 These features called pyroclastic density currents can be generated either by the gravitational collapse of eruption columns or by the gravitational collapse of lava domes. In both cases, these collapses have a mixture or generate a mixture of particles that are hot. They entrain the surrounding air. So they're a mixture of particles and air. Here's two examples. They're flowing over the surface of the Earth. And because of the cloud of ash that envelops these density currents, it's very difficult to see what's going on inside. And so as a result, there have been a number of conflicting or competing models for how these flows advance over the surface of the Earth. And what I'd like to do is today is talk about some of the physics that governs the formation of these flows and their propagation. Much of our understanding of pyroclastic density currents is based on looking at the deposits produced by these density currents. We won't be talking about the deposits today, but of course, if you have any questions about deposits and connecting deposits, there's two mechanics I just turned it on. No, you turned it off. I don't think there are two ones. OK. Just go ahead and ask. And what I'd like to do, my remote is not working. What I'd like to focus on today is how processes that occur at the smallest scale in these flows, individual particles, ultimately govern the large scale dynamics of these flows. There's a chance for me to remind you if you have any questions at any time, please interrupt and ask. From the introductions, it looks like we're heavy on seismology and interpreting deformation signals, but there is a broad range of people here. So if I use words that don't make any sense or I use equations and you wonder where they come from, interrupt and we'll see what we can do. The flows produced by volcanic eruptions do involve multiple components or multi-phases. The plenian eruption column on the right is a mixture of particles and gas that's rising vertically. It's the collapse of these kinds of columns here on the right that generate the pyroclastic flows that go down the sides of volcanoes that we'll be talking about today. When these pyroclastic density currents enter the ocean, there's a third phase that becomes important, the liquid in the ocean. And one of the challenges with understanding or modeling these kinds of flows is obviously they're very complicated, right? These are clearly turbulent flows. But all the phases that you see here, the particles, the gas, and the liquid water, interact with each other. They interact by exchanging mass, momentum, and energy. The kinds of questions we would like to answer are listed here. We'd like to understand what controls and governs the size of the particles within the flow. Why do we care about the size of particles? Now, if we know the size of particles, we can interpret the motion of them to get constraints on the velocity. What else do we care about particle size? Volcanologists are obsessed with particle size distribution and particle size. It's what we see at the end, right? In fact, the last topic here is most of our information and insights into volcanic phenomena still come from interpreting deposits. And those deposits contain information in the lithology about particle size, size distribution, and other attributes. And so if we can understand what governs the size and size distribution of particles, we can better interpret deposits. The other questions might be a little bit more obvious why you might care, right? How fast do these currents travel? How far will they go? What is the internal structure? The internal structure affects how these flows travel over the landscape. And the reason it's very difficult to understand the internal structure is illustrated on the top, where all we get to see is the outer envelope of fine ash particles and what's going on inside is hard to see. And it's because, again, it's hard to see what's going on inside that there's a lot of uncertainty about some of these processes. So I will argue that two of the big challenges with developing models for pyroclastic density currents or understanding them are the following. First, there's a wide range of length and time scales that govern the mechanics that we see, right? The pictures you just saw involve scales that range from hundreds of meters to tens of kilometers. These flows consist of little tiny particles, micron-sized particles. The momentum transfer at the large scale occurs on time scales of hours, but at the small scale when particles collide, those are micro-second phenomena. Okay, and second point is, again, that many of the critical processes do occur at the length scale of the individual particles. And so one of the challenges for both understanding these phenomena and then, of course, the next step to develop models is to figure out how we can integrate our understanding of mass, momentum, and energy conservation from the smallest scales of the individual particles to the large-scale phenomena that we see. And what I'd like to do in today's presentation is show you a variety of different ways we can go about making that connection between small-scale physics and large-scale physics. So to illustrate the nature of the phenomena we would like to understand, the processes we like to study will begin by considering an example of a flow consisting of particles and surrounding gas. On the right-hand side, what we're looking at here is a snapshot in time of the concentration of particles produced by a collapsing eruption column. A mixture of particles and gas erupts vertically on the left of this box. I probably should have brought some batteries. I'll just use my hands. It erupts vertically on the left, rises. Volcanic materials are more dense than air. And because it's more dense than air, this eruption column collapses under the