Key Note Lecture: Why is the desert not flat? The interesting physics of windblown sand.
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Leibniz MMS Days 20187 / 20
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Mathematisches ModellComputeranimationZeichnungBesprechung/Interview
Transkript: Englisch(automatisch erzeugt)
00:00
Stefan for the introduction and for the nice invitation also yesterday to the Conference dinner and I also had the opportunity to see some really interesting talks yesterday already. I welcome you back and Well, here's the question. Why is the desert not flat? Maybe you've thought about it Probably most of you have already seen sand dunes somewhere and maybe on pictures, but maybe also in real life and
00:27
Well, where do they come from how do they form and and these kind of things I want to discuss now Here is my main collaborator Marc Lemmel. He was a PhD student now for a couple of years in Leipzig here with me and he's now finishing
00:47
Here is some other thing that we have some collaborators in Israel This was a JIF project a project funded by the German Israel German-israelian foundation and That allowed us to go to the desert and also look at the dunes and the ripples and study them and cut them and so on
01:08
Yeah, so the desert is often perceived as threatening like here in this very old quote from a Chinese writer Who thinks that?
01:21
Desert is really bad and you shouldn't go there But Other people might perceive it also as interesting and scientifically fascinating Here is a quote from Ralph Bagnoldt who is really the founder of the field of quantitative studies of dunes and moving sand and
01:43
He's really emphasizing a lot the Fascinating Structures that you observe in the desert and that really make you wonder how how these beautiful shapes come about and move around
02:03
From well, okay from from very simple Mechanisms we come to the mechanisms in the moment. Here is oops. So, okay, here is a bit what people have done Well who felt threatened by the desert so here you see there is a road and
02:22
People don't like it if the dunes move on to the road. So here they have built a particle accelerator, so it looks like a hut or a Little house, but it's really supposed to speed up the flow so that the dunes move faster across the street Didn't work so well, so they went back to this method
02:44
Which they have to use a lot there they dig out some diamonds in the desert and they want to bring them to the sea to Put them on the ship on the boat and then they need to clean the the roads That is another hazard in the desert dust storms
03:03
But there you can also maybe see that there is a positive thing about it as people here from the tropos know very well Dust from the Sahara is very important for many ecosystems in particular for the Mediterranean, but also these
03:21
Dust clouds they move very far. They move to America and they you find that they fertilize some regions even in the United States, so there is a Positive and negative aspects of that and here you can also maybe see a positive aspect
03:41
Deserts can produce sand deserts sand dunes can produce nice landscapes. So that is an overgrown desert photo that I took in New Zealand, but Something similar is probably well known to many of you those who come from Berlin They live on such a desert and in fact, I also live in Berlin and my house is on top of such a dune
04:03
so But it's not that well visible anymore because people have a lot of houses on top Yeah, you can also wonder about Dunes in the context of extraterrestrial remote sensing you could say, okay If you understand how these dunes form maybe we can learn something about the conditions on Mars without really going there
04:26
By just watching the dunes and then deducing what's going on there Well, okay, so Let's see. Where where do they come from? And what are they? Made of well, really you need only two ingredients. So it's pretty straightforward
04:44
we need sand and we need wind and Well sand okay, it's not all this everywhere exactly the same but still if you go to a beach you find sand Here in Germany or you go in California and it's kind of the same sand more or less
05:03
yes, so it's recognizable as a characteristic Well form of matter that pops up almost everywhere and it's a bit funny You know whether there are differences in composition of the grains. It's not all this quartz it could be some other stuff and so on but it's it's a widespread phenomenon you find it everywhere and
05:26
You could wonder why yeah, why is this so such a Widely observed phenomenon and and in fact this has to do with the transport So it is not independent of the question. We are asking here
05:41
Well wind is also all this the same in another sense It's it's turbulent and that means it's self-similar. So you find Structures, but you find the same structures all over a wide range or really huge range of scales So it isn't simple, but in a sense it is very uniform is very
06:09
It's very Very much the same on In all situations you could say and In a sense then these two ingredients are
06:23
Well, not simple, but but they have some hidden simplicity definitely here is the self-similarity and with the grains is Okay, you have just a single type of particle many of them So it's not too complicated after all it could be much more complicated
06:41
But still I want to show you that both of these phenomena are able to give you very Downton Downtonly complex Phenomena like here this avalanche on the on the downwind side of the dune
07:02
If you want to simulate something like this on a computer Which I wish you good luck So that is sand alone Just say I'm just send no no wind yet really crucially involved here It's just an avalanche going down and you see this is really
07:21
pretty complex already of course if you add the wind doesn't get any simpler and In fact here is some wind on the back of the dune throwing the grains here on the slip face where they where they go down in these avalanches and Oops
