WEBVTT 00:00:00.000 --> 00:00:02.940 align:middle line:90% [SQUEAKING] 00:00:02.940 --> 00:00:03.916 align:middle line:90% [RUSTLING] 00:00:03.916 --> 00:00:05.380 align:middle line:90% [CLICKING] 00:00:05.380 --> 00:00:16.328 align:middle line:90% 00:00:16.328 --> 00:00:18.620 align:middle line:84% JOHN SOUTHARD: So let's start with unidirectional flow. 00:00:18.620 --> 00:00:20.660 align:middle line:84% Oh, here, I should tell you my plan of action-- 00:00:20.660 --> 00:00:22.180 align:middle line:90% my tentative plan of action. 00:00:22.180 --> 00:00:25.760 align:middle line:84% We have four hours for three to four classes. 00:00:25.760 --> 00:00:28.340 align:middle line:84% And I've made up four PowerPoints. 00:00:28.340 --> 00:00:31.040 align:middle line:84% I'm not quite finished with the fourth, but it'll come along. 00:00:31.040 --> 00:00:34.880 align:middle line:84% And so the first one is on fluid dynamics 00:00:34.880 --> 00:00:37.640 align:middle line:84% that are relevant to sediment transport. 00:00:37.640 --> 00:00:40.040 align:middle line:84% And then there's one on sediment transport, 00:00:40.040 --> 00:00:42.880 align:middle line:84% one on bedforms and bed configurations, 00:00:42.880 --> 00:00:47.920 align:middle line:84% and finally one on sedimentary structures created by flows. 00:00:47.920 --> 00:00:52.080 align:middle line:84% And I'm hoping to get one and maybe 00:00:52.080 --> 00:00:56.700 align:middle line:84% most of two today done, because the third and fourth are heavy. 00:00:56.700 --> 00:00:59.250 align:middle line:84% They're long and heavy and I think we need more than just 00:00:59.250 --> 00:01:00.190 align:middle line:90% one hour to do them. 00:01:00.190 --> 00:01:02.010 align:middle line:90% So that's my point. 00:01:02.010 --> 00:01:03.970 align:middle line:84% It's been so long since I've given classes 00:01:03.970 --> 00:01:07.970 align:middle line:84% that I can't really figure out how long a presentation is going 00:01:07.970 --> 00:01:10.530 align:middle line:84% to take me because I might go off on tangents and things 00:01:10.530 --> 00:01:11.490 align:middle line:90% like that. 00:01:11.490 --> 00:01:12.490 align:middle line:90% All right. 00:01:12.490 --> 00:01:16.250 align:middle line:84% Osborne Reynolds, famous name in fluid dynamics. 00:01:16.250 --> 00:01:21.210 align:middle line:84% And I mention him because he did a classic experiment way back 00:01:21.210 --> 00:01:26.050 align:middle line:84% in the late 1800s-- a tank with a tube coming out of it 00:01:26.050 --> 00:01:30.250 align:middle line:84% and a valve at the bottom so that he could make a flow 00:01:30.250 --> 00:01:31.570 align:middle line:90% in the tube. 00:01:31.570 --> 00:01:33.870 align:middle line:84% And he had a little dye injection system as well, 00:01:33.870 --> 00:01:39.570 align:middle line:84% because he wanted to see what happened to the dye in the flow. 00:01:39.570 --> 00:01:42.730 align:middle line:84% These are directly from his sketches. 00:01:42.730 --> 00:01:49.890 align:middle line:84% So A, at low flows, the dye streams along the tube 00:01:49.890 --> 00:01:51.510 align:middle line:84% without anything happening to it. 00:01:51.510 --> 00:01:52.850 align:middle line:90% Well-- come on in-- 00:01:52.850 --> 00:01:57.570 align:middle line:84% it might expand very slowly, but nothing much happens to it. 00:01:57.570 --> 00:02:00.530 align:middle line:84% But when you increase the velocity, 00:02:00.530 --> 00:02:04.370 align:middle line:84% the dye wavers and then breaks into turbulence. 00:02:04.370 --> 00:02:07.810 align:middle line:84% And to visualize the turbulence, this is a sketch. 00:02:07.810 --> 00:02:10.690 align:middle line:84% He shows all these fluid eddies moving along. 00:02:10.690 --> 00:02:14.890 align:middle line:84% And this is a classic experiment. 00:02:14.890 --> 00:02:18.350 align:middle line:84% So I think this is a pretty good definition of turbulence. 00:02:18.350 --> 00:02:21.723 align:middle line:90% 00:02:21.723 --> 00:02:23.390 align:middle line:84% And a little bit more about turbulence-- 00:02:23.390 --> 00:02:26.690 align:middle line:84% if you had a flow through a duct or a channel 00:02:26.690 --> 00:02:30.450 align:middle line:84% and you released little tiny buoyant markers which 00:02:30.450 --> 00:02:32.170 align:middle line:84% would float along-- neutrally buoyant 00:02:32.170 --> 00:02:35.050 align:middle line:84% markers-- every one would take a different path and a very 00:02:35.050 --> 00:02:35.950 align:middle line:90% irregular path. 00:02:35.950 --> 00:02:37.850 align:middle line:84% So that's one element of turbulence. 00:02:37.850 --> 00:02:42.450 align:middle line:84% Every motion downstream is very irregular. 00:02:42.450 --> 00:02:44.170 align:middle line:84% And if you had your little magic velocity 00:02:44.170 --> 00:02:48.070 align:middle line:84% meter to put in the flow and you measured the time velocity, 00:02:48.070 --> 00:02:51.690 align:middle line:84% instantaneous velocity, and plotted it-- this is a bad plot. 00:02:51.690 --> 00:02:52.990 align:middle line:90% I drew this cartoon. 