Lecture 3: Bed Forms

Key Takeaways

So these are these are the variables you'd have to take into account if you're going to if you're going to capture the reality of of bed configurations and and the usual flow flow depth, flow velocity, sediment size. The fluid density is important. Fluid viscosity is important. And then there's sediment density and gravity. Now, I have to make a few comments about The particles have weight. And that's the combination you the density and gravity that makes weight, right? But but also density fluid density sediment sediment density itself is important by itself. And I want to show you now uh See how lucky I am here. Yeah, okay. Um they act together. And obviously weight is important. That makes the sediment negatively buoyant. But particle density gives the particle inertia going through the fluid. So if you had a turbulent fluid, the particle tends to go by itself and not be affected by the turbulence. So uh And here's the thought experiment. Did I tell you about thought experiments? I love thought experiments. Uh Einstein loves thought thought experiments. His whole theory of relativity was based on some thought experiments. I saw Einstein once. What do you think of that? 1952 in Princeton. He was walking on a sidewalk near his home and I was sitting there in the car and I watched him walk by. >> [laughter] >> All right, so look, you're you're in a zero gravity spaceship up there in space and you have a big tank of water, closed in tank of water. And you have a way of shooting a particle into the tank and watching what happens with it. Now, the particle has no weight at all. But it's still the the it's difference in density still is important because it has inertia. And and if the flow in there were turbulent, uh you and you shoot the particle, it would try to take its own path not unaffected by the turbulence, right? And I showed you this. I think I showed you this. It's a reminder about what buoyancy is in the first place. And here's one of my all-time heroes, >> [snorts] >> Archimedes. Uh so rho s and g together account for the motion of the particle. We don't need to worry about the weight the weight per unit volume. Rho s and g take care of the weight per unit volume, so we don't need to worry about it. So what's what's most important for us are I think depth, velocity, and sediment size. And there are various ways of non-dimensionalizing. And this one I think is useful. This is different from the from the from the PowerPoint number three you had. Different in some ways, but anyway, there it is. So um we can we can use those three-dimensional variables uh flow depth, flow velocity, and sediment size non-dimensionalized. But what I'm going to do, and you can make a three-dimensional diagram out of it, section this way, section this way, section that way. And let me show you some results. Um It's non-dimensional, but the graphs that I'm showing you have a uh these variables are normalized to water to 10° water temperature. So that it all comes out nicely on the graph, and I'm going to make some more comments about that soon. Um so here's the sections. All the all the all the diagrams are normalized to 10°. I don't expect you to see a lot of this, but I'm going to show you the next slide in more detail. This is a flow depth versus uh see So what you see is for for for low velocities, there's no movement. Then you have ripples. Then you have dunes. Then you have upper plane bed. But these lines down here are for equal Froude number, Froude number about one. And and beyond that, you get antidunes. And if you made dunes way down here somewhere, you'd find that the anti the the dunes and the antidunes would interact with each other somehow, and I've never done that in the lab. I can't tell you what it would look like. This is one of my favorite slides. Um this is another section u versus velocity versus sediment size for this is for a flow depth of about 0.25 to 0.4 m. A lot of data. Almost all these data come from the laboratory. My laboratory, a lot of other people's laboratories. And uh it plots very nicely, interestingly I think. Over over for for for fine sediments, you form ripples and then they change to upper plane bed at certain point. I told you that already, I guess. Um For another range of sediment sizes about in here, ripples go into dunes and the dunes go into plane bed. But beyond about half millimeter there are no more ripples. Ripples don't form, only dunes. As soon as you go from no motion, you develop dunes. And the antidunes would be way up in here somewhere. This is Froude number one right here. Does that make sense to you? And I think I have a cartoon of this in your in your notes, which shows this in nice. And let me go back here. What I like about this is you can fit a curve, a very natural normal curve with no no scatter. It really works. Which means we're doing something right. >> [clears throat] >> I have a colleague named Dave Rubin. We've been together for a long long time. He he picked up on this and he and what is Steve McCaul? Uh made a this little complicated, but this is the three-dimensional graph that I just told you about. But but it it extends up to to considerable depths. And you get stuff out in here. These are sections through that graph. And you have to imagine volumes volume volumes of exist existence fields. And uh as far as I know, nobody's improved upon that, which seems strange because it's really important to think about greater flow depths, not just the typical flow depth like this in laboratory channels. It's seldom greater than about a meter because you have to have an enormous enormous channel to make uh different things. All right, so um now we're limiting ourselves to for water on Earth gravity and sediment particles, you know, quartz density sediment density and and water. Um but uh you can easily adjust this for different gravity. And I'll make a few comments pretty soon about about Mars. But you know, there are zillions of planets out there in the universe that that would have would have flowing liquids moving