07:40
So sorry that was one too far. So if you add the wind, let's Click again Jumps all this too. Maybe I try here again Okay, so if you add the wind you get this kind of streak like
08:05
Motion of Sand over a here is a a wet sand surface a wet beach so to speak or solid beach where you can drive thoughts over the car and You see how the sand is transported by the wind
08:21
So that's what really happens if you add the two things together And this is really the process which creates all the structures in the desert And you can look at it on a more microscopic basis Or particle based
08:42
Description like like here in this movie Produced by a collaborator of us together with the BBC and that should start Okay So there you see a movie of this So called saltation process of the hopping of the sand so now you know really everything
09:01
even on a very detailed level and Now we should be able to answer the question Why the desert is not flat All the all the necessary ingredients are there and so an interesting aspect you see here is okay
09:23
You you form these dunes definitely in the desert, but on top of these dunes you see these ripples And you could ask well. Why do we get dunes and ripples? Why don't we get like could be something else or Why are there these small things and then the big things and apparently nothing much in between?
09:43
So well probably to answer this question is not enough to stare at the movie I showed you or the other movie before or whatever. I mean it will not From looking at that you will not immediately say aha. That's why we have ripples and dune so
10:01
Probably we have to do some mathematical modeling so or some physical modeling and there are many many many different ways How people approach this problem so you can say well, we have turbulent wind and the wind is blowing over these Sharply edged structures so quite probably we get flow separation now. We got a lot of
10:22
Interesting flow physics here And that's what people who have a big computer would do with it So they say okay, let's do direct Navier-Stokes simulations, or let's do a large eddy simulation or something like that So that's beautiful, and it's very impressive
10:42
But okay, I'm not I don't have a stanford supercomputer But there is this poor man's supercomputer here Which is called a nepka that you also find on the beach or in the desert so what you see here is a bit of Some some grass here, and the wind is coming from the left
11:03
And so you see what happens behind the grass you have some flow separation exactly as this movie shows you and This is where the sand is dropping out of the wind because when the flow separates like here you get very low wind velocities So the sand is raining out of the wind
11:22
Sand is first moving with the wind and then it's raining out and it's accumulating here and so if you want to know how this Stagnation zone behind such a backward-facing step looks like you can also use this poor man's supercomputer To find out what it is
11:42
And there are many things in between in fact so on my iPad. I have a App called wind tunnel Which can also do this but the engineers if I show it to them they are Not very amused because that is not science here
12:04
That is an app that really uses techniques that are produced for the movie industry Where people need to do animations quite often nowadays and for for the movies And so they need flows and flows have to look realistically
12:21
Because otherwise the audience would leave the cinema If you want to sell them a big waterfall and your hero has to jump down or something if the waterfall doesn't look realistic Then people don't like the movie So they face the problem of producing a realistically looking but not scientifically sound
12:43
animations of such flows and in fact there is not a very strict distinction between all these things as you maybe know if you have Well, I'll show you this here. Maybe you know if you have Read the book or seen the book by Galavotti about
13:04
Hydrodynamics Where he writes That basically nobody knows What these simulations do because there are no Proofs really that show that you can you know for general conditions
13:22
Really simulate the Navier-Stokes equation And Well, here are some grain scale simulations That people have been doing recently and so you see Simulations are definitely useful in this field at least if you want to make these small structures the ripples
13:41
So here you see some ripples that were produced on the computer and here you see how the grains are jumping and these Models that are used here are very simplistic They make many approximations in particular this these spheres that are jumping here are not very hard grains They are relatively soft and so on so
14:02
But it's done. Okay, you can do something for large dunes. It might be with billions of particles inside. It might be a bit different the situation Might not be that good and maybe there you see that there is a reason to use more coarse-grained Modeling and theory instead of just brute force simulations
14:24
Okay, here is again the edge of a dune at the slip place here here at the avalanche is going down here You see the sharp brink and the ripples on top Okay So here you can still you can still claim the price if you have something useful to say about this equation here
14:45
You can get a million dollars it was claimed once by a Mathematician, but then okay people found out that she had a error in a proof of a previous theorem on which she built to To claim the million dollars and so she she didn't get it. Okay still around for you
15:04
Good. So what really matters if you want to model these things or if you want to do fake Flows for for the movie industry is you should not violate any fundamental physical principles and in fact, we had
15:22
two very beautiful talks yesterday in this room just before and after the the early morning coffee break Where this point was really made very very clear and I really enjoyed these talks a lot And so there are some structurally robust things that that you never should violate and these are symmetries and the