00:02:52.990 --> 00:02:54.510 align:middle line:84% They shouldn't be leaning backward. 00:02:54.510 --> 00:02:55.990 align:middle line:90% They should be pretty much even. 00:02:55.990 --> 00:02:57.460 align:middle line:90% But anyway, you get the idea. 00:02:57.460 --> 00:03:00.460 align:middle line:84% So the fluctuations in velocity in a turbulent flow 00:03:00.460 --> 00:03:04.700 align:middle line:84% would be something like 5% to 10% of the mean flow. 00:03:04.700 --> 00:03:07.320 align:middle line:84% So it's substantial, but only a small part. 00:03:07.320 --> 00:03:10.452 align:middle line:90% 00:03:10.452 --> 00:03:11.660 align:middle line:90% You could also-- if you had-- 00:03:11.660 --> 00:03:12.720 align:middle line:90% I love magic things. 00:03:12.720 --> 00:03:16.280 align:middle line:84% So if you had a magic powder and you sprinkled it into the flow, 00:03:16.280 --> 00:03:21.620 align:middle line:84% you would see integrating swirls of masses of fluid called 00:03:21.620 --> 00:03:25.900 align:middle line:90% eddies going down the flow. 00:03:25.900 --> 00:03:29.380 align:middle line:84% If you've ever seen a river in flood, a muddy river in flood, 00:03:29.380 --> 00:03:31.440 align:middle line:84% and you look at it, at the surface, 00:03:31.440 --> 00:03:33.820 align:middle line:84% you see all these eddies at the surface. 00:03:33.820 --> 00:03:34.720 align:middle line:90% It's very impressive. 00:03:34.720 --> 00:03:36.240 align:middle line:90% I love to see that sometimes. 00:03:36.240 --> 00:03:40.700 align:middle line:84% But this is the kind of thing you can visualize. 00:03:40.700 --> 00:03:45.300 align:middle line:84% So this is my definition of turbulent eddies. 00:03:45.300 --> 00:03:46.780 align:middle line:90% Now, if you have a question-- 00:03:46.780 --> 00:03:49.700 align:middle line:84% I didn't say, but if you have a question or comment, 00:03:49.700 --> 00:03:50.860 align:middle line:90% flag me down. 00:03:50.860 --> 00:03:53.340 align:middle line:84% I'm glad to stop and deal with things. 00:03:53.340 --> 00:03:54.750 align:middle line:90% Keep that in mind. 00:03:54.750 --> 00:03:56.950 align:middle line:90% I'd be glad to do that. 00:03:56.950 --> 00:04:01.290 align:middle line:84% OK, so let's think about this flow through a tube. 00:04:01.290 --> 00:04:02.830 align:middle line:84% It's a good example of what we have 00:04:02.830 --> 00:04:05.270 align:middle line:90% to deal with in fluid flows. 00:04:05.270 --> 00:04:11.130 align:middle line:84% So you need four variables to account for this flow. 00:04:11.130 --> 00:04:13.810 align:middle line:84% Obviously you need the flow velocity in the tube diameter, 00:04:13.810 --> 00:04:16.230 align:middle line:84% but also the fluid properties, fluid density 00:04:16.230 --> 00:04:17.870 align:middle line:90% and fluid viscosity. 00:04:17.870 --> 00:04:20.390 align:middle line:84% Those are four variables you need to deal with. 00:04:20.390 --> 00:04:25.070 align:middle line:90% 00:04:25.070 --> 00:04:31.630 align:middle line:84% So if you tried to graph a four-dimensional diagram, well, 00:04:31.630 --> 00:04:32.690 align:middle line:90% that's impossible, right? 00:04:32.690 --> 00:04:34.110 align:middle line:90% You can't possibly do that. 00:04:34.110 --> 00:04:37.510 align:middle line:84% So you'd think that we're stuck in dealing with this 00:04:37.510 --> 00:04:39.270 align:middle line:90% and representing this. 00:04:39.270 --> 00:04:42.890 align:middle line:90% But-- oh, this is an example. 00:04:42.890 --> 00:04:45.730 align:middle line:84% This is just an example I threw in of existence fields. 00:04:45.730 --> 00:04:48.010 align:middle line:84% You probably in some PCAM or thermo course, 00:04:48.010 --> 00:04:52.230 align:middle line:84% you've had to deal with the phase diagram for water, ice, 00:04:52.230 --> 00:04:54.030 align:middle line:90% vapor, water. 00:04:54.030 --> 00:04:55.250 align:middle line:90% And that's the kind of thing. 00:04:55.250 --> 00:04:59.830 align:middle line:84% But you can't do that in four dimensions very easily. 00:04:59.830 --> 00:05:03.270 align:middle line:84% So there's a technique in mechanics 00:05:03.270 --> 00:05:05.830 align:middle line:90% called dimensional analysis. 00:05:05.830 --> 00:05:09.110 align:middle line:84% And you can get really useful information about something. 00:05:09.110 --> 00:05:11.750 align:middle line:84% You don't have a solution, but you have some idea 00:05:11.750 --> 00:05:13.090 align:middle line:90% about the physical effects. 00:05:13.090 --> 00:05:14.170 align:middle line:90% So here's what you do. 00:05:14.170 --> 00:05:16.710 align:middle line:90% 00:05:16.710 --> 00:05:18.523 align:middle line:84% Buckingham's theorem-- Edgar Buckingham, 00:05:18.523 --> 00:05:19.690 align:middle line:90% I don't know much about him. 00:05:19.690 --> 00:05:21.190 align:middle line:90% He was an American physicist. 