influence of gravity and travels off to the right. The colors that you see here are particle concentration. Red is high and blue is low. And you can see that there are large variations in particle concentration here. And because of the large variations in particle concentration, there are fundamentally different ways in which particles interact with each other and the surrounding gas. Let's start at the bottom where the concentration of particles is the highest. Here, mass, momentum, and energy exchange occurs as particles slide past each other. When the flow becomes more dilute, the momentum exchange is dominated by collisions between particles. And when the flow is the most dilute at the edges of these flows, momentum is exchanged between the gas and the particles. As the gas flows by the particles the flows of the particles flow through the gas. So in a little bit more detail, to understand how these flows work we need to understand in the concentrated regions what happens when particles slide past each other when they undergo enduring frictional contact or interactions. When the flow becomes more dilute we need to understand what happens when particles collide with each other, how much momentum do they exchange and whether they might break up. And then when the flow is the most dilute we need to understand how the motion of a particle is coupled to the motion of the gas. If we'd like to develop models for how these phenomena work, we just need to solve the equations that describe conservation of mass, momentum, and energy. This is a very complicated, busy slide. For some of you this will make lots of sense. For others this will be completely foreign. But let me talk you through what physics is going on here so I can explain conceptually at least how we can try and understand from a small scale phenomena to large scale mechanics. So for each of the components or phases that we're interested in and so when I say a phase it could be the gas or it could be particles we know that their motion and behavior is subject to the conservation laws of mass, momentum, and energy. So these are listed here. The first equation is a statement of conservation of mass. Conservation of mass has the change of mass conservation of phase one times the density of phase one. Changes in some control volume material enters or material leaves. And that's characterized by the divergence this next term of the mass times the velocity. The second equation that you see here for conservation of momentum says that the change in inertia what's inertia? Momentum is mass times velocity. So the term on the left hand side describes a change of momentum of a material, phase one, and it's how do you change momentum of something? You apply forces to it, right? It's the only way to change momentum. And so the various complicated terms you see on the right hand side are the various forces that are applied to mass and density current. The first term describes changes in momentum because of collisions between particles. The second one would describe frictional interactions between particles. The third expression here describes momentum exchange when phase one interacts with phase two. That could be the gas influencing the particles or the particles influencing the gas. And the fourth term describes the effects of buoyancy. So again, we change inertia because of all the different forces that act on the particles. And the last set of equations here describes conservation of energy. We can change the amount of thermal energy in our current, the term on the left hand side where the energy is conducted. That's their first term, conduction of energy. Or we can transfer energy between different components. Here are components one and two. So the point of showing you these equations is really to emphasize two things. First, equations for conservation of mass momentum and energy apply to all the phases that we're interested in. And one of the complexities is all the phases interact with each other. The particles interact with each other. The gases interact with the particles. Well, conceptually simple, if you've seen conservation laws before. It's just mass momentum and energy conservation. The real complexity enters through all the different terms that have a bold letter here. And there are a variety of different closure relationships that describe what these transferred terms are. We need to, for example, have a model for turbulence. And so much of the effort in developing models for pyroclastic density currents or, generally, these systems that contain suspended particles goes into figuring out how do we describe the various expressions that appear on the right-hand side of these equations. Clojure Par told me that everyone here will know a conservation but the Navier-Stokes equations are where they come from. And so I did not choose to derive this for you. If you'd like to see a derivation of these equations, we can probably find half an hour and do it on the blackboard. So just let me know. Let's take a look at a scale of individual particles in these density currents and then look at their consequences for large-scale phenomena. And we'll do this with three different examples depending on how time goes. The first is we'll look at some of the consequences of collisions between particles in these density currents. The second problem we'll look at is the role of boundary conditions and how these density currents propagate. And the third problem in the substrate in the case we'll look at water affects the propagation of density currents. And I guess the thing to keep in mind for all these exercises or questions we will go through, what we're really trying to understand is how phenomena and physics at the small-scale influence the large-scale. So first one, what happens when particles collide with each other? I chose to put this