15:47
ensuing conservation laws So if you have such a symmetry like the gradient or the divergence of the velocity is zero. Yeah, then You don't worry about the gradients of the pressure That's what we learned yesterday for instance
16:02
Or if you have the second law, you shouldn't better violate it if you if you want to cook up constitutive equations for for rheology But for me the It matters in a sense, especially the other way around because I mean as long as you don't
16:23
Don't violate these fundamental symmetries You can have big errors and the people in the audience will not leave your movie if you show them An animated flow and that's very good news So it means that you don't really have to be super super precise and you can still get out not only
16:43
Reasonably looking but even I would say scientifically valuable things But in the in the in in the opposite case if any Symmetry is violated even by a very small amount. That's something you must not neglect
17:01
So you can neglect details, but you cannot Neglect details that are structurally critical, especially you cannot You cannot neglect details that Are in conflict or they break the underlying symmetries here And that's what we really need for the for the dunes and and the ripples and and everything
17:25
because there is an symmetry breaking involved here it's a turbulent symmetry breaking spontaneous symmetry breaking and now we have to understand that's the reason why the desert is not flat and Then the desert is not flat but it could look fractal or it could look much more wild than it really looks
17:45
and so there is another thing there is a broken scale invariance in the problem and in fact, really a Mesoscale emerges here and that prevents that it looks Completely wild that explains why there is only big dunes and small ripples and nothing in between
18:03
and then there is another aspect sorting that somehow again breaks this rule and Leads to some structures that shouldn't really be there but are there and that we have only explained very recently. So in fact the the paper will only
18:20
Get out next month or so Nature physics and if you want to look in the literature, there is something in the abstract book I quoted a bit of the work we did Okay, so here's the first ingredient this spontaneous symmetry breaking in turbulence
18:43
So what really happens here? I sketch it for you and I don't show you so many equations as in other talks But here is one equation coming so Here is the wind blowing over some height profile H of X and
19:02
Here is what a Analytical boundary layer calculation for this problem tells you that's a very old work by I forgot to put the the reference by hunt and co-workers Cambridge mathematician applied mathematician hunt is Done in in the 70s 80s and so so for many years or even decades. He worked on this problem
19:26
Still you shouldn't take it too seriously, but it's a very simple simple thing that that he tells us namely the the the perturbation here of the shear stress or the the wind speed you can say
19:43
by such a Such a hump is well there's first is the Bernoulli effect that all of you probably have seen in school Yeah, if if the flow goes over such a hump It's a constriction basically in the flow So the speed has to go up above the hump and that means okay
20:02
You have a bit of stagnation here when you have a speed up and so it looks like this That's the Bernoulli effect and you see if the hump is symmetric. This is also symmetric and there is another Term here it comes from coarse graining the Navier-Stokes equation and It comes from turbulence. That's the Reynolds stresses and
20:24
This term is funny because here you see it breaks the symmetry if you put the two together you get a broken symmetry of the flow over a symmetric heap And That means if the wind speed goes up here but goes down at the top of the heap
20:45
Top of the heap and we've seen that before if there is sand carried by the wind if the wind speed goes down Sand will rain out. So here it rains sand on the top of the heap so the heap will grow so we have a growth instability obviously and
21:02
so any small perturbation will start to grow and and you should get a very rough and wild desert as much as you get a very wild and rough sea if the wind is blowing over the water. Okay, so you see an interesting thing here
21:21
So why this is again, I mean, I wouldn't put my hand in the in the fire for that but but but in a sense I would also because We should forget these coefficients that are hard to calculate and probably dutchy The calculation is probably not super reliable, but there is something here. I mean first of all, this only depends on the
21:46
derivative of the height profile and that makes a lot of sense. If this wind is turbulent and self similar and fractal and scale free then it should not matter about the absolute height. So it should really only depend on a dimensionless
22:03
object which is the spatial derivative of the height profile and then you see okay this is essentially a derivative and that is kind of another derivative, a smeared out derivative that comes from the pressure of course, that's the Bernoulli effect. So it's a very simple structure, but I believe it let's say even though the whole calculation is
22:26
well, you could argue a long long time about it mathematically speaking. Okay, so that's what we have. We have spontaneously broken symmetry from turbulence and from the wind flow and that makes it
22:46
gives you sand raining on the top of a heap and that's why you can have dunes. So then we could ask well are all wavelengths unstable and do they all grow and apparently as we already said it's not
23:03
the case. There are these very small structures and there are these huge dunes, but there is not so much in between. So why, what is going on here? There's some other ingredient in the problem and a related question is are all dunes the same?