00:05:21.190 --> 00:05:23.030 align:middle line:84% And he was one of a few people who 00:05:23.030 --> 00:05:27.550 align:middle line:84% developed this idea of dimensional analysis. 00:05:27.550 --> 00:05:31.070 align:middle line:90% You can look him up on YouTube-- 00:05:31.070 --> 00:05:35.370 align:middle line:84% you can google him and look him up on the internet. 00:05:35.370 --> 00:05:37.150 align:middle line:90% So here's the theorem. 00:05:37.150 --> 00:05:41.890 align:middle line:84% Now, I went through the proof of this back maybe 60 years ago. 00:05:41.890 --> 00:05:43.470 align:middle line:84% And it's not difficult. But you're 00:05:43.470 --> 00:05:46.350 align:middle line:84% going to have to take my word for it that it works. 00:05:46.350 --> 00:05:48.030 align:middle line:84% The number of dimensionless variables 00:05:48.030 --> 00:05:51.202 align:middle line:84% corresponding to the number n of original variables 00:05:51.202 --> 00:05:52.660 align:middle line:84% that describe the physical problem, 00:05:52.660 --> 00:05:54.320 align:middle line:90% it's equal to n minus m. 00:05:54.320 --> 00:05:57.400 align:middle line:84% n is the number and m is the number of fundamental dimensions 00:05:57.400 --> 00:06:00.560 align:middle line:90% mass, length, and time. 00:06:00.560 --> 00:06:03.440 align:middle line:84% This is a time-honored and very useful 00:06:03.440 --> 00:06:06.400 align:middle line:84% thing to do in fluid mechanics and other mechanics. 00:06:06.400 --> 00:06:12.840 align:middle line:84% So the way it comes out, rho UD over mu-- density, velocity, 00:06:12.840 --> 00:06:16.840 align:middle line:90% duct size, and viscosity. 00:06:16.840 --> 00:06:21.320 align:middle line:84% And it's called his number, in his honor, or Reynolds number. 00:06:21.320 --> 00:06:22.445 align:middle line:90% I say a Reynolds number. 00:06:22.445 --> 00:06:24.320 align:middle line:84% There are other Reynolds numbers coming along 00:06:24.320 --> 00:06:25.620 align:middle line:90% of the same kind of thing. 00:06:25.620 --> 00:06:28.720 align:middle line:90% 00:06:28.720 --> 00:06:31.400 align:middle line:84% So we've collapsed four dimensional variables 00:06:31.400 --> 00:06:33.160 align:middle line:84% into just one dimensional variable. 00:06:33.160 --> 00:06:36.760 align:middle line:84% All you need to specify to describe the slope of the tube 00:06:36.760 --> 00:06:37.755 align:middle line:90% is Reynolds number. 00:06:37.755 --> 00:06:39.380 align:middle line:84% Nothing else, just the Reynolds number. 00:06:39.380 --> 00:06:40.620 align:middle line:90% It's a very powerful tool. 00:06:40.620 --> 00:06:43.160 align:middle line:90% And we're going to be using it. 00:06:43.160 --> 00:06:44.960 align:middle line:84% So let's look at another problem which 00:06:44.960 --> 00:06:49.450 align:middle line:84% is relevant to sedimentary geology, flow past a sphere. 00:06:49.450 --> 00:06:51.250 align:middle line:90% What's the drag force? 00:06:51.250 --> 00:06:54.690 align:middle line:84% What's the drag force when it's moving in a viscous fluid? 00:06:54.690 --> 00:06:57.610 align:middle line:90% Again, we have four variables. 00:06:57.610 --> 00:06:59.690 align:middle line:90% The same ones-- rho UD over mu. 00:06:59.690 --> 00:07:01.930 align:middle line:84% But U is now the approaching flow. 00:07:01.930 --> 00:07:03.310 align:middle line:90% D is the diameter of the sphere. 00:07:03.310 --> 00:07:06.030 align:middle line:84% So the drag force is a function of the Reynolds number-- 00:07:06.030 --> 00:07:07.383 align:middle line:90% another Reynolds number. 00:07:07.383 --> 00:07:08.550 align:middle line:90% Does that make sense to you? 00:07:08.550 --> 00:07:11.650 align:middle line:90% 00:07:11.650 --> 00:07:14.770 align:middle line:84% But it's not quite as simple as it looks. 00:07:14.770 --> 00:07:16.560 align:middle line:90% Why? 00:07:16.560 --> 00:07:18.690 align:middle line:90% Why is that not too simple? 00:07:18.690 --> 00:07:23.890 align:middle line:84% Here you have a sphere held there and a fluid flows by it. 00:07:23.890 --> 00:07:26.050 align:middle line:90% And it's a drag force. 00:07:26.050 --> 00:07:30.770 align:middle line:84% But there's another way it could be done. 00:07:30.770 --> 00:07:35.577 align:middle line:84% You could drop a sphere into a body of still water. 00:07:35.577 --> 00:07:36.910 align:middle line:90% And there's still a force on it. 00:07:36.910 --> 00:07:37.750 align:middle line:90% It's a gravity force. 00:07:37.750 --> 00:07:39.333 align:middle line:84% And it's moving relative to the fluid. 00:07:39.333 --> 00:07:40.570 align:middle line:90% But what's the difference? 00:07:40.570 --> 00:07:42.910 align:middle line:84% Tell me the difference between those two cases. 00:07:42.910 --> 00:07:46.290 align:middle line:90% 00:07:46.290 --> 00:07:47.730 align:middle line:90% I'll give you a hint. 00:07:47.730 --> 00:07:48.910 align:middle line:90% It's the T word. 00:07:48.910 --> 00:07:52.730 align:middle line:90% 00:07:52.730 --> 00:07:55.170 align:middle line:84% In the case of holding the sphere steady 00:07:55.170 --> 00:07:58.570 align:middle line:84% and letting the flow by it, the flow is likely to be turbulent. 