 Our next speaker is Tom Su, who is an associate professor at the University of Delaware. And his title is understanding wave-driven fine sediment transport through 3D turbulence and resolving simulations, implications for offshore delivery of fine sediment. Tom, thanks a lot. Thank you. Thank you for the invitation, and I've been enjoying the meeting the past few days. So today I'd like to discuss a few of the numerical investigations that have been involved in the past few years. And the goal is to... Sorry. The goal is trying to understand fine sediment transport in the wave-bottom boundary layer. And as I will mention later, this is actually a very important process in terms of trying to understand the offshore delivery of fine sediment in the coastal ocean. I'd like to first acknowledge my co-author, my current graduate student, Charlie and post-doc, Yu Xiao. And my former graduate student, Emory Osmere. And Dr. Ba Chenda from UFlorida have provided us with the original version of the code and also have provided a lot of important insight in the fluid mechanics aspect of this problem. And also, funding is supported by NSF and ORNR. And I also want to mention that our work has been inspired by many collaborators working on a similar subject, but they were mainly focused on laboratory and the field of observation. But those are really the motivation of our study. So first, it turns out wave boundary layer is a very important conduit delivering... I would say it's one of the important conduit delivering fine sediment offshore. And therefore, this is an important problem to be studied because it is important to our understanding of offshore delivery of sediment in sediment source to sink. And this is achieved by this process called wave supported gravity driven mud flow. And so I will elaborate a little bit more using this eel river as an example. So during the river flooding event, it turns out the eel river plume actually just go all the way north and attach to the coast. And therefore, the initially deposited sediment is also very close to the shore. However, researchers has found that most of the more long term deposit of those fine sediment is actually located much more offshore in about 60 to 90 meter water depths. So it becomes a puzzle how this large amount of offshore cross shell delivery of fine sediment can occur. And by more detailed field observation in this case by Tchaikovsky, he shows that it turns out during the large wave event, a lot of sediment is actually suspended in pretty high concentration in the wave boundary layer. And then they were then delivered by the offshore directed gravity flow. And so the important thing or I should say a little bit counter intuition here is that those are very fine sediments with a settling velocity only on the order of one millimeter per second. So you would expect that those sediment in this kind of a typical wave current bottom boundary layer condition, they should be pretty much suspended and well mixed, more well mixed in the entire water column. But in fact, what you see here is that they are mostly confined in the wave boundary layer. And it turns out what he was trying to argue here is that turns out the suspended sediment actually can actively damping the turbulence. So in this case, what you see here is a very sharp negative sediment concentration gradient located near the top of the wave boundary layer. And this is the so-called the LUTO client. And the existence of LUTO can actually effectively confine the fine sediment within the thing wave boundary layer and then you can accumulate enough buoyancy anomaly and drive the sediment offshore. And so this is sort of the process that's driving the offshore delivery of a fine sediment. But as you can see, it's all within the wave boundary layer. But an important thing here to be noted is that the wave boundary layer thickness is only on the order of 10 centimeter. So it's a very thin layer near the bed. And if we want to model sediment source through SYNC, we may want to use some coastal modeling systems such as ROMS. And Courtney Harris is going to have a clinic about ROMS this afternoon. But the important thing to be noted here is that in this kind of coastal modeling system, you are not able to resolve the process very close to the bed. Okay, so in other words, this wave supported gravity flow or the associated wave boundary layer processes has to be parameterized. So therefore, if you go back to the literature, you see people like Don Wright, Carl Friedrichs and Malcolm Scully that have provided this kind of Richardson number control type of concept trying to estimate the total amount of a suspended low in this problem. And then later, Courtney Harris has proposed, and her colleague has proposed a more complicated formulation. They call it a near-bed-turbid layer formulation, which more sort of explicitly incorporates bottom erosion, deposition, entrainment, and wave-bottom boundary layer processes so that she will couple this into, in this case, will be econ-set and then show that the model is able to predict the offshore delivery of FISAB. But then if the goal is to predict the total transport rate, not only you need to estimate the salmon load, you also need to estimate the flow velocity that delivers the salmon. So to estimate the velocity, you will typically require a parameterization on the bottom drag coefficient. And this leads me to the next motivation here. Turns out the suspended salmon can also actively changing the bottom drag coefficient experienced by the tidal current or the wave. Using this Amazon as an example, researcher has found that when the tidal current is propagating over a thick layer of mud, turns out the tidal current experienced so-called a reduction of drag coefficient. And this is attributed to the observed Lutocline, again, because Lutocline's sediment dams the turbulence and causing the drag reduction. However, more interesting thing is that if you look at the literature about wave, a lot of people actually reported that when wave propagates over a thick layer of mud, wave actually often experience large wave energy dissipation. And so here I'm showing you a data provided by Alex Shearman from UFlorida. What you see here is a time series. The color represents sediment concentration, but I look at this as a time series of the state of the seabed of a mud during the passage of a storm. And this is located, I think, in the inner shaft of