Key Note Lecture: Why is the desert not flat? The interesting physics of windblown sand.

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Windblown sand creates a distinct hierarchy of mobile landforms on Earth on some celestial bodies, ranging from tapestries of meticulously carved ripples to vast fields of shifting dunes. They are often perceived as aesthetically appealing, yet economically and ecologically threatening. But how do they form, and what determines their characteristic shapes, sizes, and migration dynamics? I will sketch three crucial physical mechanisms that govern this whole phenomenology: spontaneous turbulent symmetry breaking, broken scale invariance due to an emergent mesoscale, and aeolian sand sorting. Together they give rise to the notion of a forbidden wavelength gap between ripples and dunes and explain why it can (only) be inhabited by a peculiar bedform known as megaripples, which might actually be better characterized as mini-dunes. K. Kroy, G. Sauermann, H. J. Herrmann, Minimal model for sand dunes, Physical Review Letters 88 (2002) 054301. M. Lämmel, K. Kroy, Analytical mesoscale modeling of aeolian sand transport, Physical Review E 96 (2017) 052906. M. Lämmel, A. Meiwald, H. Yizhaq, H. Tsoar, I. Katra, and K. Kroy, Aeolian sand sorting and megaripple formation, Nature Physics, to appear.

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for the introduction and for the nice invitation also yesterday to the conference there and I also had the opportunity to see some really interesting talks yesterday already I welcome you back and well here's a question why so those are not flat maybe you've thought about it probably most of
you have already seen the sand dunes
somewhere and maybe of pictures but maybe also in real life and well where they come from how the formant and and these kind of things so I want to discuss No
and here is my main collaborator it a mark them and he was a PhD student now for a couple of years and I've seen here with me and he is now finishing here's some other thing that we have some collaborators in Israel this was a just project a project funded by the German Israel at German 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 yeah sold the desert is
often of perceived as threatening like here in this very old quote from Chinese a writer who thinks that a there's really bad in Yutian go there but other people might perceive it also as interesting and scientifically fascinating here's a quote from Mark Roth Bagnall is really the founder of the field of quantitative studies of students and of moving sent and they he's really emphasizing a lot the fascinating of structures that you observe in the desert and that really make you wonder how the how these beautiful shapes come about and moves around and from well OK
from from very simple mechanisms
it under the mechanisms in the moment years of so cares here is a bit but people
have done who were who felt threatened by the desert so here you see there is a road and people don't like it if it's move onto the road so here they have builder particle accelerator still looks like a hot seller a little house but there it's really supposed to speed up the flow so so that the dunes move faster across the street it didn't work so well so they went back to this method of which they have to use a lot there they dig out some diamonds in the desert and they want to bring them to the C told the mother ship that the boat and then they need to clean the the ropes that is
another hazard in the desert dust storms but there you can also maybe see that there is a positive thing about it is people here from the drop us know very well what dust from the start is very important for many because systems goes in particular for the Mediterranean but also by dust clouds they move very far they moved to America and the you find that they are 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 deserts can produce and deserts of sand dunes can produce nice landscapes so that is an overgrown desert of photo that I took in New Zealand but something similar this probably won't know until many a few of those who come from Berlin they live on such a desert and in fact I also live in Berlin and my houses on top of such a tube so but is not bad well civil anymore because if people have the of houses and yeah you can also I wonder
about dunes in the context of extraterrestrial remote-sensing you could say OK I see understand how the students for maybe we can learn something about the conditions on mars without really going there but just watching the dunes and then did you seeing what's going on there well OK so let's see where where they come from and what are they and made off well really
you need only 2 ingredients so it's pretty straightforward we need sense and we need wind and well Center OK he's not all this everywhere
exactly the same but still if you go to a beach you find Santa here in Germany or you go in California and kind of the same scent moralists so is recognizable as a characteristic but form of matter that pops up almost everywhere and it's a bit of fun you know whether there are differences in composition of the grains is not all this courts could be some other stuff and so on but it's it's a widespread phenomenon you find it everywhere and you could wonder why you know why is this so such 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 well wind is also
all this the same in another sense it's it's terrible and and the that means it's similar so will find structures but you find the same structure so over white range sure really huge range of scales so it isn't simple but in a sense it is very uniform is very and is very very much the same on in all situations you could say and in in a sense then these 2 ingredients are well not simple but that they have some hidden simplicity definately here's the self similarity and where the grains is OK you have just a single type of particle and many of them and so I C is not too complicated after all could be much more complicated but still I I want to show you that both of these