00:07:58.570 --> 00:08:03.370 align:middle line:84% And the sphere will have to react to certain differences 00:08:03.370 --> 00:08:05.890 align:middle line:84% in the speed of the flow because of the turbulent eddies 00:08:05.890 --> 00:08:06.850 align:middle line:90% going by. 00:08:06.850 --> 00:08:09.370 align:middle line:90% Whereas if you drop the sphere-- 00:08:09.370 --> 00:08:13.132 align:middle line:84% a negatively buoyant sphere-- into a body of water, 00:08:13.132 --> 00:08:14.590 align:middle line:84% there's no turbulence in the water. 00:08:14.590 --> 00:08:15.410 align:middle line:90% It's still. 00:08:15.410 --> 00:08:19.250 align:middle line:84% And that makes a small but non-negligible difference 00:08:19.250 --> 00:08:19.943 align:middle line:90% in how it works. 00:08:19.943 --> 00:08:21.110 align:middle line:90% Does that make sense to you? 00:08:21.110 --> 00:08:23.722 align:middle line:90% 00:08:23.722 --> 00:08:25.430 align:middle line:84% Incidentally, we're going to get to this. 00:08:25.430 --> 00:08:27.610 align:middle line:84% I'll tell you more about this later. 00:08:27.610 --> 00:08:29.730 align:middle line:84% Now let's look at open channel flows. 00:08:29.730 --> 00:08:31.155 align:middle line:84% That's clearly an important thing 00:08:31.155 --> 00:08:32.530 align:middle line:84% to think about when we're dealing 00:08:32.530 --> 00:08:35.830 align:middle line:84% with the sediment transport, by unidirectional flows. 00:08:35.830 --> 00:08:39.330 align:middle line:84% And that's what this hour is about. 00:08:39.330 --> 00:08:41.370 align:middle line:84% Say you're standing out there next to a river 00:08:41.370 --> 00:08:44.770 align:middle line:84% and the sun is shining and you try to look sideways 00:08:44.770 --> 00:08:47.940 align:middle line:90% at the flow downstream. 00:08:47.940 --> 00:08:50.900 align:middle line:90% What is it like? 00:08:50.900 --> 00:08:52.940 align:middle line:84% So I have to introduce two things here. 00:08:52.940 --> 00:08:54.960 align:middle line:84% A steady flow-- this is definitions. 00:08:54.960 --> 00:08:58.220 align:middle line:84% A steady flow means no change with time. 00:08:58.220 --> 00:09:04.620 align:middle line:84% And a uniform flow means same at all cross sections downstream. 00:09:04.620 --> 00:09:05.120 align:middle line:90% All right. 00:09:05.120 --> 00:09:07.400 align:middle line:90% So here are the forces involved. 00:09:07.400 --> 00:09:10.120 align:middle line:90% What pulls the flow down slope? 00:09:10.120 --> 00:09:13.860 align:middle line:84% Well, it's the downslope component 00:09:13.860 --> 00:09:15.620 align:middle line:90% of the weight of the fluid. 00:09:15.620 --> 00:09:19.312 align:middle line:84% You all know about doing vectors and figuring out 00:09:19.312 --> 00:09:20.520 align:middle line:90% components of vectors, right? 00:09:20.520 --> 00:09:24.500 align:middle line:84% But there has to be a resisting force if it's a uniform flow. 00:09:24.500 --> 00:09:27.400 align:middle line:84% And that's the friction force at the base. 00:09:27.400 --> 00:09:30.060 align:middle line:84% So these two are balanced when you have uniform flow. 00:09:30.060 --> 00:09:30.720 align:middle line:90% Make sense? 00:09:30.720 --> 00:09:33.900 align:middle line:90% 00:09:33.900 --> 00:09:35.278 align:middle line:90% So what variables do we need? 00:09:35.278 --> 00:09:37.820 align:middle line:84% Now we're going to do the same thing in dimensional analysis. 00:09:37.820 --> 00:09:39.112 align:middle line:90% What are the variables we need? 00:09:39.112 --> 00:09:41.220 align:middle line:84% Mean flow, velocity, and depth, obviously. 00:09:41.220 --> 00:09:42.740 align:middle line:90% Density and viscosity. 00:09:42.740 --> 00:09:44.350 align:middle line:90% But there's one more-- 00:09:44.350 --> 00:09:47.750 align:middle line:90% the acceleration due to gravity. 00:09:47.750 --> 00:09:50.510 align:middle line:90% And why is that important? 00:09:50.510 --> 00:09:53.330 align:middle line:84% That's not an easy question, but you need to think about it. 00:09:53.330 --> 00:09:54.688 align:middle line:90% Why do you need gravity here? 00:09:54.688 --> 00:09:56.730 align:middle line:84% You don't need it because of the downslope force, 00:09:56.730 --> 00:10:02.950 align:middle line:84% because that's all taken care of by the weight of the fluid. 00:10:02.950 --> 00:10:05.030 align:middle line:90% Surface waves. 00:10:05.030 --> 00:10:08.710 align:middle line:84% Wind blows over the surface and it can create surface waves. 00:10:08.710 --> 00:10:11.510 align:middle line:84% So that's an additional thing about the flow. 00:10:11.510 --> 00:10:14.830 align:middle line:84% It turns out that waves develop on the surface not because 00:10:14.830 --> 00:10:17.510 align:middle line:84% of wind, but because of an instability that 00:10:17.510 --> 00:10:21.162 align:middle line:90% develops at high flow speeds. 