23:21
You know if it's just turbulence and this everything is scale free then all the dunes should look the same at least if you have let's say the same wind conditions and so on which you never have in practice. So if you look at the field from above here aerial photograph or Google Earth in fact, then you you see okay, they all look a bit different, but that's because the wind is not blowing everywhere in the same way and descent
23:45
availability is a bit different and so on and so on. But if we would zoom in on a nice specimen, a nice example, and then another one they really should all look the same, but that's not the case.
24:03
So if you look at these dunes and and study them in detail and compare different ones and that's something what that was first really systematically done by Gert Salomon who was a PhD student in Paris many years ago when I was a postdoc there around 2000.
24:22
And he was sent by his supervisor Hans Herman to the desert to do these measurements and compare systematically the dunes and here you see he's working together with some geologists. Everybody very funny-looking and what he did is then he he got this data for the structures and then he looked at cuts through the symmetry plane of these
24:44
dunes and here you see many dunes or cuts through the symmetry plane and he then tried to rescale them to superimpose them on a master plot and what he discovered is quite funny. You can do this, but there's something strange because you have to rescale asymmetrically. So you rescale the
25:06
the x-axis differently from the y-axis or the length differently from the height and you see that this has been done here because the slit phase really always has the same slope in every dune. That's the angle of repose. It's a critical angle where the avalanches go down and so these slopes should all be the same, but they are not because
25:26
you need asymmetric rescaling or affine rescaling to superimpose these structures. So there is a length scale involved and a small dune looks different from a large dune where a small dune might be
25:40
20 meters long and a large dune might be 50 or 70 meters long. So why is 70 meters or 50 meters long? Why is this big and why is 20 meters or 10 meters small with respect to what? That's the question. And well, the answer is obvious. There is only one scale in the problem and I showed you that before. It's the grain.
26:04
It's the sand grain. Well, that's really tiny. 0.2 millimeters. Yeah, 250 microns or something like that. And in fact, this is really well defined and that has to do with the sorting that I will mention again in a minute.
26:20
Because if wind blows over the desert, as we have seen, the small grains are carried away. They are dust. They go to the Amazonas and fertilize the vegetation there. And the bigger grains, they just stay behind. They're not moving at all. So if you have transport by wind over a long distance, you get
26:43
more and more well-defined sand. That's how the phenomenon of really well-defined sand is created in the first place. And so there is really this very well-defined scale. But it's really tiny compared to a 50 meter or 20 meter dune. So why does the dune care 50 meter or 20 meter if the grain size is
27:03
200 microns? And the reason is that there is an emergent scale that comes from the hopping of the grain. And so the individual grains, as we saw in the movies, they are hopping in this saltation process. And so this hop length is, of course, more on the 10, 20 centimeters up to meter scale.
27:25
And that is the emergent scale that really interferes here. So what technically enters here is a length scale that we introduced together at about the same time in a paper, and it's called the saturation length.