sediment particles under some gravity. And there are some constraints. There aren't too many liquids uh that have different densities and viscosities. I mean, you can you can use motor oil and honey I suppose to have higher higher viscosities. But but the density of condensed matter liquids don't have a great range of densities. But just keep in mind that this is just one little thing on Earth, and we have a wide range in the universe that we're not going to know anything about. Um Oh, and here's here's an issue. I don't know whether you've been thinking about this. It's the boundary shear stress that moves the sediment. So why don't we use the boundary shear stress on that graph instead of depth and velocity? Uh but there's a problem here. Now, this is an old old old slide that I made in 1975, and I was calling it flat bed instead of instead of upper plane bed. And uh And this is a graph of bed shear stress versus mean velocity. And it doesn't just go up monotonically upward. There's that little bump there, and the next slide uh explains it more. So this is boundary shear stress versus velocity, and here's that curve I showed you. And there's a range of boundary shear stresses for which you can have one, two, three different flow velocities. Now, why would that be? Can you think about why that would be? Strain your brain a little bit here. I don't get any responses, so I think I'll go on ahead. All right. So as you increase the velocity over rugged bed forms, dunes and ripples the boundary shear stress the total boundary shear stress is high because of because of all that form drag, right? Remember form drag? And but then the dunes wash out to plane bed, and all of a sudden there's no form drag, only skin friction. So you would expect to have overlap in the graphs. Um This is just a glance at. And there's a cartoon of it. There's an area a couple of areas in here for which there is overlap of data. It gets really messy in here. And that's just because uh we're dealing with a non monotonically increasing value of the uh of the of the flow stress of of the stress. And there it is, you have to live with it. How do you get around it? So when? So in the three-dimensional graph that you showed, um are those just for like subaqueous dunes, or do they also apply to aeolian? They're for water. Okay. Okay. Well, water or they would they would be good for any other liquid, but oh, and let me point this out. I forgot to point it out. These graphs are for a given ratio of rho s over rho, density ratio. That was that was one of the dimensional variables. There were three, you know, velocity, uh flow velocity, and and and water depth and sediment size, but there's another one. This is all for that density ratio, quartz sand and water, for example. Uh so you have a whole different diagram with whole different existence field, similar but not the same, if you have a a different density ratio. Now, we made some experiments was with tungsten grains. We bought a ton of tungsten particles. They then tungsten has density almost as high as gold gold. And and we we made bed forms. As this is a project I did in South Africa with some colleagues in South Africa. I don't have a copy of the publication. Had I would have tried to put something in here. But anyway, um that's that's the that's the way you could do it is to somehow partition the drag so that you you look only at the skin friction part. And there's various um techniques that have been developed for drag partitioning and none of them works perfectly. Some of them work okay. But but if you didn't do that, if you didn't do that, then you can't use total boundary shear stress. That's just a a point that you need to know about. This has probably occurred to you. Are ripples and dunes different? Well, obviously they are. They're different in size, they're different in behavior, and they're different in origin as well. And uh um there's there's something called a spectral gap. Ripples current ripples in, you know, water on Earth are seldom bigger than about a decimeter. Dunes, however, uh are seldom less than about a half meter even in shallow flows. So, um there's there's a gap, a spectral gap, in sizes there. Ripple spacing is almost independent of flow depth. You can have you can have flows that are half meter deep and you make ripples. You can have flows that are 10 m deep and you have the same ripples down there if you have the same near bed flow velocity. Dunes on the other hand, the dune spacing goes as the water depth by something like a factor of 5 to 10. So, they really do change with water depth considerably, which is good for interpretation because if you can measure dunes can if you can back out dune size from your outcrop, then you'd have something to say about the about the water depth. This is something I'd like to address and I've been thinking about it for years. There've been various papers written by various people on um uh making stability analyses to explain the dynamics of ripples and dunes. May you start with a plane a planar bed and you and you have a flow over it. You make a little disturbance. And [clears throat] sometimes that disturbance generates bed forms. And you saw that when I was talking about the the the incipient ripples earlier last last time. Um but sometimes it gets washed out again and it's unstable. And and so, you have to do that kind of thinking to try to account for why there are ripples in the first place or why there are dunes in the first place. I'm not addressing that. But you should be aware that's a problem. Uh how about Mars? Now, I'm going to come back to Mars because, you know, these planetary sedimentologists have to worry about things on Mars, right? And uh So, so if you if you you could redo this diagram just the way it was, but plug in different gravity, which you can do, and and here are the results that I figured out a long time ago. From one kind of bed form to another takes place at lower velocity on Mars by a factor of about 7.74. And if you look at um at the change uh change from from one kind of bed form