00:10:21.162 --> 00:10:22.870 align:middle line:84% And I'll say a little bit more about that 00:10:22.870 --> 00:10:24.430 align:middle line:84% because there are things called antidunes. 00:10:24.430 --> 00:10:26.930 align:middle line:84% You ever heard of-- how many people have heard of antidunes? 00:10:26.930 --> 00:10:27.910 align:middle line:90% All right, good. 00:10:27.910 --> 00:10:30.710 align:middle line:90% Anyway. 00:10:30.710 --> 00:10:34.630 align:middle line:84% Because those are waves on the water surface 00:10:34.630 --> 00:10:36.930 align:middle line:84% that can be stationary or moving upstream, 00:10:36.930 --> 00:10:38.570 align:middle line:84% and they affect the sediment transport. 00:10:38.570 --> 00:10:39.630 align:middle line:90% So we need five. 00:10:39.630 --> 00:10:41.750 align:middle line:84% Well, that tells us by dimensional analysis, 00:10:41.750 --> 00:10:46.710 align:middle line:84% how many dimensionless variables would we have? 00:10:46.710 --> 00:10:49.190 align:middle line:84% We had four variables in the previous 00:10:49.190 --> 00:10:51.350 align:middle line:84% and we got one dimensionless variable, 00:10:51.350 --> 00:10:54.070 align:middle line:84% three less than the number of variables. 00:10:54.070 --> 00:10:55.832 align:middle line:90% So how many would we have here? 00:10:55.832 --> 00:10:56.790 align:middle line:90% You'd have two of them. 00:10:56.790 --> 00:10:59.550 align:middle line:90% Right, OK. 00:10:59.550 --> 00:11:01.950 align:middle line:84% So we have another Reynolds number, 00:11:01.950 --> 00:11:04.330 align:middle line:84% this one would be based on flow depth and flow velocity. 00:11:04.330 --> 00:11:06.780 align:middle line:84% There are lots of Reynolds numbers around. 00:11:06.780 --> 00:11:08.150 align:middle line:90% It's based on depth. 00:11:08.150 --> 00:11:10.230 align:middle line:90% But we need another one. 00:11:10.230 --> 00:11:12.110 align:middle line:90% It's called the Froude number. 00:11:12.110 --> 00:11:15.870 align:middle line:84% And it has g in it, U squared over gd. 00:11:15.870 --> 00:11:17.910 align:middle line:84% Sometimes people take the square root of that 00:11:17.910 --> 00:11:19.243 align:middle line:90% and call that the Froude number. 00:11:19.243 --> 00:11:23.630 align:middle line:84% Anyway, because of certain possible surface gravity waves. 00:11:23.630 --> 00:11:27.350 align:middle line:84% Here he is, William Froude, engineer, fluid dynamicist, 00:11:27.350 --> 00:11:28.210 align:middle line:90% naval architect. 00:11:28.210 --> 00:11:29.910 align:middle line:90% Did a lot of stuff. 00:11:29.910 --> 00:11:32.550 align:middle line:84% And I've always wondered how he pronounced his name "frood" 00:11:32.550 --> 00:11:33.490 align:middle line:90% or "frowd". 00:11:33.490 --> 00:11:36.590 align:middle line:84% And I finally recently learned that it's "frood". 00:11:36.590 --> 00:11:39.030 align:middle line:90% So it's the Froude number. 00:11:39.030 --> 00:11:41.120 align:middle line:84% AUDIENCE: I've also heard "froid" number. 00:11:41.120 --> 00:11:42.162 align:middle line:90% JOHN SOUTHARD: Say again. 00:11:42.162 --> 00:11:44.852 align:middle line:84% AUDIENCE: I've also heard "froid" number. 00:11:44.852 --> 00:11:46.560 align:middle line:84% JOHN SOUTHARD: Freud as in Sigmund Freud? 00:11:46.560 --> 00:11:48.480 align:middle line:84% AUDIENCE: Yes, pronounced that way. 00:11:48.480 --> 00:11:48.980 align:middle line:90% Yeah. 00:11:48.980 --> 00:11:50.920 align:middle line:84% JOHN SOUTHARD: They probably mean this. 00:11:50.920 --> 00:11:52.940 align:middle line:84% They almost certainly mean the Froude number. 00:11:52.940 --> 00:11:53.880 align:middle line:90% AUDIENCE: Yes. 00:11:53.880 --> 00:11:55.480 align:middle line:90% JOHN SOUTHARD: Freud number. 00:11:55.480 --> 00:11:57.860 align:middle line:84% I hesitate to think about what that would describe. 00:11:57.860 --> 00:12:01.840 align:middle line:90% [LAUGHTER] 00:12:01.840 --> 00:12:06.440 align:middle line:84% Anyway, so let's think about the velocity structure of the flow. 00:12:06.440 --> 00:12:09.640 align:middle line:84% And we have our little magic-- here's another magic-- 00:12:09.640 --> 00:12:10.980 align:middle line:90% I love magic things. 00:12:10.980 --> 00:12:12.600 align:middle line:84% We have a little current meter that we 00:12:12.600 --> 00:12:16.420 align:middle line:84% can place at various positions above the base of the flow. 00:12:16.420 --> 00:12:18.820 align:middle line:84% And we measure the time average velocity, 00:12:18.820 --> 00:12:21.520 align:middle line:84% just time it for a minute or two minutes or five minutes. 00:12:21.520 --> 00:12:23.280 align:middle line:90% And you get a profile. 00:12:23.280 --> 00:12:26.000 align:middle line:84% And let's talk about the profile. 00:12:26.000 --> 00:12:29.880 align:middle line:84% What's characteristic about it is it's 00:12:29.880 --> 00:12:33.560 align:middle line:84% fairly evenly distributed in the upper part of the flow. 00:12:33.560 --> 00:12:38.720 align:middle line:84% But it rapidly goes down to 0 at the bed. 00:12:38.720 --> 00:12:43.520 align:middle line:84% And we need to think about why that is. 00:12:43.520 --> 00:12:46.480 align:middle line:84% There's something called the no-slip condition. 