phenomena able to give you a very dancing and dauntingly complex phenomena like here this avalanche on the on the downwind side of the deal if you want to simulate something like this on a computer which I wish you good luck so that is stand alone just say just said no no wind gets really crucially involved here it's just an avalanche going down and you see this is really pretty complex already as course if you add the wind doesn't get any simpler in insect here is some went on the back of the dual of throwing the grains here on on the slip phase where they where they go down and these avalanches and so sorry that was 1 too
far so if you add the wind but think again jumps so this tool we trying to the OK so if you add the winter you get this kind of streak like motion of the of sand over 80 here is a a white sensor fizzle with speech so to speak our solid beach where you can drive for over the car and you see how this and is transported by the way so that's what really what happens if you add the 2 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 and or particle based
the description like like here in this movie produced by our collaborator of fast together with the BBC and that should start OK so there you see a movie Office of so-called saltation process of the hopping of descent so now you know really everything so even on a very detailed level and now we should be able to answer the question of why the
desert is not flat for all the all the necessary ingredients are there and so interesting aspect you see here is OK you you form these dunes definitely in in the desert but on top of the students you see these reports and you could ask well why do we during sent ripples why don't we get it could be something else over why are there the small things and then the big things and apparently nothing much in between as so well probably to answer this question is not enough to stare at the movie I showed you the the movie before or whatever and you what from looking at that you will not immediately say that's why we have proposed and doing so Berlin we
have to do some mathematical modeling sellers physical modeling and there are many many many different ways in how people approach this problem so you can say well we have turbulent wind and the wind was blowing over these sharply etched structures so quite probably we get of flow separation yeah of interesting flow physics here and that's what people have a big computer would do with it Salazar encouraged to direct Navier-Stokes simulations or let's do a large eddy simulation of something like that so that's beautiful as very impressive but OK I'm not I don't have a Stanford supercomputer but there is this poor man supercomputer year which is called an that cut that you also find on the beach or in the desert so what you see here is a bit of sometime grass here and the wind is coming from the last and so we'll see what happens behind the grass you have some flaw separation exactly as this movie shows you and this is where the sandis dropping out of the wind because when the flow seperates like you you get very low wind velocities so the Sanders' raining out of the wind Sanderson 1st moving with the wind and then it's raining out it's accumulating here and so if you want to know how this stagnation so behind such a backward facing step looks like you can also use this poor man supercomputer to find out what it is and there are many things in between insects so on my iPad I have today at cold
wind tunnel which can also do this but the engineers so if I show it to them they not very amused because that is not science here that is an app that really uses techniques so that are produced for the movie industry where people need to do animations quite often nowadays for for the movies and so they need flows and flows have to look realistically because otherwise the audience would leave the cinema and if you want to sell them big waterfall and you're a hero as to jump dollar something of the waterfall doesn't look that realistic and people don't like the movie so they face the problem of producing realistically looking but not scientifically sound of animations of such flows and in fact there is not very strict distinction between all these things as you maybe know if you have well
I show you this year maybe no if you have
read the book a lot seen the book by gonna what about it's that he writes that basically nobody knows what these simulations to because there are no proofs really that show that you can you know general conditions really similar to Navier-Stokes equation and well here are some of the grand 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 the small structures the ripples so you see some ripples that are produced on the computer and you see how the grains are jumping and these models that are used here are very simplistic they make many approximations and particle that this these spheres about jumping here I'm not very hot brains there of soft and so on so but it's done OK you can do something for large dunes it might be worth billions of particles inside it might be a bit different but that the situation it might not be that couldn't maybe that you see that there is a reason to use more coarse-grained to modeling and the theory instead of just brute-force simulations now OK here's again the edge of a dual monitor slip trace here here of the avalanches going down here you see the sharp and the report OK I am so you can
still learn you can still claim the price said if you have something useful to say about this equation here you can get the million dollars it was claimed wants by mathematicians but then pay people found out that she had arrow in a proof of a previous theorem on which she built a tool to claim that million dollars and so she she didn't get it OK still around for you so I was really matters if you want to model these things or if you want to do fake flows for a for the movie industry that is you should not violate any fundamental physical principles and in fact we had so very beautiful talks yesterday in this room just before and after the of the early morning coffee break where at at 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 at violate and these are symmetries and the ensuing conservation laws so if you have such a symmetry like the gradient or of it to the emergence of the velocity is 0 have then you don't worry