to another takes place uh larger by a factor of about 1.36. That's my I think my almost total contribution to to um planetary sedimentology. No, there's going to be another one coming along, too, that I'll mention later. So, now we're on to oscillatory oscillatory flow bed forms, which are just as important. How do you make oscillatory bed forms in laboratory? We we've done this. It's there's a tank, horizontal tank, sediment bed, and you have wave generator, either a paddle back and forth or you could have a piston going up and down. And the waves go down to the other end. And what you have to do is put in a total wave absorber at the other end so you don't get reflected waves cuz then you'd have standing waves and that we don't want that. Um but you can also do this and we did this big time in building N9 back about 20 years ago with Bill Arnott, one of his students. You can have a liquid pendulum in which you take uh uh a tank with reservoirs and you move the the level of water in the reservoirs back and forth with some sort of piston. And it works and you can make nice nice bed forms that way. This looks very clever. You have a still water and a thing that that moves back oscillates back and forth and you can make ripples with it. But the ripples aren't the same as the other. So, people have written papers about that. They have to admit that it doesn't really work for natural environments. But they've done it. Now, so this is this is the first order here. This is this is this is the the the big message if you want to look at it that way. Details later. So, as you keep increasing the oscillatory velocity, there's there's there's no there's no current involved here. You have straight two two dimensional ripples, regular straight two dimensional. And then at certain point and I'm going to get into this more uh couple of slides. And they're small but they get sort of three dimensional. And then they get larger and larger into the large three dimensional. And finally, at the highest velocities, you get a plane bed again. That's the basic message here what goes goes on. But we'll try to go beyond that. So, uh here we go again. We're going to make another dimensional analysis. And uh and uh so, we I assuming that you're you're doing it. And um uh use either oscillation period T, orbital diameter D0, or maximum velocity max orbital velocity UM. And it turns out and I'm going to show it in the next slide. Those three aren't independent of one another. There's a relation UMT = pi D0. So, only two of them can be chosen independently. And what we're going to do is choose is choose uh period and velocity for that. But I just want you to aware that that that those are the only two you need to account for what waves do on the bottom. And uh so, you get up another three dimensional graph, you know, I'm keep giving you these three dimensional graphs. Oscillatory velocity UM, oscillation period T, sediment size D. And uh this is what I mentioned here that you have this relationship, which I'm not proving to you, but there it is. Now, you can section various ways. There's three ways you can section, right? And uh it gets a little complicated. But I have to point out that in a in a laboratory tank or channel with waves I'm sorry. Let me start again. If you had a an oscillatory flow duct like that liquid pendulum thing, you you you're at liberty to to specify any orbital diameter, any orbital velocity, any wave period you want. But real waves don't work that way because the way waves work, um there's a certain range there's only a certain range of those variables that are actually produced at the bed under shallowing shallowing water waves. So, um if you think of that three dimensional graph, there's some volume in there which is realistic for waves and the other areas are not realistic for waves uh even though you can make them in the laboratory. That's how we have to live with that. Um but but in this in this permissible volume, if I can call it that, there are existence fields, three dimensional existence fields, same way there was for unidirectional flow. Does that make sense to you? You can picture in the there's this volume in there that things could be happening under waves. And and there's there's various kinds of small versus large straight crested versus versus three dimensional are going to be in there somewhere. >> [clears throat] >> Every ripple you can possibly make would be in this three dimensional diagram. But the trouble is not every point in the diagram is occupied by a bed configuration. That's what I just pointed out to you. Um so, how do you get data on these things? Well, uh experimental tanks and channels been all done often. There's there's there's a size limit, you know, you can build an enormous enormous wave channel and make real waves. And they had one at the at the uh um uh US Army Corps of Engineers uh Waterways Experiment Station. They had one of these enormous tanks. But but you're still limited. You know, out in nature there are plenty of 10 to 15 second wave periods. And you can't make one of those in the laboratory. So, there's there's a definite limit. Or you can make observations in shallow ocean and there's there's been there's been studies to do that. But it's tough because uh you have to it has to endure storms. You have to record the stuff somehow. You have to wait a long time till a storm comes along. But but people try to do it and it's a valuable thing to do. So, this is a graph that I took from my notes. It's just one section uh a velocity period section for um for sand size about about 0.01 0.02 mm. Fine sand. And and let me tell you some things about this. These these downward sloping lines are contours of equal D0, which has to be in there because you're you've collapsed the three dimensional down into two dimensions. And these and these these uh planes of equal D0 would come out as lines through the graph. Um I'm not showing you all the nature of the data points, but all of the solid diamonds and the open circles are are um um relatively low velocities and oscillation