00:12:46.480 --> 00:12:49.520 align:middle line:84% The fluid at the boundary has the same velocity 00:12:49.520 --> 00:12:50.800 align:middle line:90% as the boundary. 00:12:50.800 --> 00:12:53.340 align:middle line:84% It's not like tilting up the table, putting a brick on it, 00:12:53.340 --> 00:12:55.120 align:middle line:84% and having the brick slide down the table, 00:12:55.120 --> 00:12:59.460 align:middle line:84% because there's actual a jump discontinuity in velocity. 00:12:59.460 --> 00:13:01.960 align:middle line:84% But that's not the way fluid flows are. 00:13:01.960 --> 00:13:05.800 align:middle line:84% The fluid motion is always 0 in contact with the boundary. 00:13:05.800 --> 00:13:08.680 align:middle line:84% So now you can think about why is the profile much steeper 00:13:08.680 --> 00:13:11.040 align:middle line:84% near the base than it is higher up. 00:13:11.040 --> 00:13:12.160 align:middle line:90% Think about it. 00:13:12.160 --> 00:13:14.720 align:middle line:84% Somebody come up with an answer here. 00:13:14.720 --> 00:13:20.080 align:middle line:84% Why would-- again, I'll give you the hint-- the T word. 00:13:20.080 --> 00:13:23.532 align:middle line:90% How about the T word? 00:13:23.532 --> 00:13:25.740 align:middle line:84% AUDIENCE: Does the surface roughness near the surface 00:13:25.740 --> 00:13:26.960 align:middle line:90% disrupt turbulence? 00:13:26.960 --> 00:13:27.680 align:middle line:84% JOHN SOUTHARD: I'm sorry, I couldn't hear you. 00:13:27.680 --> 00:13:29.780 align:middle line:84% AUDIENCE: Is the surface roughness near the bottom 00:13:29.780 --> 00:13:30.838 align:middle line:90% disrupt turbulence? 00:13:30.838 --> 00:13:32.380 align:middle line:84% JOHN SOUTHARD: Well, that's relevant, 00:13:32.380 --> 00:13:33.740 align:middle line:90% but there's more to the story. 00:13:33.740 --> 00:13:35.500 align:middle line:84% And I'm going to get to that pretty soon. 00:13:35.500 --> 00:13:37.500 align:middle line:90% This is a simpler answer. 00:13:37.500 --> 00:13:41.290 align:middle line:90% 00:13:41.290 --> 00:13:44.273 align:middle line:84% It's a turbulent flow and the turbulent eddies 00:13:44.273 --> 00:13:45.190 align:middle line:90% are doing their thing. 00:13:45.190 --> 00:13:47.010 align:middle line:84% But the closer you get to the bottom, 00:13:47.010 --> 00:13:49.650 align:middle line:84% the less possibility there is for the turbulence 00:13:49.650 --> 00:13:52.370 align:middle line:90% to exchange momentum vertically. 00:13:52.370 --> 00:13:54.030 align:middle line:84% And that goes to 0 at the boundary, 00:13:54.030 --> 00:13:55.930 align:middle line:84% because the flow is always parallel 00:13:55.930 --> 00:13:58.230 align:middle line:90% to the boundary at the boundary. 00:13:58.230 --> 00:14:01.327 align:middle line:84% So over most of the flow, there's very effective-- 00:14:01.327 --> 00:14:03.410 align:middle line:84% I don't need to hold that, because I use my hands. 00:14:03.410 --> 00:14:05.610 align:middle line:84% It's very effective mixing back and forth, 00:14:05.610 --> 00:14:08.490 align:middle line:84% eddies exchanging positions and evening out 00:14:08.490 --> 00:14:10.710 align:middle line:84% the flow structure, the velocity. 00:14:10.710 --> 00:14:13.770 align:middle line:84% Whereas you go down near the bottom, and the turbulence 00:14:13.770 --> 00:14:15.970 align:middle line:90% becomes imperceptible. 00:14:15.970 --> 00:14:21.010 align:middle line:84% And so the flow has a very steep gradient right 00:14:21.010 --> 00:14:21.950 align:middle line:90% near the boundary. 00:14:21.950 --> 00:14:24.970 align:middle line:90% 00:14:24.970 --> 00:14:26.990 align:middle line:84% And it's called the viscosity-dominated layer. 00:14:26.990 --> 00:14:29.532 align:middle line:84% Now, you know about viscosity I'm going to have a slide on it 00:14:29.532 --> 00:14:30.410 align:middle line:90% pretty soon. 00:14:30.410 --> 00:14:33.170 align:middle line:84% It's basically a measure of the resistance to shearing 00:14:33.170 --> 00:14:35.610 align:middle line:90% in a continuous medium. 00:14:35.610 --> 00:14:38.200 align:middle line:84% And so here's that profile we had. 00:14:38.200 --> 00:14:39.900 align:middle line:90% And it's turbulent up in here. 00:14:39.900 --> 00:14:43.100 align:middle line:84% But down near the base, the turbulence is almost damped out 00:14:43.100 --> 00:14:45.780 align:middle line:84% and any horizontal motions are very weak. 00:14:45.780 --> 00:14:50.100 align:middle line:84% And so the flow here is dominated by viscous effects, 00:14:50.100 --> 00:14:51.620 align:middle line:90% not turbulence effects. 00:14:51.620 --> 00:14:55.060 align:middle line:84% And that's a basic characteristic of channel flows 00:14:55.060 --> 00:14:58.620 align:middle line:90% you need to know about. 00:14:58.620 --> 00:14:59.980 align:middle line:90% So some terminology. 