27:42
And I will explain it a bit. So this is the length that you need for the wind to really pick up the grains. Yeah, if the wind moves up here, and first maybe there are even no grains here. But then also here the wind speed is increasing. So the wind has to really erode
28:02
grains on the whole windward slope. And so this doesn't work immediately, but there is some hopping involved and some population balance, so to speak, of grains. The grains that hit the ground splash new grains and so on. And that is how this length scale emerges. And it's kind of the really most enigmatic and
28:23
and much most debated scale and problem in this field to understand the saturation length. But essentially you can easily understand why it is so large. It is given by the grain size, of course. It's the only elementary scale in the problem.
28:40
But then there is the density ratio between quartz and air, which somehow helps you to scale it up. That's what is behind these long hops really is mathematically speaking or in terms of of the formulas. There must be the density ratio between quartz and air and that gives you these large jumps and this meso scale. So that having said that I mean it should be immediately clear to you that if you
29:07
go to if you go to submarine dunes then you will not have such a meso scale and this structures will be will be much smaller. And that is indeed true. I think this comes only later. Sorry, I have
29:26
here it is, okay. So here you see an animation of a small heap growing and you see that the slip face also emerges. So this is a consequence of of this
29:43
characteristic length scale is that you have a minimum dune size and in particular you also have a transition here in the shape. You create this slip face only for the larger dunes. And it depends on how much influx you have and many things but the physics behind is this emergent scale.
30:03
So in here I've sketched the idea. So you remember this plot where we have the profile and then we have the wind speed in red that goes over the that you have above the above the structure. And I said it rains on top and that's why it grows. Now if you have a
30:23
saturation gradient or this meso scale that kind of shifts not the wind speed but really the sand transport with respect to the wind speed. So the wind speed goes up and down like this but the sand transport doesn't react immediately it reacts with a lag. So that's really the problem.
30:42
So you shift the the reaction of the sand slightly with respect to the reaction of the wind to the profile and that's how you destroy your nice symmetry breaking and that's why small structures cannot grow and only large enough structures where this small shift is not
31:01
big enough to undo your symmetry breaking, your turbulent symmetry breaking. That's why only this large structure can grow and the small one has to be eroded away. And you see here a photograph that you can really make small dunes underwater because there you don't have this density mismatch between quartz and the driving medium. Water is equally heavy more or less than
31:26
quartz as quartz and then you can have very small dunes. Well, let I skip maybe that's if you those who like the equations can ask me later, I think.
31:40
So what we've seen now is that there is a really a characteristic scale and that if you think about it a bit more explains that you can only have structures that are kind of below this characteristic scales or far above and so it explains why there is a wavelength gap and why there can only be these large structures and then the tiny structures on top and nothing else.
32:04
But there is one catch to this argument and and that's what kept us busy for a long time. And so there is a counterexample and that's mega ripples what people call mega ripples and here you see a picture you see small ripples here but then you see also these bigger ones.
32:22
So that's mega ripples and mega ripples shouldn't really be there according to what I said. And the reason why they are there you can see here. This is a cut through a mega ripple in Israel where we went with our collaborators to the desert and studied them and you see there is something strange here.
32:40
There's a sand, but there is some cores of grains on top here. So there is some sorting involved and there is the special grains are obviously needed here to make these structures. And so we wanted to understand this a bit better because the geologists always told us, you know all these
33:00
heavy grains they always accumulate on top of these mega ripples and so on. And so I never believed that. I said no, no, no, this is not how it works. It's really the heavy grains that make the mega ripples. So first you need to accumulate bigger grains and this is done by sand sorting and that is what I want to explain you now for the last five minutes or so.
33:25
So people do indeed find if they took, well for a long time already, they took sand samples from these mega ripples and they find very strange grain size distributions. Not what I argued you should see in the desert and you should see for the dunes.
33:41
It's not a very sharp monomodal distribution. It's more like a bimodal distribution and that's really what we should explain. So why is there small grains and large grains and how does this all come about and that's what I want to say now. Well, the wind is really sorting these grains and that's how the mega ripples can grow and here is how it works.
34:04
If you have erosive conditions, you can only, wind is not too strong, let's say, but you can, small grains can hop, larger grains can't hop. What do you get there? If you don't have too much influx, you will get this. So you erode away the small grains.