periods. And I've tried to and then the the the ones up in here, the the the squares, open squares, solid squares, and some other things are for are for a much uh much larger oscillation ripples that get produced. And I've tried to contour. These are these are uh uh and I don't think I Did I say this? Did I say Yeah, dash curves, ripple spacing. I tried to contour the ripple spacing. And they And they And they increase very regularly up from lower left upper right. But there's another curve in here, the solid curve, and that's an important curve. Everything below that curve is two-dimensional bedforms, and up above that is three-dimensional bedforms. Now, it's not a definite cutoff. It's not like one of those boundaries in ripples and dunes in unidirectional flow. There's a gradation. There's a There's a range in here around that line in which the ripples start to be three-dimensional and then become three-dimensional. I made that long ago, and I never followed up and made others like it. But there it is. Some pictures. It It's probably won't surprise you. Um ripples oscillation ripples small-scale oscillation ripples typically straight crested regular. They're tuning forks often, you see. Um this is from the This is from the from the Moenkopi in your Vegas nice section. A lot of interesting stuff in it. There again, you have a tuning fork junction. >> [clears throat] >> And still another from the same place. I don't know where that's from. That's a lens cap up on the top. But again, straight crested regular. They're sort of rounded off at the top, and I'm not sure why. This is classic classic small-scale straight crested oscillation ripples from the from the Ferron from the from the Ferron Sandstone member of the Mancos. And uh looking straight down on it. There's pen or pencil for scale over there. Um and a similar kind of thing from the Cardium up in Alberta. Now, >> [clears throat] >> what's going on here? Explain that to me. The hint, of course, is that we're doing the oscillation ripples. So, what What do you make of that? I have to challenge you people guys now and then, you know. Well, uh what I should have done is put the next slide in and turned it upside down. Because if you did that, it would just look like oscillation ripples. This is a slab that came off something, and it fell upside down. That's what ripple a ripple bed looks like upside down. >> [laughter] >> I've I've never seen that except just in one place, but Okay, and now on a broader scale, this is this a big a big flat sand tidal sandbar off uh off the coast of of Eastham in Cape Cod in Mass Bay. And um See, you see, if you look at just a little area here, it would look sort of like what we're doing. But when you look at all the whole field there, there's a lot of sinuosity and tuning fork junctions and things like that. There's a whole series of these bars, one here, one here. There's even There are You can count four or five bars at at spring low tide where it's where it's the the water's lowest. It's an amazing place. All right, some ripples. Um this um You You can see this one looks symmetrical. This one is sort of asymmetrical, but you can see the laminae inside the ripples indicating that the ripples were moving in one direction, shifting in one direction. And um and that that can happen that can happen in oscillatory flow uh even even when it's purely oscillatory. Um and I'll tell you more about that. They can get really big. We made this in a in a oscillatory flow duct with a long period. And they're big. This These are These are centimeters here. This is an amazing photograph. I didn't take it. This my my long-term college colleague and mentor, John Harms, uh gave me the slide, copied the slide for me. And this These are This is a half a meter, I think. Half a meter scale. And uh these are big. They're meter plus scale. Uh they're probably in coarse sand, I'm guessing. They're very straight crested regular, and I've never seen one of those in my in my doings, but uh he he showed Now, this is my favorite outcrop. It's the wind. Does the spacing between the oscillatory ripples vary with flow depth the same way you have with unidirectional flow, and can you like backtrack what Well, go Go back to the graph with all the data points on it. Remember, and we con- contoured the the spacing. So, it it varies with both uh both variables, not just one. All right? Um This That's That's a rock hammer. You see the rock hammer? And if you look at that, you can recognize there are hummocks and there are swales. And And they're isotropic in the sense that they don't bend one way or bend the other way. And I remember looking at this outcrop. It's a little bigger than what I took the picture of. And you can You can sense that the that the the hummocks are arranged in a hexagonal pattern. And in the middle of the hexagon, there's a swale. And I even in one place, and I can't point it out to you, there's a place where within the swale, there's a little miniature hummock right in the swale. It's amazing. My favorite outcrop. But, you know, I went back here uh some years afterward, maybe eight or 10 years. It had fallen apart. A tragic loss. It had fallen apart, and it's not there anymore. Um I don't remember where I took this photo. There's a rock hammer there. But it's again sort of hummocky swaley, although it has some lineation to it. And it's somewhat asymmetrical. And this you want to keep this in mind when we talk about combined flow bedforms. It's uh it's it's not that great a picture, but it shows some interesting things. Here's a close-up from straight down on a hummock. And you can convince yourself that it's three-armed, one this way, one that way, and one that way with a sort of a peak to it. Uh and this I think this was from somewhere somewhere in Canada. I was looking at it with Roger Walker, but I can't remember where. This is another one of my favorite chunks of I carried this out of the outcrop from the Wood Canyon in southern Opal Range. And uh here's the scale. A hummock here, a swale, a hummock over here. And the whole