00:14:59.980 --> 00:15:02.000 align:middle line:84% It's not too important for our purposes. 00:15:02.000 --> 00:15:04.540 align:middle line:84% But there's a turbulence-dominated region. 00:15:04.540 --> 00:15:06.740 align:middle line:84% And a viscosity-dominated region is what they 00:15:06.740 --> 00:15:08.660 align:middle line:90% call a buffer layer in between. 00:15:08.660 --> 00:15:09.900 align:middle line:90% It's just terminology. 00:15:09.900 --> 00:15:13.780 align:middle line:84% And it's not to scale, obviously. 00:15:13.780 --> 00:15:14.320 align:middle line:90% All right. 00:15:14.320 --> 00:15:16.388 align:middle line:90% So now let's see. 00:15:16.388 --> 00:15:17.680 align:middle line:90% Oh, I can't remember your name. 00:15:17.680 --> 00:15:19.440 align:middle line:90% Kuh, Kuh, Kuh-ren? 00:15:19.440 --> 00:15:20.580 align:middle line:90% AUDIENCE: Koh Ze-Wen 00:15:20.580 --> 00:15:21.372 align:middle line:90% JOHN SOUTHARD: Koh? 00:15:21.372 --> 00:15:22.500 align:middle line:90% AUDIENCE: Ze-Wen 00:15:22.500 --> 00:15:23.800 align:middle line:90% JOHN SOUTHARD: OK, you-- 00:15:23.800 --> 00:15:27.420 align:middle line:90% 00:15:27.420 --> 00:15:31.100 align:middle line:84% we have to think about not just smooth planar boundaries, 00:15:31.100 --> 00:15:34.060 align:middle line:84% but in our case, as sedimentologists, we 00:15:34.060 --> 00:15:36.140 align:middle line:84% have to think about rough boundaries. 00:15:36.140 --> 00:15:39.220 align:middle line:84% And it seems simple, but it's not really as simple 00:15:39.220 --> 00:15:42.260 align:middle line:90% as it seems. 00:15:42.260 --> 00:15:44.360 align:middle line:90% This is a tough slide. 00:15:44.360 --> 00:15:45.700 align:middle line:90% It's in the notes. 00:15:45.700 --> 00:15:49.180 align:middle line:84% So we have something called dynamically smooth flow 00:15:49.180 --> 00:15:51.180 align:middle line:90% and dynamically rough flow. 00:15:51.180 --> 00:15:55.740 align:middle line:84% And dynamically smooth flow is like what I showed you. 00:15:55.740 --> 00:15:58.020 align:middle line:84% It's a viscosity-dominated layer. 00:15:58.020 --> 00:16:01.380 align:middle line:84% And the surface grains or particles 00:16:01.380 --> 00:16:03.960 align:middle line:84% are immersed in this viscosity-dominated layer. 00:16:03.960 --> 00:16:06.100 align:middle line:84% And it's as if it was a planar boundary. 00:16:06.100 --> 00:16:08.260 align:middle line:84% As far as the flow is concerned, it's 00:16:08.260 --> 00:16:10.020 align:middle line:84% as if it's over a planar boundary. 00:16:10.020 --> 00:16:15.260 align:middle line:84% But for stronger flows, the particles 00:16:15.260 --> 00:16:17.920 align:middle line:84% stick up above the viscosity-dominated layer. 00:16:17.920 --> 00:16:20.680 align:middle line:84% There basically is no viscosity-dominated layer. 00:16:20.680 --> 00:16:23.160 align:middle line:84% And the particles are shedding turbulence. 00:16:23.160 --> 00:16:26.980 align:middle line:84% And the turbulence extends right down near the grains. 00:16:26.980 --> 00:16:30.500 align:middle line:90% So that's worth keeping in mind. 00:16:30.500 --> 00:16:32.480 align:middle line:90% So this may help you. 00:16:32.480 --> 00:16:33.390 align:middle line:90% We'll see. 00:16:33.390 --> 00:16:37.870 align:middle line:84% A boundary can be physically smooth and with all viscous drag 00:16:37.870 --> 00:16:39.150 align:middle line:90% and no roughness. 00:16:39.150 --> 00:16:40.530 align:middle line:90% It's dynamically smooth. 00:16:40.530 --> 00:16:42.213 align:middle line:90% But it can be physically rough. 00:16:42.213 --> 00:16:43.630 align:middle line:84% And when it's physically rough, it 00:16:43.630 --> 00:16:46.642 align:middle line:84% can be dynamically smooth because it's 00:16:46.642 --> 00:16:48.350 align:middle line:84% all viscous drag and pressure drag, which 00:16:48.350 --> 00:16:50.310 align:middle line:90% I'm going to talk about soon. 00:16:50.310 --> 00:16:53.630 align:middle line:84% And on the other hand, at higher velocities, 00:16:53.630 --> 00:16:56.310 align:middle line:90% it can be dynamically rough. 00:16:56.310 --> 00:16:58.590 align:middle line:84% So that's the difference between them. 00:16:58.590 --> 00:17:01.310 align:middle line:84% I haven't told you what Re* is, but I'm going to get there 00:17:01.310 --> 00:17:02.050 align:middle line:90% eventually. 00:17:02.050 --> 00:17:04.672 align:middle line:90% 00:17:04.672 --> 00:17:07.130 align:middle line:84% Boundary Reynolds number-- there's another Reynolds number. 00:17:07.130 --> 00:17:09.297 align:middle line:84% Boundary Reynolds number, roughness Reynolds number, 00:17:09.297 --> 00:17:11.450 align:middle line:84% it's a kind of dimensionless boundary shear stress. 00:17:11.450 --> 00:17:12.450 align:middle line:90% And it's useful. 