23 August 2011

“How to Build a Volcano”: Followup from Dr. Ed Llewellin

Posted by Jessica Ball

I was lucky enough to get an email from Dr. Ed Llewellin, one of the volcanologists featured in National Geographic’s “How to Build a Volcano”, with commentary on my review of the show. He’s given me permission to post excerpts from his message here, which will clarify a few things that I commented on, as well as expanding on the science presented in the show and correcting a few faulty assumptions that I made. Here we go!

Dear Jessica,

I just stumbled across your blog post on ‘How to build a volcano’. I am glad that – on balance – you found the show entertaining. I have only just seen it myself (a DVD arrived from the director yesterday – it won’t show in the UK until November). I thought you might be interested to hear my perspective on the science in the show, and the way it was presented. Up front I should say that I will focus on the slug experiment, as that was ‘mine’. I am copying this to Michael, Ben and Joe, in case they wish to comment on the PF experiments.

As I’m sure you know, the key to successful laboratory modelling of natural systems is to ensure that they scale appropriately. The rise of gas slugs (or ‘Taylor bubbles’) up pipes has been fairly well investigated by chemical engineers, who are mainly interested in industrial applications. This work has shown that the key dimensionless parameter (a unitless number that represents a property of a physical system) that controls slug behaviour is the ‘dimensionless inverse viscosity’ Nf, which is given by (Eq. 1):

where rho is the liquid density, g is gravitational acceleration, D is the conduit (or pipe) diameter, and mu is the dynamic viscosity of the liquid. Given a few caveats regarding the role of surface tension, if the value of Nf in your lab system is the same as the value of Nf in the natural system, then the behaviour should be the same. Perhaps the most widely-known example of this dimensionless approach to scaling is the use of the Reynolds number in fluid dynamics. In fact, it is possible to define a Reynolds number (Re) for slugs, which is related to Nf directly (albeit via a very messy function). (The Reynolds number gives a ratio of inertial, or driving forces to viscous, or ‘slowing’ forces in a flow.)

If we make reasonable assumptions about the values of the various parameters in Eq. 1 in a volcanic setting – for example at Stromboli – then we expect Nf to fall in the range 2 < Nf < 10^4 (equivalent to 5×10^-2< Re < 5×10^3). The upper end of this range is difficult to access at the laboratory scale, because of the small values of pipe diameter D. The large-scale slug experiments were motivated, in part, by a recent paper by Suckale et al (doi:10.1029/2009JB006917). This paper describes numerical experiments, and concludes that slugs break up catastrophically for Re >10. This finding implies that gas slugs are unlikely to form at Stromboli and other persistently active basaltic volcanoes – which is highly counter-paradigmatic!

We wanted to test this hypothesis. In order to make the sternest possible test, we wanted to see if we could produce gas slugs at very high Re. In order to do this, we needed a large diameter pipe and a low viscosity liquid (see Eq. 1). You say in your blog that we should have used “something much more viscous than water” but, in fact, that would have given us a proportionately lower Reynolds number. With our setup, we produced slugs at Re ~ 40,000. In our view this, raises serious questions about the validity of Suckale et al’s interpretation of their simulations, and confirms that slugs can indeed form in volcanic conduits. We have subsequently written a comment on Suckale’s paper (doi:10.1029/2010JB008167) which includes data from the experiments at Mt Boom so some of the work, at least, has resulted in publication. (Also, see Suckale’s reply to the comment here: doi:10.1029/2011JB008351)

Your point about the “lovely smooth-sided  tube” is well-founded. Inevitably, when we model a system, we seek to simplify it sufficiently to render analysis tractable, whilst maintaining the essential features of the system. I don’t think anyone believes that the conduit at any volcano is a smooth, vertical cylinder, yet that is the almost ubiquitous assumption underpinning numerical and laboratory models. It is worth bearing in mind that the most thermally efficient geometry for delivering magma to the surface is via a vertical, cylindrical conduit, and we would expect that a dyke morphology would evolve, over time, towards this cofiguration. This is the reason that lava curtains from fissure-fed eruptions rapidly evolve towards point-source eruptions, and why sheet-like lava flows evolve to transport lava in pipe-like tubes. Given the extreme longevity of Stromboli’s plumbing system – eruptions have barely changed there for at least 1500 years – if any volcano has evolved a pipe-like conduit, it is probably Stromboli.

In short, you are right that the experiments were “pretty preliminary”, but I hope it is clear that they were also “rigorous enough to be used for scientific research”. The producers kindly gave the me the pipes, tanks, couplings etc. after the show, and I have shipped them back to Durham. I am currently arranging to install the kit here, as a facility for large scale conduit experiments. I have dozens of further experiments that I plan to conduct with the kit, and I plan to invite other volcanologists to use it too.

I realize that you were judging the quality of the science on the information presented in the show – you had nothing else to go on. This highlights the tension at the heart of all science outreach activities – where do you draw the line between making science accessible, and dumbing it down? We both know that volcanology grad students make up a small proportion of Nat Geo’s demographic, so the production team inevitably have to compromise. As you guessed, the science team had essentially no directorial control over the finished product, but I, personally, think that they did a pretty good job of balancing depth against accessibility.

I would also add that, whilst the chronology was changed a little to make the narrative smoother, the facts were never changed. You say that you “highly doubt” that we didn’t know what we were going to find when we climbed Stromboli, but that is absolutely true. The team at the Stromboli observatory do a great job of monitoring the activity there, but in conditions of poor visibility, they still rely heavily on direct visual observations of the crater terrace. We worked closely with the monitoring team, and with colleagues from INGV, so we had access to all the data that the observatory had. We knew before we ascended that the strombolian activity was rather less than usual, but we didn’t expect lava flows, which probably broke out whilst we were at the summit (it really was very cloudy!). We immediately radioed our discovery to the observatory staff, which precipitated a flurry of activity – they called in a helicopter the next day to make further visual observations, including thermal imagery, to confirm the extent of the flows. As I think we mentioned in the show, lava flow activity at the crater terrace is unusual, and seems to be a precursor to more violent paroxysmal activity. There has been a recent paper on this by Calvari et al (doi:10.1016/j.epsl.2010.11.015). The eruption we witnessed followed this pattern, and there was a major explosion about two months after our visit. (Here is a link to Stromboli Online’s photos of the events Dr. Llewellin mentions.)

…On balance, I found making the show to be very rewarding, and I hope that it has brought a different type of volcanology – investigative experimentation – to a broader audience. The fact that you took the time to write about your views on the programme shows that it has stimulated discussion.

Best wishes,

Dr. Ed Llewellin, Lecturer in Volcanology
Dept. Earth Sciences, Durham University

A big thank-you to Dr. Llewellin for taking the time to comment so thoroughly on my post! He’s corrected some muddled assumptions I made in the review, and given me new fluid dynamics material to digest.