bed, presumably, was like that, hummocky swaley. On a medium scale, you know, a couple decimeters. And uh and if you look closely, and this is getting ahead of ourselves, the stratification here is medium-scale hummocky cross-stratification. And I'm going to say a lot more about that coming up soon in the next in the next session. Um Now, I'm going to take a shortcut here and show you a couple of graphs that show that there are things called orbital ripples spacing consistently just a little less than than the orbital diameter and through a transition in what are called suborbital ripples to an orbital ripples largely independent of the of the of the of the wave spacing, but it is dependent particle size. Uh you you get um um in fine sand, only in fine sands and in very long excursion distances, you get ripples that look like current ripples. This is from a classic paper written by my colleague Ed Clifton way back. He died a few years ago. Um in which he plotted, and I think I have the the um the or- the uh axis where lambda, that's the spacing, over over the square root of D. I don't know why he did that cuz it's not not dimensionless. Uh and the horizontal axis is the D D zero D zero over D. Let me go back. Um and so, there's a trend here, and those are the orbital ripples. And then they breaks through some messiness and comes out to a big group of anorbital ripples. These are data from both laboratory and field. It's not the only one. Um let's skip that. Um In a more recent study, this is from Pat Wiberg and her colleague uh back in the late '90s. The same kind of They plotted They They plotted uh uh spacing over over D and D zero over D. So, it's a really dimensionless. And you can see there's a whole bunch of points here both from field and laboratory data that are orbital ripples. They go They They go with the space They go with the with the with the spacing. But there's a whole bunch out here which are totally separate. Those are all only field data, and those are anorbital ripples. So, it seems strange, doesn't it, that that you can make make both orbital ripples and anorbital ripples in the lab, but the only ones you see in the field are anorbital ripples. Here's another example um from a paper we wrote in 2005 uh in which these are the These are the I won't go into details, but these are the These are the vortex ripples, and these are the the the um orbital ripples, and those down in the in the left-hand corner are anorbital ripples. So, this summarizes what I'm trying to tell you here without any a lot of details. But somehow they're different. There's some sort of instability that makes them different. I've wondered for a long time, and my colleagues have also wondered at the same time with me, about whether anorbital ripples are really just like reversing current ripples. Because suppose you have a very long orbital diameter and a fairly substantial velocity over the bed. So, for the 10 15 20 seconds the flow flows this way, current ripples are going to try to form. You know, they're opportunistic. They form whenever the current velocity is right. And then And then it reverses. You go back the other way. They're still there, but they flip over and grow some more and go back and forth and back and forth. And you end up with with with anorbital ripples that are basically current ripples that can't make up their minds which way to go, if you really want to look at it that way. I'm not sure I'm right about that. And I've talked with colleagues about it, and there's there's some agreement among us that that's the way it works. Now there's something called ladder back ripples or or cross ripples which to me are mysterious. Look at that. I forget where I took that. That's my scale so I took that picture. Um and you can you can see there's a major oscillation ripples and then in the troughs there are some minor smaller oscillation ripples. They're almost the same size I guess. Uh here's another example. That's a watch for scale in the middle. So so these these these are the main uh oscillation ripples. But but look at the look at all the smaller ones in the Now now is is that because of something how how it works under these conditions or is it the you made the large ripples first and then things changed and you got oscillation from the other direction which seems to me to possibly and I don't know how you tell the difference. So uh here here here are the two ways you maybe could make them. Non-parallel oscillations or single component under certain conditions and that's what I want to get to next. Um Ed Clifton who I mentioned um organized some data from various places shoaling waves. Waves coming in shoaling finally breaking on the shore. And uh and out in the the fairly deep water you get active uh long crested or after oscillation ripples we're looking at. Then they get irregular. Then you get cross ripples for reasons I have no idea why and then when the when the swash finally the waves break and run up the the the beach you get sort of what what he called lunate mega ripples. They're just they're they're not oscillation ripples anymore. I have no idea how this formed. Pentagonal oscillation ripples. No idea how it formed. I took that when uh Paul Myrow was just finishing his doctoral thesis up there in in in St. John's in Newfoundland and we went across to Bell Island and well a lot of interesting stuff in there it is. I don't know any I don't know anything about it. So now this may be counterintuitive to you but oscillation ripples formed in purely oscillatory flow What if the like one of the uh like orientations of the ripples is 3D and one is 2D? Yeah are you talking about the pentagonal ripples now? Maybe maybe there are three or more different oscillation components. Maybe something like that. I don't know. I know it's amazing. So ripples formed under purely oscillatory flow aren't always symmetrical. Um now way back in hour one I told you about how under shoaling waves there's a certain fast and short slow and long. The water doesn't go anywhere on that basis. But because sediment