about the gradients of the pressure and that's what we learned yesterday Frances or if you have the 2nd law you shouldn't better why elated if you if you allow I want to cook up a constitutive equations so for for rheology and but for me it and the in it matters in a sense especially the other way around because I I mean as long as you don't don't violate these fundamental symmetries You can have big arrows 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 reasonably looking but even I would say scientifically valuable things but in the core in the in in in the opposite case if any symmetry is violated even by a very small amount that's something you must not neglect so you can neglect details but you cannot neglect details that are structurally critical especially you cannot you cannot neglect details that in conflict or that the underlying symmetries here and that's what we really need for they for the dunes and and the rebels and it and everything because there is a symmetry breaking involved here is a terrible 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 and so there is another thing there is a broken scale invariance of the problem and in fact really a mesoscale emerges here and that prevents that it looks completely while that explains why there's only big fumes and small ripples and nothing in between 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 aren't there and that we have only explain very recently so in fact the the paper will only get out the next month or so nature Physics and if you want to look in the literature there is something in the abstract book but I as a quoted to that of the work we did but OK so here's the 1st ingredient is spontaneous symmetry breaking in internal lands so what really happens here sketch it for you and I don't show you so many equations as another talks about here is I 1 equation and coming so here is the winds blowing over some my profile facts and here is what they and let the goal of a boundary layer calculation for this problem tells you that's very old work by half forgot to put the the reference by Hunt and co-workers Cambridge mathematician applied mathematician hunters diamond in the seventies and eighties and so so for many years or indicates he worked on this problem as still you shouldn't take it too seriously but it's a very simple and simple thing that that he tells us namely the the the perturbation here of the shear stress or the the the the the wind speed you can say the FBI such a such a hump as well as 1st is the but Bernoulli effect that all of you probably have seen in school yeah if if if the flow goes over such it it's a constriction bait basically in the flow so this speed that has to go up of about the harm and that means OK you have a bit of stagnation year-end have speed up and so it looks like this as the Bernoulli effect and you see if the hump a symmetric this is also symmetric and there is another terms here that comes from coarse graining then the Stokes equation and it comes from turbulence that's the Ramos stresses and that this term is funny because I use it breaks the symmetry and you put the 2 together you get a broken symmetry of flow over a symmetric heap and and that means if the wind speed goes up here but goes down at the top of the heap the air top of the heap and we've seen that before if there's sand carried by the wind the wind speed goes down sand will rain out so here it rains sand on the top of the heap so that people grow so we have a growth and stability obviously and so any small perturbation world will start to grow and and you should get a very rough and why it's desert as much as you get a very wide and rust see if the wind is blowing up the water OK so you see an interesting thing here so why does this again I mean I wouldn't put my hand and in the in the fire for that but but but in a sense I would also because should forget these coefficients that are hard to calculate and probably Duchy of the calculation is probably not super reliable but there is something here and 1st of all this only depends on the derivative of the profile and that makes a lot of sense if this wind is tervalent and of self-similar and and fractal and scale-free and it should not matter about the absolute height so it should really only depend on a dimensionless object which is the spatial derivative of the high profile and then you see a K. this is essentially a derivative and and that is kind of another derivative of smeared out derivative that comes from the pressure of course that the Bonelli effect so it's a very simple structure god I believe it let's say that you can fill the whole calculation this well you could argue a long long time about it mathematically speaking OK so so that's what we have we have
so spontaneously broken symmetry from from from turbulence and and from from the wind flow and that makes it gives you sound raining on the top of of the heap and that's why it's where you can have dues so
then we could ask well our all wavelengths unstable and the all grow and apparently as we already said it's not the case there these very small structures and the suture humans but there is not so much in between so why what what is going on here there's some in some other ingredient in the problem and that that
that are related question is are old use the same you know if it's just turbulence and this everything scale-free than all the dunes should look the same or 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 at who Google Earth infect then you are you see OK they all look a bit different but that's because the wind is not blowing everywhere in the same way and the center of availability is a bit different and so on and so on but if we what's Suominen a nice so specimen a nice example and then another 1 there really should all look the same Dyer has 2 case so if
you look at these students and and study them in detail and compare different ones and that's something what that was 1st really systematically down by gets and was a PhD student in Paris many years ago when I was a post of their around 2000 and he was sent by his supervisor Hans-Hermann 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 that he he he he got this data for the structures and then he looked at cuts through the symmetry plane of these dudes and he's seen many