in the form of a question. So as we go through this first example, you can think about the question so here you're looking at two examples of photographs of density currents, one from Alaska, one from Washington state and the United States and you see a lot of small particles that we call ash in these density currents. And the first question I'd like to address is how much of the ash that we see is produced within the flow itself and what do I mean by produced by the flow itself? How much of this ash that we see here is erupted directly out of the volcanic vent or instead might be produced within the flow you see here as particles slide past each other or they collide with each other. And second, as if we... it turns out we generate mass through interaction between particles, does it have any effect on the density currents themselves and is it reflected in the deposit? So I will briefly describe two different ways in which we characterize what happens at the small-scale and then we'll see how it influences the large-scale. If you go back to that picture I showed you of the collapsing eruption column one way in which particles interact with each other is sliding past each other and this happens at the base of these flows where the particle concentration is high. So one way in which we can measure this is to go into the lab, take volcanic particles and let them move past each other. The way we do this is we have an apparatus we have two concentric cylinders we fill the gap between the cylinders with particles and we're held in place by a plate. We can make the plate spin and as it spins the particles go around in a circle. A picture of particles in the upper right and to determine how much small particles we make we can weigh the big particles before and after the experiment and determine how much mass goes into making small particles. And that's plotted on the lower right how much small particles we make as a function of how fast the particles move The fact that we see a straight line here means that the rate at which we make particles small particles is proportional to how far the particles move. If we understand how fast we make small particles we can develop a model for the rate at which we make small particles and take this model and put it into those governing equations I showed you a few slides ago. If you remember we had a bunch of equations that were conservation of mass momentum and energy there are terms on the right hand side that I said we don't know. We can get those terms on the right hand side by experiments like this. We can do the same thing for when particles collide with each other. We go into the lab we take two particles we shoot them at each other we measure their mass before and after the collision and we could then determine how much mass is made when particles collide. And so that's what I'm plotting on the vertical axis the mass of small particles generated as a function of the collision speed of the two particles. So under normal circumstances you would say this is a terrible relationship, right? There's a lot of scatter. It turns out if you do lab experiments with natural volcanic materials and you try and measure some physical property you always find a tremendous amount of scatter. And hopefully everyone's seen real volcanic materials and you understand why this is the case. Real pieces of pumice are heterogeneous the bubbles are always a little different their shapers not perfectly spherical and because of the complexity and the shape and the internal structure of these materials the physical properties you tend to measure tend to be quite scattered. The big open circles nevertheless are actually averages and there's a much nicer relationship if we start averaging all these measurements. So what we end up by doing these experiments where we measure how much mass is lost when particles collide is an expression of how much mass is lost per collision to put that into our governing equations we need to know then how often particles collide and what is the speed of that collision. And we can use things called kinetic theory that people use to describe how gases behave to build up a model for what goes on and derive an equation that we can put into those governing equations I call it R here for the rate at which you produce small particles and it depends on the rate at which they collide theta here is something called the granular temperature a measure of the variations of velocity in a current in a flow alpha is the concentration d is the particle size so there are ways to take experimental measurements integrate over small scale physics to drive an equation that can describe macroscale phenomena Good question so the question is does the type of material matter and absolutely so this is a specific type of pumice there's not a huge variability from one type of material to another because most salicylic pumice turns out to be about the same but so everything in the box I haven't defined any of these terms but essentially it's the rate at which particles collide their concentration their size rose density gamma is the experimentally determined parameter and so gamma you can think of it as an empirical parameter that describes how easily a material breaks up and so that would be different for every type of material but I guess it's analogous to friction experiments is a friction coefficient good question so throughout this process in fact these particles get progressively more and more spherical these numbers here don't change the amount of ash in the previous experiments actually the rate at which when particles slide past each other the amount of ash that's produced does vary as the particle shape varies and afterwards I'm happy to have a whole bunch of hidden slides coming up in three that look at that component and I cut them out to save time but for