transport rate is so steeply climbing a function of the of the flow velocity that you end up getting net transport towards shore and you can get asymmetrical purely purely oscillatory flow. Seems counterintuitive but it happens. Now a little bit on the aeolian bed configurations. I'm not going to say a lot about it. I mentioned I mentioned barchans early on when we talked about sediment transport. Those those are miniature. These are major. These are big big ones. I forget where that is even and here's a more distant view from the air of an of an isolated barchan. Um so I'm not going to say anything more about barchans. Read Bagnold's book if you want to know about barchans. So but classic wind ripples. Now at first glance you look at it and say oh they're they're oscillation ripples underwater. But they they're very distinctive in their in their shape. They're asymmetrical and they have grain size segregation that's very different from what you'd find in oscillatory flow ripples. They can get fairly good size. Here are some that are getting up pretty big. There's not a scale on there except for the bush. Unfortunately I should have put a scale in. Uh but they're they're decked with smaller scale um wind ripples as well. Now if you look at the dunes this is a coast a lot of active coastal dunes along the coast of Oregon for example. I'm out there with with with my colleagues. They take me out there to show me the stuff and you can see the the the stoss surface of the dune strong strong aeolian transport no ripples plane bed transport reach the crest and they and the the the grains that are deposited at the crest slide down the crest. This is a view of the same dune of the same dune with Here's a slip face at angle of repose and the grains slide down as little little miniature grain flows out out on out onto the This is this is an earlier dune that this one is overriding. Now I I have to say some things about combined flow bed forms. But I'm not happy with it because I don't know much about it. I don't think anybody knows much about it. It's it's a jungle when you think about it. You have all the all the things that go on in unidirectional flow everything is going on in oscillatory flow and everything in between when you combine the two flows in various ways and you're going to get a enormous variety of bed configurations and therefore an enormous variety of sedimentary structures. And it's it's it's a jungle. It's it's a dog's breakfast as John Grotzinger likes to say. Um so that's the topic. How do you make oscillatory How do you make uni uni combined flow bed configurations? Well you can do it in the lab if you have a unidirectional flow and a parallel oscillation it's pretty easy to do and we've done it in our laboratory. Um but if they're at right angles it might be doable in the lab. I once thought about writing a proposal to build a flow channel with flow and reservoir tanks on the side and you can you can rock the channel back and forth to make an oscillation while the current's flowing. I never did it but I thought it would be a cool idea to do. We didn't do it. Oh wait a minute wait a minute. And then the third would be to uh if you have more than one oscillatory component plus unidirectional flow. This would be very difficult to do and I think it's been done uh not into the literature. You'd have to have a big wave tank with wave makers here and wave makers over here and wave makers over here. Plus you'd have to pump water from one side of the tank to the other to produce the current. And that's a big that's a big job and I don't think much has been done on it. So um here we go again with another dimensional analysis. You need you need um not just max orbital velocity and unidirectional flow velocity. And period uh period and size. So here I have four variables instead of three. Well now I cannot and I don't think anybody can visualize a four-dimensional diagram. All right I mean it's I think that's beyond our capabilities. So what you'd have to think about is you make one of those three-dimensional graphs for every value of the of the fourth variable. And and you can do that. I mean it's an enormous job and it would take a lifetime of experimentation to fill in a graph like that. So um this is from before. Right? And uh uh from earlier and uh now we're dealing with this. Oscillatory velocity versus oscillation period versus sediment size and you'd have to do one of those for every value of unidirectional flow added onto it. It gets really messy. Um we don't have to do this. There's another way of There's a velocity symmetry value but it's not important to worry about. So I'm not going to say anything. So we're we're far from filling these diagrams. That's the way it is. Here's some bed Here's here's some nice papers in case you're interested you can pursue some of these papers. Ours is one of them. Um this is this is a There was a student one of Bill Arnott's students from University of Ottawa Simone Douma came down to build and operate a giant flow channel oscillatory flow channel with unidirectional flow as well. Um she was she she and I built this thing with some help from other employees. She was she was the person who was the best arc welder of any of the employees and students I've ever had. I I I teach these people how to do that cuz we build things and uh she was really good at it. So here are some of the results that she got. This is this is for this is for small scale bed forms range from as you might imagine symmetrical to somewhat 3D to very 3D and on into basic current ripples. Right? And you can do the same kind of thing for large ripples. Again symmetrical for almost purely oscillatory flow. They they they they get a little three-dimensional and they they're somewhat symmetrical. Then they get to be more three-dimensional and and and uh uh more asymmetrical. And then you finally get to dunes in unidirectional flow. So that's a way of looking at it. That she made these conclusions based on all the experiments all the runs she made in the in the duct. And this is her graph