 So I want to talk a little bit about the turbulence behavior in the flow and the context of the boundary layers and also the role of bed roughness. So we have our flow with flow depth L, and this black line represents our flow speed. And when it starts flowing down due to friction at the bottom, that's the top of our boundary layer that goes to the bottom, and then we have this laminar sublayer at the bottom. So if we go back to thinking about the way particles behave in the laminar sublayer, right at the surface, the flow speed zero, so our particles just sit there, if we're tracing water molecules. A little bit higher up, the molecules will just move in a straight line downstream, and they'll be parallel to each other, and there's no mixing. If we go up to the to the turbulent area, we can trace molecules, and they'll move much further downstream on average than the ones at the bottom of the flow, but they also get mixed around. So sometimes they might even move a little bit back upstream, and at some point you won't be able to trace which particles, which going on in my drawings here, right? This is all mixed up. So one of the ways that this flow speed is affected is as you get closer to it, you're getting, there's more drag and more influence from before, so you have particles move, but maybe they don't have quite as much variation, and there'll be some zone in here where you have your transitional flow, where there's a little bit of mixing. One of the ways that velocity gets transferred from the main flow down into the flow is to have fast-moving particles up here come down and join this lower part of the flow here, and then sometimes other, some of these particles get kicked up, and it becomes more turbulent. So there's some, there's some mixing in this zone, and you end up with bursts of turbulence can come down into this lower layer, I'll draw, draw some more down here, which increases the flow speed going down straight. So I'm going to erase my massive turbulence here, keep that in mind, but we're going to talk about what happens if you have something besides a flat surface. In flumes, we can create a flat surface, but they're pretty rare in nature. So in this ideal case, your flow is laminar at the bottom, but if we add a grain here that acts as a barrier, when this water molecule intersects the grain, it can't flow through it. So it gets deflected up around over the grain or around the sides of the grains here. So whenever there's something that disrupts the flow, it actually causes an increase in the turbulence. So disruptions to the flow increase turbulence. And this is, these disruptions to the flow are not captured in our Reynolds number. The Reynolds number is defined for a flow with smooth sides and a very specific geometry. And so one of the key things about bed roughness, we can use the Reynolds number as a guide, but if we have a rough bed that's disrupting the flow and creates extra turbulence, the flow will be more turbulent than as described by the Reynolds number. And when you have more turbulence, your boundary layer tends to shrink and you can get more sediment transport. Thanks for watching.