sure everything evolved material these properties vary with time because the attributes of the particles vary with time and you can build that into these models so again the equations or the models are the following we have a set of equations for conservation of mass, momentum, and energy and we have these equations for all the components we're interested in so what I've written down here these equations for all the phases that we're interested in where the first line is for the gas the second line will be big particles the third line will be small particles produced when particles slide past each other and the fourth line will be small particles produced when particles collide with each other and to understand what goes on then at the small scale what I've outlined in boxes are all the physics that describes the small scale processes so our big particles which was the second line when the particles collide or slide past each other they lose mass and so each of these terms that says negative r represents a mass loss from the big particles through those interactions and that becomes a source of mass for the smaller particles either as they slide past each other or they collide with each other and in our conservation of momentum and energy equations they're going to be analogous momentum and energy exchanges that occur when particles interact so conceptually that's the idea of how we incorporate small scale physics into large scale dynamics so I'll take you through one example the model problem will be a density current that enters some domain from the left it travels to the right we need to specify initial conditions so in this case an initial speed a concentration of particles 2.5 volume percent and for illustrative purposes we'll start with a flow that just consists of one centimeter size pumice particles and nothing else and it's hot and so what we're looking at here now is a snapshot in time of the distribution of those particles in the density current so the vertical axis represents vertical position within the current horizontal axis is distance the current is traveled again this is a snapshot at some point in time so you're looking at a slice through the current colors concentration of particles red is high yellow is low and the scale is logarithmic on the top I'm plotting where we see the big pumice next is the ash produced when particles collide with each other and on the bottom is the ash that produces particles slide past each other in the region where the concentration is high so I guess there are a couple things you might notice here these are snapshots at the same point in time the ash produced by collisions and the ash produced when particles slide past each other occupy more or less the same region and space they become well mixed because of the turbulence in these flows second the small particles have advanced much further than the big particles right they're small they can move with the air much faster and so they separate from the larger particles and in this particular case 7% of the big particles ends up going into making small ash size particles and I'm going to skip over the rest and just summarize what we learn again the point here is to understand the following question when we look at these pictures here where is this ash being generated is it generated from the original materials coming out of the eruption column or is some of it being generated as the flows travel over the landscape what we find typically is 1% of the mass of the large particles ends up going into making small particles the small particles that are generated increase the distance these flows travel they do this by changing the pressure and the density of the flow the small particles that are generated do separate from the larger particles and one signature of this process in deposits is that the particles that we see because they've been colliding with each other or they're sliding past each other change their shape they get progressively more round and we can in fact quantitatively relate the mass lost to the shape of the particles and so when we go to a deposit like this one in Mount St. Helens we can measure the shape of the particles and make an estimate of how much of their mass they lost to small particles that then separated to go back up into the atmosphere questions about this first question where do small particles come from I'd like to look at some of the mechanics behind how you carry big particles within these density currents again pyroclastic density currents are mixtures of gas and particles and they're flowing because of gravity and maybe once again I'll put this in the framework of a question we'd like to answer this is a cross section through the deposit of one of these pyroclastic density currents from Greece the coast plateau top so this whole exposure you see here are materials mostly pumice deposited from that eruption you can see some large fragments in here this is a meter size block of rock colors different from the surrounding it's an example of what we call a lithic fragment meaning it's a fragment of the surrounding country rock that was entrained and carried by the density current that's a pretty big piece of rock what's interesting about this deposit we're 10 kilometers away from the vent and this density current traveled over water to get to this location so the question we'd like to address now is how is it possible for this mixture of pumice particles and ash to carry big blocks of rock like this so far and so far over water so remember the picture I showed you at the beginning we have a collapsing eruption column collapsing under the influence of gravity and the particles are being transported off to the right the different ways particles interact with each other particles also interact with the substrate over which they travel illustrated on the bottom