which is a good one. Oscillatory flow velocity versus unidirectional flow velocity. Uh and this is for a particular size 0.14 mm size 8 second period which is pretty realistic of things in nature. And you can see you get no movement. Lots of rugged bed forms plane bed. And and she has these lines which she explains in the text of the paper that that these those are gradations. This is a gradation between symmetric large ripples asymmetric large ripples asymmetric small ripples and symmetric small ripples with no definite boundaries. So this is one of these diagrams so we don't have a lot of nice boundaries the way we did in unidirectional flow which we have to live with. Uh this this was one that I did with Bill Arnott. We published a paper earlier than that. And it shows the same kind of thing with data points. And there's another one. Oh, there's not another one. There's one in the addendum, which I didn't include here. Uh a more recent paper by uh uh Perillo et al. Mauricio Perillo, my young colleague. Uh and they did a a very similar kind of duct and similar experiments in the Oh, look at this. And uh and they produced this just the same kind of graph, but it's nice to look at cuz it has colors in it. And and that's that's in the addendum there. I'm pretty sure it's in the addendum if you want to look at it sometime. Um photo to come, but I don't have any photos. You know, I've I've never taken a photo of what I think to be or known or know to be a combined flow bed form. And that's just the way it is. Uh there are photo photographs from from the experiments, and I don't have access to them. I tried to get them, couldn't get them easily enough. All right, so now it is getting late. And it's time to start on number four. So now we're dealing with sedimentary structures. We're going to look at rocks now. See what the structures are like. Now, [clears throat] I I don't want to insult your intelligence, but a stratum or stratum, distinctive layer of deposited sediment. And it can be tabular, can be non-tabular. Okay. Um and and there's there's like conventional lamina versus bed. One thin and one thick major one. This is a terrible term. Never use this term laminations. The it's either lamination or laminae, one or the other, but not laminations. This is the this is the editor. This is the copy editor in me speaking. No, really, I'm serious. A lot of people say that. Okay, and you know the difference between texture and structure, right? We're dealing with structures here, not textures. Modes of deposition. All right. It this is pretty simple to understand. You can have fallout without traction. Clearly, you can do that. It's happened happens many times. Or you can have fallout with traction. Particles are coming down being added to the bed, so we get aggradation. Um differential transport is a little tricky. I want to show you that. And of course, there's mass deposition like debris flows grinding to a halt, which is out scope of this presentation. So So here's the flow, a non-uniform flow. It's deepening and slowing as it goes downstream. You have a flow velocity U, a sediment transport rate QS at at both sections. But you can see that the sediment transport rate is greater here than down here. So sediment must be being stored on the bed. That makes sense. I mean, that's that's bookkeeping. And um and so that's and well deposition, you have to think of it can be one or both of two of those factors. And uh we'd like to know how to figure out which is which is which. I don't think that's an easy job, but you have to be aware that's how deposition works. And mass deposition, I'm going to not go through this very fast. I'm going to go through this very fast. Debris flows are important. The Bouma A, the the lowest part of a turbidity current deposit. Uh here's here's the Bouma sequence. You probably know about the Bouma sequence. This part down here is is massive and uh and involves mass flow. We did some experiments on that once with a with a master's student. So here's another way of looking at it. If you have flow of a thick mass of sediment, but it's flowing, that the the the shear stress, the shear is least up in the top. So that means it will freeze earlier at the top and freeze gradually downward until finally the whole thing is a plug of sediment, immobile. Try to think of this nice way of looking at it. So um we can deal with planar planar lamination. Sometimes people call it planar lamination, plane parallel. Don't call it horizontal lamination because it's not horizontal. It may have started out horizontal, it may not have, but when you see it, it's use not. So planar planar lamination, call it planar lamination. Two kinds. One, obviously, you get a flow dropping sediment without further traction. And you can if it if the if the surface is planar, it's going to be build building up a a deposit, planar laminated deposit. >> [clears throat] >> But you can also, and I think I've made this clear to you already, you can have deposition during tractive traction, active traction in the plane bed regime. And so you build up a planar laminated bed during transport. >> [clears throat] >> I think this is from Bill Bill Arnott's field area. I was on his thesis committee, and we went out for a glorious week in Montana to his field area after he passed his thesis defense. And uh nice lamination. That's a 15 cm scale. So these laminae are are a a a fraction of a centimeter thick. Which is very typical. It gets a little more complicated. I think this is in the same section we were looking at. And planar laminated planar laminae, but looking here, you can see some vague foresets in here. So something happened to the current, and it decreased, and then it started up again. That's how I interpret that anyway. But it's a little tricky. Um a couple more slides. You probably seen planar lamination in the field. So there's an idea floating around, and uh one of my grad students, Chris Paola, was partly responsible for this. The idea that the plane the bed isn't perfectly planar. There's very low amplitude, very long