Chavallaya. What you see here is that you see a diverse range of seabed state from the more well-mixed condition to the formation of a Lutocline. But a more interesting thing here is that if you look at the wave dissipation rate, it is really becoming very large only during the waning stage of the storm. And if you look at the bottom, it seems to be associated with a sudden contraction of the mud layer. And more data provided by Peter Tchaikovsky in the same place, he's able to show that in this condition, turns out the wave boundary layer is not even turbulent. You don't have a minus five-third slope here. So it's pretty much a lamarized wave boundary layer. So it seems that the large surface wave dissipation rate is associated with a sudden lamarization of or non-turbulant type of bottom wave boundary layer. So our goal here is trying to understand through numerical simulation how the suspended sediment can modulate turbulence and causes transition of this different diverse seabed state. So because the goal is trying to understand how sediment are changing the turbulence, so in the beginning we decided that we want to use a turbulence-resolving approach instead of the Reynolds-average approach because we believe that we are able to resolve the turbulent sediment interaction better this way. And also, we're going to look at sediment-fine sediment. So the sediment velocity is in the range of a 0.1 to 1 millimeter per second. So therefore, we will ignore the inertia effect of the particles. And therefore, we will use the something called equilibrium approximation where we can approximate the particle sediment velocity as local fluid velocity plus settling velocity plus some high-order terms associated with Stokes-Eimer. But in this study, I'm just going to also ignore the high-order terms. And then if you substitute this relationship into the standard two-phase equation for fluid and the sediment and then making the Bucinica approximation, you end up have this simplified governing equation in which you look at how sediment changing the turbulence simply through a stratified flow analogy. So that's why you see this term is associated with the Richardson number, which I'm going to come back to talk about a little more later. And then you see that the sediment is just updated by a standard mass conservation. And we're solving this 3D equation with a high accuracy pseudo-spectrum scheme previously used for deranium-mercal simulation for turbulent flow. And now I think it's very good to summarize some of the non-dimensional parameters controlling this problem based on the governing equation that I've shown. So first is the Reynolds number. The Reynolds number really controls the wave intensity in the wave boundary layer. And if you go back to look at the air shelf where people see wave-supported gravity flow, the most energetic condition is about wave velocity, amplitude, 0.55 meters per second, wave period is about 10 seconds. So if you look at the Reynolds number, it's only below 1,000. There's two things. First of all, Reynolds number 1,000 is only in the intermittently turbulent condition. So the wave boundary layer, even without sediment, is not fully turbulent. And also, because the Reynolds number is relatively low, so we are actually able to resolve all the scale of turbulence all the way to the chronograph scale in this specific case with about 10 million grid points. And the second thing is that if you look at the non-dimensional settling velocity which definitely controls the problem, what I'm going to show you again is we're only going to look at typical fine sediment in the range of 0.1 to 1.5 millimeter per second. And I also want to mention that we do not explicitly incorporate flocculation dynamics. We're just going to try a range of different settling velocity and see how the result is different. And finally, the problem must also be controlled by the sediment availability. In the older version of the model a few years ago, we started by prescribing the sediment concentration in the water column through the initial condition. And then in the meantime, we do not allow sediment to get eroded or leave the domain. So in other words, throughout the entire simulation, the sediment availability is prescribed and is fixed. The only reason we do this is because it's just easier to implement numerically. And also, my student will tell you that while this is more similar to the river flooding condition in which the sediment input is really not controlled by the bottom suspension, but it's more controlled by the river input. But in any case, in this case, we can really quantify the problem by a fixed bulk Richardson number that essentially controls the total amount of sediment in your domain. But we have to admit that in more common situation, sediment is resuspended and can be deposited to the bed. And so in this case, we really need an erosional, depositional boundary condition and then the sediment availability is part of the solution of your simulation. And we have been implementing this recently and I'm going to talk about the result today, which is going to be a major focus of my talk today. But before I do that, I still want to give you a quick summary of what we have found using our old model result with a fixed sediment availability or Richardson number. At the Reynolds number, 1,000, we also try different settling velocity, but the most important thing is that our simulation result actually revealed the existence of four different flow modes. For example, as we increase the sediment availability. For example, in the very dilute situation, we have sediment concentration pretty much well mixed in the entire wave boundary layer and the flow is more turbulent. And then when we start to increase the sediment availability, we start to see the formation of luteocline, but the flow remains turbulent near the bed. And I'd like to see if I can show you an animation to illustrate this. So this is the part that I have to, because now I can only see this on my screen, but this morning somebody has teach me a trick. Okay, so what you see here, the top panel is the step shop of sediment concentration under the wave and the top panel is the more turbulent mode 1 and the bottom panel is the one that you actually see the formation of luteocline and what you see here is that there are two iso-surface of concentration I'm showing you here. The blue one is more dilute and the yellow one is more concentrated. As