when particles travel over water the particles may hit the water surface and they may sink so I'll call this a leaky boundary as opposed to a saltation boundary on the right where particles can bounce off the boundary they might lose some momentum but they stay within the flow so to understand how particles interact with their substrates we can once again do experiments these experiments are pretty straightforward we take compressed air and we propel particles at different types of surfaces and look at what happens we can measure the speed at which particles collide with the substrate we can look at the angle of that collision we can measure the speed at which particles come in and the speed at which they leave and look at how much energy is lost oh well I was going to show you a video of what that looks like it's not so important in this case it's colliding with water okay so I think what you can imagine what happens when particles collide with different surfaces we use high speed video cameras to document what comes in what goes out to get quantitative information I'll show you only a subset of measurements to give you a flavor of what we have to work with and how we interpret these what I'm plotting on the vertical axis is how much momentum is retained after a particle collides with a water surface as a function of the angle of that collision I'll call that a pitch angle 90 degrees would be vertical 0 degrees would be horizontal so a couple things you know anything that retains no momentum what are those particles you come in with some momentum you come out with no momentum those are the particles that sink so we can also determine which particles sink and there's a pattern here as the angle gets bigger and bigger you're less likely to bounce off the surface and I think if you go outside to the ocean and you want to skip a rock over the water surface if the angle of collision is too big the rock doesn't bounce but we can once again use these kinds of measurements made experimentally the scale of individual particles to measure how much energy is lost during a collision this is a property people call a restitution coefficient we can also measure how many particles sink we can also measure the effect of the mass of the particles the impact velocity and similarly determine a relationship between these other variables and I will skip the other slides and take you straight to an example so the point of these experimental measurements is simply to determine a boundary condition that describes what happens at the bottom of the flow what is the mass and momentum exchange as particles travel over a surface the example we'll look at is very similar to what you saw before we'll let a density current enter a region from the left travel to the right this time however we'll start with two size particles bigger particles and smaller particles and what I'm going to do is compare a flow that travels over water with one that travels over a solid surface the difference being over water particles can sink in the water and they're lost from the flow if particles are lost from the flow their mass is not within the flow and these density currents are driven because they have a difference in density the more mass you have the further you go so once again we're looking at a vertical slice through these density currents color's concentration, red is high, yellow is low scales logarithmic the top two panels show the case for a flow that has traveled over a solid surface the bottom two panels for a flow that has traveled over water for each panel we have each of these two cases we have on the top where we see the small particles the big particles, small particles so for a flow that travels over a solid surface on the top you see that we have a region of high concentration near the base of the flow those are the particles bouncing along over the base of the flow for the flow that travels over the water we don't have this region of high concentration because those particles sink into the water and as a consequence the flow that travels over land maintains a higher concentration it travels faster and it travels further to get a better sense of how the particles are transported within these flows we can introduce what we call Lagrangian tracers Lagrangian tracers is a particle that travels with the flow you take the local velocity it's interaction with other particles and you can compute its motion it satisfies an equation that says the change in its velocity with respect to time is governed by all the forces that act on that particle so in the example I'll be showing you we simply introduce a number of particles that range in size from 1 micron up to 10 meters and we can keep track of how they're transported and the experiences they endure as they're transported in the density current I'm going to summarize all in one plot so we're going to compare a flow that travels over water with a flow that travels over land and what I'm plotting on the vertical axis is the amount of particles transported in fact the quantity in the vertical axis is analogous to the deposit thickness as a function on the horizontal axis of distance traveled and I separate particles into two sizes small particles with the light color big particles in the light color small particles in the dark color the flow on the left is the flow that travels over water the ones on the right are the ones that travel over land and last we have two horizontal sets of panels at the top one corresponds to a dilute current 2.5 volume percent particles the next panel for a concentrated flow and last this vertical dashed line shows the maximum distance 1 centimeter size particle can be transported in that current so the big take home message here is quite simple for concentrated or dilute currents that travel over water they travel roughly the same distance