dunes or cuts through the symmetry plane and he then tried to rescale them to superimpose them on a massive plot and what he discovered is quite funny you can do this but there's something strange because you have to rescale isometrically so you rescale the at the 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 all this has the same slope and every unit does the angle of repose it's a pretty angle whether yet on just go down and so the slopes should all the be the same but they're not because of you need assymetric rescaling or are fine rescaling tools superimposed these structures so there is a length scale involved and small view looks different from a large you're small you might be 20 meters long and a large you might these 50 or 70 meters long so why is 70 meters or 50 meters long widest this big and why is 20 years or 10 years small with respect to what that's the question and that well the answer is obvious there is only 1 scale in the problem and I showed you that before it's the grain it's the sand grains well that's really tiny 0 comma decimal 2 millimeters in type 2 100 50 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 because if wind blows over the desert and as we've seen the small brains are carried away their dust they go to the Amazon us fertilize of their education there and the bigger brains they just stay behind they're not moving at all so if you have transport by went over a long distance you get more and more well-defined set that's how the phenomenon of really well-defined sand is created in the 1st place and so there is really this very well-defined scale but is really tiny compared to a 15 meter or a 20 meter deal so why does the due care 15 year a 20 meter if the grain sizes to microns and the reason is that there is an emerging scale that comes from the hopping off the grain and the so the interval grains as we saw in the movies they are hopping ends in the saltation process and so these hop length is of course more that 10 20 centimeters up to mirror scale and that is the emergence scale that really interferes here and so what technically enters here so is a length scale that we introduce together at about the same time in in in in the paper and it's called the saturation length and I will explain it a bit so this is the length of that you need father went to a really pick up the grain said the went moves up here and 1st maybe there I even though grains here but then also hear the wind speed is increasing so the wind has to really to grains on the whole winter at slope and so it that this doesn't work immediately but there's some popping involved in some population balance so to speak of cranes the rains that hit the ground splash new brains and so on and and that is how this length scale images and it's kind of the really the most enigmatic and and much of the most debated to scale and and problem and 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 of the problem but then there is the density ratio between quarks and their which somehow helps you to scale it up that's what is behind these long hops really is the right mathematically speaking or in terms of yeah of the formulas they must be the density ratio between courts and and that gives you the a large jumps in this measles can so they that's having said that I mean it it should be immediately clear to you that if you go to work if you go to submarine dunes then you will not have such a mesoscale and this structures will be but much smaller and that is indeed true I think this comes only
later sorry I have here it is
OK so he is the animation also small heat growing and you see that the slip face also emerges so this is a consequence of of this characteristic length scale is that you have a minimum due in size and in particular you also have a a transition year in the shape you create this would face only for the larger larger news and it depends on how much in flux you have in many things but that is the physics behind is this emergent scale so in here I've sketched out of the idea so you remember this plot here you have the profile and that we have built wind speed the new rat that goes over the the that you have above the above the structure and I said it rains on top and that's why it grows now should have a saturation gradient or this mesoscale that kind of shifts and not the wind speed but really they sent 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 act it reacts with the lack so that's really problem so you shift the the reaction of the sand sliding with respect to the reaction of the went to the profile and that's how you destroy your nice symmetry breaking and to that's why small structures cannot grow and only a large enough structures where this small shift is not a big enough to undo we or symmetry breaking it and symmetry breaking that's why only this large structure can grow in the small 1 has to be eroded away and you see here on of a photograph that you can really make small views on the water because there you don't have this density mismatch between quarks and driving medium water is equally heavy more or less than the courts as courts and then you can have very small dealings I
am at I skipped maybe that's the few those who like the equations can ask me later I think so what
we see 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 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 but there is 1 catch to this
argument and and that's what kept us busy for a long time so there is a counterexample and that's mega ripples what people call mega reports and you see a picture you see small ripples here but then you see also these bigger ones so that's mega ripples and mega rebels should 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 omega revolt and his role where we went with our collaborators desert and and study them and you see there is something strange sheared error does sand but there is some coarser 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 want to understand is a bit better because the geologist so this told us you know all do this this migraines they all this accumulate on top of these mega rebels and and so on and so I I never believed that as a minimum of this is not how it how it works it's really be heavy grains that make their own the make report so 1st you need to accumulate bigger grains and and this is done by sense sorting and that is what I want to explain you now for the