you can see in the first flow mode, it is very turbulent throughout the entire water column. But in the second flow mode, what you see here is that the top blue color is less turbulent compared with the first one and this is associated with the location where we see the luteocline. So meaning that in this case, you really have a two-layer system for a typical stratified flow and the luteocline really just separates these two. And what's more important is that if you then further increase the sediment availability or the cell-holding velocity, what you find is that the flow becomes almost not turbulent. If I can show you another animation here, what you see here is that now you see everything is much more calm and maybe during the flow reversal, we start to see some flow instabilities, but those instabilities never become mature turbulence. And in fact, if I further increase the sediment availability, I'm going to have a completely lamerized bottom boundary layer. So the important thing is that we also try to prioritize this kind of boundary layer that we see. But I want to mention some of the important implications over this. That is the transition from flow mode 1 to flow mode 2 where you increase the sediment concentration, this may implies the formation of wave-supported gravity flow that I mentioned in the beginning. And then of course, as I mentioned, if you have a transition from the flow mode 2 to flow mode 3 and 4, that is a lamerized bottom boundary layer, this may suggest the occurrence of a large wave dissipation or it could be suggesting the termination of the wave-supported gravity flow. And therefore we like to parameterize those processes and at that time we decided that it turns out there's something called a carrying capacity concept which was commonly used in the tidal boundary layer. Now we believe that we can actually use it in the wave boundary layer situation. But I'm going to go back to this in the next few slides. But the important thing right now is that what's going to happen now if we allow sediment to get suspended from the bottom and not prescribing it. And so what we did was that we recently extended the curve into a pseudo-hybrid spectrum compound finite difference scheme. This will allow us to better incorporate variable viscosity and the long linear bottom boundary condition. So in this case, with this long linear bottom boundary condition, we can adopt this continued erosion deposition formulation as a bottom boundary. So we use the erosion formula provided by Sanford and Mar which the erosion is controlled by the critical shear stress and the empirical coefficient M and the deposition is calculated by the cycle influx. And then at this point I think it's actually very interesting to show you based on this new boundary condition what we're going to expect to see. So the idea is this. You have a clear fluid turbulent flow as an initial condition and now you start to suspend sediment. And what we know is that once the sediment is suspended in the water column, it's going to damp the turbulence and reduce the bottom stress. This is called drag reduction. So the question is that as you suspend more sediment you're going to reduce the bottom stress more. The question becomes, at the final equilibrium what is your reduced bottom stress? Okay, and if you look at this, if you look at the wave average picture of these two formula you said net erosion equals to deposition. You can do some calculation and realize that yes, the final equilibrium stress at the equilibrium shows that the equilibrium stress has to be reduced to alpha times the critical shear stress. So for example, and then of course the total amount of sediment suspended will be proportional to the difference of the original clear fluid stress minus the final equilibrium stress. So the implication here is very clear. That is, let's say if you have a sediment bed that has a very small critical shear stress you're going to have a very small final equilibrium stress then of course you're going to suspend much more sediment. Okay, so that's the idea. So what we're going to see here is this. So we expect the resulting flow mode that we're going to see now may be dictated by the erodeability parameter specifically the critical shear stress. Another thing is that notice the set-holding velocity is also involved in this bottom erosion deposition so it's also going to depend on set-holding velocity. And finally, this carrying capacity formulation dimension before doesn't even involve critical shear stress. So we believe this parameterization has to be revised. So to test the effect of critical shear stress we did four different simulations with critical shear stress ranging from very small value of 0.1 per scale all the way to 0.6 per scale. And if you look at the model result you see that this is a time series of a domain average sediment concentration throughout the entire simulation and you see that indeed if you have a lower critical shear stress you're going to suspend more sediment except for the case one where we have the really small critical shear stress initially you did suspend more sediment but after maybe a few waves the total suspended load is just dropping. Okay, so clearly lower critical shear stress gives larger suspended sediment load but critical shear stress when it is too small the load will reduce again. So why is that? So I'm going to show you a few slides, why is that? So now I'm plotting the snapshot under the flow peak the left panel is the turbulent coherent structure visualized by the line of the CEI and the right panel shows the isosurface concentration. If you look at the case with the lowest critical shear stress what you see here is that there's almost no turbulence and the concentration is just flat as a sheet so essentially we believe we see flow mode four that is when the critical shear stress is too low it's suspend too much sediment then the turbulence is just completely killed and then if you look at the other two cases with larger critical shear stress we get start to see more and more turbulence coming out and later I'm going to show you that it turns out case two is associated to flow mode two and the case four is associated to flow mode one so it's right here. So now I'm showing you the plan averaged sediment concentration profile streamwise velocity profile and turbulent intensity during the flow peak and during the flow reversal and what you see here is that in case