because any time particles get near the bottom they're extracted from the flow big particles also don't get carried very far for flows that travel over land big particles not only get transported further when we have a concentrated flow big particles get carried much further and the reason for the we have a longer distance transport of bigger particles I think it's reasonably straightforward to understand you have a big particle that wants to settle under the influence of gravity through a density current a mixture of other particles and gas and what's going to make it be carried along it can bounce so we take a big particle and it's sinking and it bounces mostly it wants to bounce up and down but if it's going forward it will bounce a few times and stop moving what's the best way to carry something a long way you want to pick it up and just carry it rather than just letting it bounce along and in these flows of course you want to pick up a big rock and carry it you extract momentum from the flow by collisions and so when a high density current as the particles are sinking they're continually running into experiencing collisions with smaller particles all the other particles extracting that horizontal momentum from the smaller particles which allows it to be transported bigger distances and so the reason we see this long distance over land is simply we have a higher concentration of smaller particles that you can collide with, extract momentum and be carried along and when we have a high concentration you end up with more collisions and more momentum extraction in the interest of time since we started late I will encourage you to go look at a poster of what I was going to show you next because most of this is on a poster one thing I have not talked about is what happened we said these particles can bounce along on the surface but when a particle collides with a surface it can also kick up mass back into the flow so here we have particles settling to the bottom of the current when they collide with the bottom they can bounce but they can also make other particles bounce as well I'll call this splash and here's an example where we have a big particle coming into the a substrate and as it collides with the substrate it makes a little crater this is a hundred photographs or small particles that are ejected back into the flow and it turns out when particles collide with substrates they can eject much more mass than the original mass of the particle so it becomes a net source of mass into the current and the rest is going to be some of the consequences so let me summarize what we've learned by looking at what happens at the base of substrates first we need when we solve differential equations we need governing equations we need an initial condition we also need boundary conditions and so for density currents we need a boundary condition that describes what happens at the base of these currents and that's really a description of what happens when particles impact a surface so I began with a question how do we transport these large particles I've argued the way you carry large particles is they're continually being impacted by smaller particles extracting momentum for flows that travel over water it's very difficult to carry particles because when particles encounter the base of the flow, the ocean, or water they tend to sink and by sinking they remove that momentum they remove that mass from the density current so for in the case that I started with this coast plateau tough something that traveled 10 kilometers over water I suspect that probably what happened is the first stages of this density current traveled over water most of you might know is less dense than water so when pumice lands on the water surface it floats so the first stages of the eruption created a raft of pumice floating over the water surface and the next stages of the eruption that created this deposit that we see here traveled over floating pumice so it looks like a solid surface rather than the ocean okay, what I didn't show you in the posters that when particles impact the bottom of the flow over which they're traveling they can resuspend a large amount of mass to the extent that the runout distance of these density currents which is one of the key questions we would like to answer can be increased by an order of magnitude because you're adding so much mass to the flow okay, any questions about these boundary conditions and what happens at the base of density currents? yeah excellent question, we'll do that next yeah, good question so in that example so no, we have two size particles they don't change size maybe this afternoon we have more time allocated to the lecture I'll show you how the size evolution changes and how it affects the mechanics something I didn't point out is you know in a way the point of these equations that we're deriving and doing these simulations is to probe what the physics is that's going on and it goes to trying to reproduce any specific simulation but we can allow these kinds of processes to change if we like to interpret real field data and when we do that of course we can assess whether we're capturing the right physics in the model but not for the examples I showed you other questions? yeah, yes, okay so at the beginning it was just it was all pumice particles but once you get down to a certain size they can no longer fragment in the same way they can be scratched or abraded and so the rate of ash production changes so it does depend on size okay, so the last question is connected to that water substrate that these flows are traveling over I didn't emphasize the fact that these density currents are hot and the reason temperature matters is one of the questions we'd like to answer is how far these density currents travel as they propagate they're in training air heat is transferred