spacing features that move along the the plane bed surface in the upper plane bed regime. And and this is what makes the laminae as they go by, little laminae about a centimeter, about a couple of millimeters thick. I I I can believe it. Now, I don't need to tell you this. Difference in grain size within a lamina, that's how you see them. Um Now, here's an interesting question. I've tried to do this in the field. Next time you're in the field looking at plane planar lamination, how far can you trace a given lamina before it disappears, replaced by another, changes in some way? And uh typically, it's something like from well less than a meter to as much as a few meters if if you have a nice enough outcrop. Nice to play around with. >> [clears throat] >> Now, there's something called parting step lineation. You may have heard of parting step lineation. So you have a a lithified plane bedded succession. And when it's brings up surface weathered, it splits. It often splits along bedding planes, bedding surfaces that happen to be during plane bed that are weaker than than the surrounding strata above and below it. And um the nice thing about it, this is from uh this this is from a the sidewalk going to a a tea party, a tea plantation in Sochi. And uh and you can see it because the because of the orientation of the grains as they're being transported under plane bed conditions, produce an anisotropy, and then when when parts along a a bedding surface, that anisotropy shows up as these parting steps. It's pretty understandable. Here's another one. I can't remember where that's from. Um >> [clears throat] >> So that's all I'm going to say about about uh parting step lineation. But this Now we get into a another major part of the of the presentation. How do you interpret the flow conditions by looking at the cross-stratified bed? That's a major undertaking. And I need to make some comments about it. Um there's a forward problem. You know about forward problems and inverse problems, right? The forward problem is you have a flow over a bed, it forms bed configurations. During aggradation, sedimentary structures are formed, and you get stratification. That's But the inverse problem is trickier. You see the stratification, and you try to figure out what the bed configuration was. And then from the bed configuration, you want to know plus aggregation aggregation, what was the flow like? That's that's what you want to back out. That's the whole purpose of doing this kind of thing is making interpretations like that. And it's and it's not easy. Why? It It can be difficult or impossible because there's local erosion. Time gets unrecorded, and so local deposit geometry, which existed at one time, isn't there anymore. So that's a That's a a universal problem that we have to deal with. Anyway, um here are a few more thought experiments coming along. I got to I got to quit in a few minutes, but let me just go through this. Okay. How How can you do this? You can set up a flow over the bed to make a bed configuration. And that's been done many many times. You can add sediment above to the constant or varying rate while flow velocity is either constant or varying, and you degrade a bed under varying conditions. Um and then you can section the deposit vertically downstream, cross-stream orientation, parallel to the bed if you wanted to. And and you can see what the structures look like. But uh if this was made by differential transport, it might be difficult to figure this out. But anyway, that's the kind of thinking you have to do. So another thing you could do is what's called synthetic aggradation. We've done some of this in the laboratory. You set up a flow, you make a bed configuration. Then you make time series maps of the bed. And you artificially aggrade them uh in time steps. And you end up with a cross-stratified deposit. And and it does pretty much mimic what mimic what would happen if you if you actually aggraded the bed, which of course is very difficult. Um I guess you could stack them by computer. This is fairly easy in the sidewall transparent sidewall of a channel, but it's not easy if you're looking at a whole area. How would you do it? You'd have to do a sonar profile, sonar profile, sonar profile, and then stack them up. Could be done. And I don't know how much it's been done. We did some of it. In the natural flow environment, the obvious thing is to go out to some station out offshore in the shallow offshore and instrument it with some sort of sort of permanent tripod structure looking down at the bed and also measuring measuring the the the flow. And there there have been some good studies, but that's really difficult because uh it has to resist big storms and there are all kinds of tech tech technological problems in actually making it work. But there is some of that and that's very valuable to do. So, I think that's a good place to quit. It's after 4:00. Um I'm going to point out that facies models, you probably know about facies models. Models for interpreting sedimentary environments. This This is a nice statement, very well well worded by um in a special this the introduction of the SEPM special publication 84 in 2005. A model is a point of comparison, it's a guide for further observations, serves as a base for hydrodynamic interpretation, and acts as a predictor a predictor for new situations. That's really valuable to be able to do. And And what we're what we're dealing with here is a kind of a subset of of of facies models and that's depositional models. Look at a particular bed in a given facies. What can you back out of that bed in terms of making interpretations of of of flow conditions and sedimentation. And I think that's all I'm going to deal with. Next time I'm going to start in with cross-stratification, which is really the main thing in this presentation. And um So, that'll be 2 weeks from now, remember. 2 weeks. Uh same time, same place. And I'll finish up the presentation talking about cross-stratification in various kinds of flow environments lots of pictures. Okay. See you then.