last 5 minutes or so so people do indeed find if they took it state well for a long time already they took sand samples from from these mega rebels and they find it very strange grain size distributions not what I our argued you should see in in in the desert and you should see for the dunes it's not a a very sharp on mole distribution is more like a by mole distributions and that's really what we should explains why is there's a small grains and large grains and how does this all come about and and that's but what I want to say now well the wind is really sorting these grains and that's how the variables can grow and here is how
it works if you have a rows of conditions you can only wind is not too strong let's say but you can small grains can hop larger grains con- top and what do you get there if you don't have too much in flux you will get this so you're rode away the small grains they go to the Amazon essay and the big rains will accumulate at the surface and you can set up a simple equation of course that describes this process and once you have these larger
brains on top you can really make a major rebels out of them but upwards of what is the mechanism and what we suggested is a very heredity in the field because we suggested that these are structures that form from the larger grains are really very small humans and they're called mega ripples because people think running look almost like the ripples they are similar in size but in fact we can prove that a lot of data that we collected from the literature that the morphology and the dynamics and everything is exact exactly mapped onto that for a large students so what do you suggest is really that these these mega ripples or June so to speak made from these coarser grained so you see these how these vinyl grain size distributions emerge start with a all distribution and you have a wind that is not strong enough tool tool and pick our ball the grains but just the smaller ones and the bigger ones kind of them accumulated at the surface of course that books that are
here OK I hear is and I said picture
once you know what your what you should be looking for you can really find it so these nice little mega ripples here you really kind of proof the idea that they are many dunes made from my grains you see the big rains here they have to have a slightly different color and you also see that they look a lot like the bark June such a you previously so the implications of this
are very far reaching because I mean that the wind is not all this blowing in such a way as to accumulate these grains definitely it depends now a lot on on this sense sorting at but this sense hoarding depends a lot on the wind conditions because which grains you accumulate depends of course on the strength of wind in the wind tunnel you could argue well we could have very well-defined wind conditions and that we could accumulate a certain grain size here and we could make the students 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 then maybe comes up again at a different place and so so that's what it really looks like if you have changing wind speeds so that shows you that the structures of every contingent on the wind conditions on the intermittent terrible fluctuations of the wind and they are by far and not as stable and
robust as students and and the smaller ripples or and that brings me to the end so we we kind of ran as a little assimilation of these ideas here and we have some we create some intermittent wind fluctuations without this is of the gradient of spikes here shows some storms and then OK we all the blue stuff here is telling us how much do I decorate of the surface with these coarser grains and you see if all is the blues stuff comes up that means that's it's nicely decorated the surfaces nicely decorated with the bigger grains and then you can grow these many dealers from these mega grains and that's the red line showing up how the length scale of the of the size of these mega ripples involves 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 they go to the desert and all the mega rebels are and then you can imagine how this goes on over years and did you see OK this is a very sensitive very contingent structure that in principle encodes the whole climate history of the last years so and if you could read it and you could learn a lot about what the weather was like the solution for for over a long time right so that
all its tools such a phase diagram where you can say OK here's the grain size ratio between the small and the bigger grains and here in strength and this is only a small pocket really well these mega rebels can grow and or not destroyed by storms and in some other regions there's no sorting they cannot be created or there is no transport of big brain so they cannot be created so there's always up everything is destroyed in the storm so you can only have a small pocket where they're stable but they exist you can measure the much showed you pictures there there and we know we can under no we understand we think we understand what they are we can study them in more detail and we can analyze stayed out of that makes sense and not just confuse us of as it was
in the past well it's a summary so I tried to explain to you why there's a is not flat so we have went and causes saltation of grains and the grains make ripples but they also make use of if you take into account this tervalent symmetry breaking and I show you that there's variance so somehow broken there is a mesoscale the hop length essentially of these grains that gives you a site selection so there's not any arbitrary structures girl but only big cues and small ripples and there is 1 exception which of these mega repeals that sensitive to the sorting of descent and therefore of a very very special and very interesting and but still very poorly understood structure and with this at the end and I thank you very much
for your attention and I'm of course happy to take any questions thank you