from the particles to the air the air heats up it expands at some point the average density of the particles plus the gas is less than the ambient air these currents rise vertically and that halts their forward propagation and that's why when we add mass to the density currents they travel so much further we add mass their density goes up and they continue to propagate so temperature matters in these density currents because it affects their buoyancy and for the special case where these density currents reach the ocean that third phase becomes interesting or relevant the liquid water and if you heat up liquid water enough it undergoes a phase transition from liquid to steam and there's a huge volume expansion that accompanies that transition and a huge volume expansion may have big consequences for flow mechanics and so what we're going to do now is look at what happens when a density current enters the ocean and we'll be interested in the following three questions how much steam is generated how quickly steam is generated and last does it matter and so now we're getting at the third component of these conservation equations we looked at conservation of mass when particles interact conservation of momentum when they interact now we're interested in conservation of energy when particles interact with each other and their surroundings on the left is a schematic illustration of our water surface so that's air and there are various particles in our density current and they exchange energy with their surroundings in three different ways in three different settings in box C they transfer energy with the surrounding gas so we can go into the lab once again and measure how energy is exchanged how heat is exchanged between particles and gas they can also do the same thing when they're surrounded by water and there's a third case that turns out to be kind of special when they're floating at the water gas interface and to illustrate why this is probably the best chance I have today to explain why particle scale physics really matters let's consider two special cases we take a really hot particle these flows may erupt at say 800 degrees celsius so by the time the flows reach the ocean they may have cooled to 400 or 500 degrees celsius take that hot particle stick it completely surrounded by water some of that water will turn to steam because water boils at 100 degrees celsius but because you're completely surrounded by water those vapor bubbles will recondense in the colder water in box 3a have we released any steam to the atmosphere we haven't the steam recondenses in the water and so we have no contributions to big volume expansion or energy exchange to the atmosphere and in fact when we solve these equations we have to discretize space and time and we have some volume over which we're going to be averaging or computing certain properties like temperature if we would like to generate a finite amount of steam in this box which may represent a resolution of a numerical simulation we would have to heat all the water in this box up to 100 degrees celsius ok so now let's consider what happens in box 2 the hot particle sitting at the water surface right it will start boiling some of that water where is the steam going to go back into the atmosphere even though we're only boiling water over a very small length scale smaller than the particle itself and so even though the water temperature in box 2 has not reached 100 degrees celsius we will have a finite release of steam into the atmosphere right so there are processes that occur at the scale of individual particles that are very difficult to capture at the scale that you typically will discretize or solve differential equations ok so the way in which we characterize steam generation at the scale of individual particles is very similar to the other experiments I showed you we simply take a particle we heat it up, we put it on water and we measure how much steam it releases and the speed at which that steam is released and so we can what I'm plotting here is a massive steam release as a function of the thermal energy of the particles and this is steam release to the atmosphere the white symbols here are particles of pumice that float on the water surface the black ones are particles that are dense glass, they sink and so the steam they make recondenses in the water ok we can also measure how long these particles float at the water surface so the time scale over which they're releasing the steam and by doing so we can determine an expression I call it R once again which describes the rate at which steam is being generated and liberated to the atmosphere so we can go once again to those governing equations I showed you several times before conservation of mass, momentum and energy where our top equation is for water we have a conservation equation for mass of water, momentum of water the next is for steam and the third is particles and so we can understand what's going on here conceptually as well if particles transfer energy to the water then that water is going to boil and become steam this becomes a loss of mass for the liquid water equation and a source of mass for the steam equation and similarly as mass is exchanged from liquid water to steam there's going to be energy exchanges and there's going to be momentum exchanges and every expression you see in these boxes we have to determine experimentally by doing experiments of the scale of individual particles so I'll show you one example again it's similar to the others we have a region where a density current is going to travel left to right this time I will let it go down a slope and then reach the ocean we pick an initial velocity and particle concentration similar to a typical power-classic density current and actually I will compare measurements with a specific case there was a density