Scaling new horizons

Mayon, Phillipines, 1984. Gravity currents, in the form of pyroclastic flows, propagate down the flanks of the volcano. From http://en.wikipedia.org/wiki/Pyroclastic_flow

It’s fair to say that when most people ask what I do, I simply reply “volcanologist”, “sedimentologist”, or “geologist”, depending on the audience. On the infrequent occasions they ask further what I do, it usually gets summed up as “I see how well things go downhill”, or “I study how different flows behave”. I might even go into detail about the hazard mitigation or petroleum reservoir potential of some of these studies.

The fact is though, that on the whole, I try to keep it absurdly simple.  And, on the whole, that serves the needs of the casual question, and lets us get on with the business in hand (which, to be fair, is quite often “having a beer”).

However,  since I discovered I was moving to France for this new postdoc I have found a more insistent repetition of “what is it you’re actually going to do?” The temptation is often to pull a Barney Stinson

But, apparently I don’t wear enough suits to get away with it. So, here we go. I’ll be spending my time running scaled models of gravity currents. The interesting thing is that everyone seems to ask about the ‘gravity current’ bit, and just take the ‘scaled’ part for granted. However, the ‘gravity current’ is actually in many ways the dull and straightforward bit – very simply, dense stuff goes down hill. You put dense fluid at the top of a slope, and gravity moves it down that slope. I just record the flows and measure the deposits.

Far more important is the ‘scaled’ part of this little world of sedimentological wonder. It is easy enough to imagine that building a small model of a volcano and pouring stuff over it might produce realistic results. However, the fact is that this is very far from the truth. While it seems obvious that you can model the behaviour of large particles in a big flow by using smaller particles in a smaller flow, there is a question firstly of ‘how big do the new particles have to be’.  But there is also a question of ‘what happens with things like gravity?’.  No matter how big or small I make the flow, gravity is a constant I can do little about.

And that’s not all. Things like particle friction, and fluid viscosity also don’t change (or change in non-linear ways). So now, if you change the volume of the flow, you’re not actually changing all the parameters at the same time.  As you might imagine, this means a flow at one scale can behave completely differently to a flow of identical materials and relative height and width at another scale.

Then you get all sorts of other interesting little problems creeping up. For example, when you work with sand-sized particles, there’s a number of weird sorting mechanisms that occur. If you try and use even finer particles, you start getting cohesion – where everything from humidity to van-der-Waals forces starts to stick particles together.

In short, scaling is probably one of the biggest challenges in any kind of geophysical modelling. The scaling problems become less pronounced as you make your models bigger and bigger, but cost and practicality then become your adversaries.

There’s a number of solutions (or at least workarounds) when you’re looking at scaling of experiments, and it comes down to trying to describe the various parameters of the flow using dimensionless quantities. As the simplest example, I can look at the aspect ratio of a flow (how long it is, divided by how tall it is). Because both are measured in meters, the aspect ratio is a simple number with no dimension. Hopefully, the aspect ratio of the flows in the model would be the same as the aspect ratio of the flows in real life. And we do that for everything from particle densities, to pore-pressure and fluid viscosities.

It’s worth noting that you will almost never achieve a perfectly scaled model. But, with care, you can get close. In the words of George Box: “All models are wrong, but some are useful.”

So what do I do?

Well, for the first month of this particular project, I’ve been spending a lot of time doing the calculations and designing the equipment to ensure that the experiments I’m going to be running can actually inform us about flows which – rather than being a few meters long and centimeters high, are kilometers in length, and tens of meters high.

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About Pete Rowley

Earth Science researcher. Enjoys a good rant, beer, and watching films with Angelina in them. Dislikes reality TV, crowds, and unreasonable people.
This entry was posted in General, Geology, Hazard Assessment, Physics, Science, Sedimentology, Volcanism and tagged , , , , , , , , . Bookmark the permalink.

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