one indeed you have sediment accumulated very close to the bed there's really no turbulence here in case one and wave boundary thickness is also much thinner it's very close to the laminar solution and then if you look at case two you see that we see this nice beautiful Lutocline feature of suspended sediment you do have much more turbulence throughout the water column and the wave boundary thickness is much thicker and then in flow mode four you see the sediment concentration is really well mixed throughout the entire water column so the take home method right now is that indeed we get to still see a diverse range of flow mode but now by just simply changing the irritability of sediment and as we know we can never fully understand sediment transport without looking at the effect of sediment velocity so now I'm just looking at again Reynolds number 1,000 the same critical shear stress of 0.02 per scale but I'm running additional few cases with different sediment velocity with the case two that I showed you before now we have sediment velocity ranging from 0.17 milliliter per second all the way to 1.5 millimeter per second and first what you see here is that most cases we actually get flow mode two but for the case with the smallest sediment velocity we again has a lamarized flow mode four so apparently when the sediment velocity is also very small you're going to reduce the equilibrium stress then you're going to have more sediment suspended eventually when there's too much it's going to lamarize the boundary layer another thing is that if you look at all the cases that is actually in flow mode two you see that if you plot the total suspended load in the equilibrium as a function of sediment velocity we see that as long as if you're in flow mode two it scales with the sediment velocity of minus 1.25 power and if you go back to look at the standard carrying capacity concept it suggests a minus one power the way I see it 1.25 is very close to one so this may suggest that carrying capacity probably works still works as long as you're in flow mode two so this is very important for parameterization so I want to look at this more carefully so this is our old result using prescribed sediment availability and at that time my student generated this nice flow map basically is a function between sediment velocity and the fixed Richardson number and he got to see different flow mode and now of course we're not prescribing Richardson number but I can calculate the corresponding Richardson number or total suspended sediment in my domain in the equilibrium and if I do that and if I only show the result that's in flow mode one and flow mode two this is my new result as you can see it still fits with this map suggesting that as long as the flow is still turbulent in flow mode one and two we can still use the carrying capacity to parameterize the total suspended flow so this is a good news but what's missing right now is that we need an extra criteria to describe the onset of lamarization okay and so for that I'd like to provide a final summary that is in our in the simulation that I'm showing you today obviously it has to be dependent on critical shear stress so if I plot all the different mode that we obtained as a function of a critical shear stress and the settling velocity as you can see as you have a lower critical shear stress or lower settling velocity you tend to suspend more sediment but then you can then form a little climb but then you may completely lamarize the bottom boundary layer and using this pattern erosion deposition formula we can actually come up with an empirical relationship and then we can use our model result and fit this relationship for this empirical coefficient k here and we can actually provide two formula which one is describing the transition from flow mode 2 to flow mode 4 which is lamarize the criteria and then another one is describing the transition from flow mode 1 to the formation of a luto-climb in the flow mode 2 so in summary the evability parameter is indeed can dictate the transition of flow mode and then we show that the good news is that the suspending load can still be parameterized by the carrying capacity as long as the flow is still turbulent and then we provide two empirical formulas that can describe the borders between flow mode 1 and flow mode 2 ongoing work we really like to go back to simulate wave supported gravity flow because we hypothesize that wave stability gravity driven math flow can only exist in flow mode 2 and finally if you look at in the field you always have a small amount of sand containing the mud could be as low as 5% could be as big as 50% and laboratory experiment have showed that if you just have a 13% of sand in your sample of mud you see a very different picture first of all the sand can armor the mud and this is another important contribution from Pat many years ago that you have to use something called an active layer concept to describe this kind of complicated processes and laboratory experiment also showed that when you have a surface layer of sand it actually can form ripples so ripples can generate mortars so making this whole problem much much more complicated than what I was describing and we are very eager to do more future study on this problem thank you very impressive talk Tom I guess kind of related to the cohesion of these particles and the rheology how do you treat that I saw from the equation you only use certain velocity and boussinesic approximation right so the first thing we have been starting to try is to change the viscosity of the problem because right now we ignore the rheology you mentioned but because with this new new expansion of the code we can now even use non-Newtonian closure for the rheology and then we can actually we haven't this is just still starting we can start to actually look at the rheology on this problem but this is definitely a very important part that we haven't been really investigating very well and for all this data so diluted so the boussinesic approximation can be used that boussinesic approximation is okay because the largest concentration that we encounter typically is no more than 100 to 200 grams per liter you already have a lamarized boundary layer so we're not really looking at anything further than a few hundred grams per liter and so if you look at the density difference it's only 10-20% so I think it's still okay in terms of using the boussinesic approximation thank you