current that entered the ocean at the island of Moserat in the West Indies in 2003 and this will give us a chance to compare the numerical simulations with a specific example okay so what we're doing here once again is looking at a cross-section through the density current so vertical position on the top horizontal position on the bottom this is their slope down which the density current is traveling and on the top I'm showing you the spatial distribution of particles in space where again particle concentration is the color red is high, blue is low and it's a logarithmic scale now we have two cases two example simulations shown here and everything in these two simulations is exactly the same and that we have the same conservation equations the only difference is that in the case on the top we allow for the fact that steam is generated at the scale of individual particles and that steam can be liberated to the atmosphere in the case on the bottom we allow for what I call mean field steam generation that water can convert to steam if all of the water at the spatial scale that we resolve the simulation reaches the boiling temperature and becomes steam okay so on the top then we're accounting for the physics at the particle scale on the bottom we're leaving some of that out and these two pictures look different don't they? on the top what's the big difference? the density current is much thicker, right? it's greatly inflated and that's because when the density current reaches the ocean mass energy is exchanged from the particles to the water you generate steam the steam increases the pressure and that expands the density current and in fact the pressure increases to the point that some of the mass that enters into the ocean goes back on land in an uphill directed density current generated by the high pressure from making all the steam when the current reaches the ocean and I did not plot on here velocity for you but basically the bottom of the current is going downhill the top of the current is going back uphill because of the steam generation so I picked this particular example and we investigate in fact this particular flow because of an interesting observation made by Edmunds and Heard after this particular eruption on the right is a map of the island of Moserat at least the small part the density current in this case was produced by the collapse of a lava dome this is one of the two ways we make these power-classic density currents that traveled down a valley the density current reached the ocean where my hand is is the shoreline and what they observed after this density current is that trees were knocked down in the direction indicated by the arrows implying that there was a blast-directed landward from when the density current reached the ocean from other observations the charring of the wood they also inferred a temperature as well and in this from looking at the deposits outlined by this dashed line they could determine how much mass came back on land the field observations were that about three quarters of a percent of the mass of the flow came back on land in our numerical simulations we find similarly about 0.6% of the mass of the flow comes back on land I guess the key point of this comparison between the observations and the simulations is that physics that happens at the scale of individual particles have a consequence for the large scale dynamics and that's where I'm going to summarize I guess we still have one minute left the point of today's presentation was to examine some of the physics of power-classic density currents which are mixtures of particles and gas and they're hot and the starting point was and my premise was that much of the key physics happens at the scales of individual particles mass exchange when particles collide momentum exchange between particles when they collide or the substrate over which they travel mass exchange between the density current and the substrate that underlies them or energy exchange between particles in their surroundings, either the substrate or the surrounding gas this is very tricky because the physics is happening on short time scales at short length scales we need to figure out how to incorporate that kind of physics into large scale simulations this is the basis for what we call continuum mechanics where we use kinetic theories to describe how atoms or molecules interact with each other we can drive equations that describe how gases work or how fluids flow here essentially we have a variety of interpenetrating continuum and the interactions happen at a slightly bigger scale what sometimes people call the mesoscale so smaller than where the continuum might apply but bigger than the atomic scale nevertheless we can still characterize in my case I did this experimentally for illustration purposes what happens at the scale of individual particles we can build up models for what happens at those small scales incorporate them into large scale numerical simulations to look at the consequences of small scale physics on large scale physics and I picked the three examples today as illustrative examples in part because the large scale phenomena that we see were almost entirely driven by the small scale physics the last example being the most recent one we looked at where the energy transfer to liquid water creates phenomena that would otherwise not be seen so last and to end 45 minutes is not enough time to do justice of course to the rich topic of the phenomena associated with explosive eruptions just a couple months ago there was a review paper that came out in the annual reviews of fluid mechanics by Joe Dufek on this topic and I think it's a great resource to learn more about how models are developed including analytical models as well as numerical simulations so thanks a lot for listening we have time for more questions I'm sure