34:23
They go to the Amazonas, say, and the big grains will accumulate at the surface and you can set up a simple equation of course that describes this process. And then once you have these larger grains on top, you can really make mega ripples out of them. But what is the mechanism? And what we suggested is very
34:44
heretic in the field because we suggested that these structures that form from the larger grains are really very small dunes and they are called mega ripples because people think, well, they look almost like the ripples. They are similar in size.
35:00
But in fact, we can prove with a lot of data that we collected from the literature that the morphology and the dynamics and everything can be exactly mapped onto that for large dunes. So what we suggest is really that these these mega ripples are mini dunes, so to speak, made from these coarser grains.
35:22
So here you see these how these bimodal grain size distributions emerge. Start with a monomodal distribution and you have a wind that is not strong enough to pick up all the grains, but just the smaller ones and the bigger ones kind of then accumulate at the surface.
35:41
Of course that oops that here. Okay. Yeah, here is a nice picture. Once you know what you're what you should be looking for, you can really find it. So these nice little mega ripples here really kind of prove the idea that they are mini dunes made from mega grains. You see the big grains here.
36:04
They also have a slightly different color and you also see that they look a lot like the barkhound dunes I've shown you previously. So the implications of this are very far-reaching because I mean the wind is not always blowing in such a way as to accumulate these grains. Definitely it depends now a lot on
36:25
on this sand sorting, but the sand sorting depends a lot on the wind conditions because which grains you accumulate depends of course on the strength of the wind. In the wind tunnel you could argue, well, we could have very well-defined wind conditions and then we could accumulate a certain grain size here
36:45
and then we could make these dunes from them. But in practice the wind is changing. The strength is going up and down all the time and once you have a very strong storm this thing goes very quickly away again and and then maybe comes up again at a different place and so that's what it really looks like if you have
37:04
changing wind speeds. So that shows you that these structures are very contingent on the wind conditions on the intermittent turbulent fluctuations of the wind and they are by far not as stable and robust as dunes and these smaller ripples.
37:21
And that brings me to the end. So we kind of ran us a little simulation of these ideas here and we have some we create some intermittent wind fluctuations. This is the gray spikes here show some storms and then okay, the blue stuff here is telling us how much
37:45
do I decorate the surface with these coarser grains and you see if all this if the blue stuff comes up that means that it's nicely decorated. The surface is nicely decorated with the bigger grains. And then you can grow these
38:02
mini dunes from these mega grains and that's the red line showing up how the length scale of the or the size of these mega ripples evolves. But then there is a very strong storm you destroy the sorting and the whole thing is gone again. And that's really what people see in the in the field after a very strong storm
38:20
they go to the desert and all the mega ripples are gone. And then you can imagine how this goes on over the years and then you see okay this is a very sensitive very contingent structure that in principle encodes the whole climate history of the last years or so. And if you could read it, you could learn a lot about
38:42
what the weather was like for over a long time. Right, so that all leads to such a phase diagram where you can say, okay here is the grain size ratio between the smaller and the bigger grains and here is the wind strength.
39:02
And this is only a small pocket really where these mega ripples can grow and are not destroyed by storms and in some other regions, there is no sorting. They cannot be created or there is no transport of the big grains so they cannot be created. So there's all this so everything is destroyed in a storm. So you can only have a small pocket where they are stable, but they exist. You can measure them. I've shown you pictures.
39:25
They are there and now we understand, we think we understand what they are. We can study them in more detail and we can analyze data that makes sense and not just confuse us as it was in the past.
39:42
Well, that's the summary. So I tried to explain to you why the desert is not flat. So we have wind. Wind causes saltation of grains and the grains make ripples. But they also make dunes if you take into account this turbulent symmetry breaking and
40:01
I show you that the scale invariance is somehow broken. There is a mesoscale, the hop length essentially of these grains that gives you a size selection. So there's not any arbitrary structures grow but only big dunes and small ripples and there is one exception which are these mega ripples that
40:20
is sensitive to the sorting of the sand and therefore a very very special and very interesting and still very poorly understood structure and with this I'm at the end and I thank you very much for your attention, and I'm of course happy to take any questions. Thank you.