

enter image description here

Image source: USGS page about the Mt St Helens eruption in 1980 demonstrating the turbulence in an eruptive column.

As the flow continues to ascend, the eruptive column begins to exhibit lateral gradients in temperature, momentum and density, allowing for the mixing with the ambient air at the edges of the column - over time, this mixing continues to the core of the eruptive column by shear mixing. Effectively, 'stirred into the column by the turbulence'.(Fagents et al. 2012; Kaminski et al. 2011).

enter image description here

Image source: MTU.edu

As the entrained air heats, expands and rises, more cooler ambient air is mixed into the turbulent eruptive column (just as long as the eruption continues) - as per the MTU.edu diagram above, the plume rises by buoyant convection.

Entrainment of air into the eruptive column can be increased by the right wind conditions, as observed at the 2011 Kirishima-Shinmoe-dake volcano eruption in Japan (Kozono et al. 2014).

Additional resources

Kozono et al. 2014, Correlation between magma chamber deflation and eruption cloud height during the 2011 Shinmoe-dake eruptions, Earth, Planets and Space

Kaminski et al. 2011, Rise of volcanic plumes to the stratosphere aided by penetrative convection above large lava flows, Earth and Planetary Science Letters

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    $\begingroup$ I'm confused - if we're talking about a convective process here, shouldn't the temperature inversion in the stratosphere stop the plume? How do we attain such insane heights of 50km mentioned by @nolisgol ? $\endgroup$ – AtmosphericPrisonEscape Mar 19 '15 at 13:02
  • $\begingroup$ A better comment than was there before - the plume heights are, in general, caused by what the OP described as the air being heated and incorporated into the ash plume, causing it to become buoyant and to expand., this answer is to their question What causes the cool, atmospheric gas to move towards the plume?- essentially what entrains the air in the first place. $\endgroup$ – user889 Mar 19 '15 at 17:44
  • $\begingroup$ Also, in the MTU diagram, the text for the 'Canvective Phase' section states plume rises by buoyant convection - have added this in to the explanation $\endgroup$ – user889 Mar 19 '15 at 17:51

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