00:17:12.450 --> 00:17:16.310 align:middle line:84% Rho to the 1/2 tau 0 is the boundary shear stress to the 1/2 00:17:16.310 --> 00:17:17.730 align:middle line:90% D divided by mu. 00:17:17.730 --> 00:17:20.349 align:middle line:84% So this is a useful little Reynolds number 00:17:20.349 --> 00:17:22.430 align:middle line:90% that you have to deal with. 00:17:22.430 --> 00:17:26.030 align:middle line:84% So now to change the pace here, there's 00:17:26.030 --> 00:17:28.470 align:middle line:84% something called the Navier-Stokes equation. 00:17:28.470 --> 00:17:33.080 align:middle line:84% It's a long partial differential equation that 00:17:33.080 --> 00:17:35.400 align:middle line:90% accounts for all of fluid flow. 00:17:35.400 --> 00:17:37.880 align:middle line:84% The trouble is, it's very hard to solve. 00:17:37.880 --> 00:17:42.280 align:middle line:84% You can't solve it analytically, for most problems. 00:17:42.280 --> 00:17:45.240 align:middle line:84% And I'm not going to tell you about the Navier-Stokes 00:17:45.240 --> 00:17:50.200 align:middle line:84% equation, except to show you the two people who developed it, 00:17:50.200 --> 00:17:53.280 align:middle line:84% Claude-Louis Navier, who was a French physicist 00:17:53.280 --> 00:17:56.760 align:middle line:84% and civil engineer, and Sir George Gabriel 00:17:56.760 --> 00:18:01.440 align:middle line:84% Stokes, mathematician, physicist, 00:18:01.440 --> 00:18:02.940 align:middle line:90% fellow of the Royal Society. 00:18:02.940 --> 00:18:05.880 align:middle line:90% Big deal, right? 00:18:05.880 --> 00:18:10.000 align:middle line:84% So there's something called creeping flow. 00:18:10.000 --> 00:18:13.040 align:middle line:84% What you do is forget about turbulence 00:18:13.040 --> 00:18:18.960 align:middle line:84% and just look at the viscous fluid flow at very low Reynolds 00:18:18.960 --> 00:18:20.340 align:middle line:90% numbers, which I told you about. 00:18:20.340 --> 00:18:21.900 align:middle line:90% And it's called creeping flow. 00:18:21.900 --> 00:18:23.800 align:middle line:84% This is what it looks like past a sphere. 00:18:23.800 --> 00:18:27.560 align:middle line:84% The streamlines diverge, go around the particle, 00:18:27.560 --> 00:18:28.420 align:middle line:90% converge again. 00:18:28.420 --> 00:18:31.320 align:middle line:84% But I didn't draw it quite right. 00:18:31.320 --> 00:18:32.880 align:middle line:90% I didn't emphasize it enough. 00:18:32.880 --> 00:18:38.280 align:middle line:84% They come together slower than they went apart, 00:18:38.280 --> 00:18:41.300 align:middle line:84% which means there's a force on the particle. 00:18:41.300 --> 00:18:47.060 align:middle line:84% So this is useful for small particles in slow flows. 00:18:47.060 --> 00:18:51.320 align:middle line:90% 00:18:51.320 --> 00:18:55.360 align:middle line:84% Stokes solved the Navier-Stokes equations 00:18:55.360 --> 00:18:57.420 align:middle line:90% by ignoring viscous effects. 00:18:57.420 --> 00:19:01.280 align:middle line:84% You throw out viscosity and you have a solvable equation. 00:19:01.280 --> 00:19:04.320 align:middle line:90% No details here. 00:19:04.320 --> 00:19:13.360 align:middle line:84% But the thing about it is that turbulence is not an issue here. 00:19:13.360 --> 00:19:15.360 align:middle line:84% Fluid density is not in that because there's 00:19:15.360 --> 00:19:19.060 align:middle line:84% no fluid accelerations, or very, very weak accelerations, 00:19:19.060 --> 00:19:23.080 align:middle line:84% very slow change in the direction of the flow. 00:19:23.080 --> 00:19:27.890 align:middle line:84% And this has a practical application. 00:19:27.890 --> 00:19:29.350 align:middle line:90% You can measure settling. 00:19:29.350 --> 00:19:33.027 align:middle line:84% You can measure the settling velocities of particles, 00:19:33.027 --> 00:19:34.610 align:middle line:84% so long as the Reynolds number is low. 00:19:34.610 --> 00:19:38.550 align:middle line:84% If you have a tank of water, you add a little fine sand, 00:19:38.550 --> 00:19:41.570 align:middle line:84% silt-sized particle, and you drop it until it settles, 00:19:41.570 --> 00:19:43.730 align:middle line:90% according to Stokes' law-- 00:19:43.730 --> 00:19:46.970 align:middle line:84% and you measure the settling time, rate of settling, 00:19:46.970 --> 00:19:48.930 align:middle line:90% and you can figure out the size. 00:19:48.930 --> 00:19:54.770 align:middle line:84% Back out the size from-- that r is a radius. 00:19:54.770 --> 00:19:57.950 align:middle line:84% If you put diameter in, you change the coefficient. 00:19:57.950 --> 00:19:58.950 align:middle line:90% And this is done. 00:19:58.950 --> 00:20:02.010 align:middle line:84% This is a common thing in studying 00:20:02.010 --> 00:20:05.170 align:middle line:84% fine sediments is to measure the settling velocity 00:20:05.170 --> 00:20:07.950 align:middle line:90% and figuring out the size. 00:20:07.950 --> 00:20:10.650 align:middle line:90% It's very useful. 00:20:10.650 --> 00:20:12.110 align:middle line:90% There are devices to do that. 00:20:12.110 --> 00:20:15.830 align:middle line:84% OK, now let's look at higher Reynolds numbers. 00:20:15.830 --> 00:20:22.610 align:middle line:84% So here's a solid surface that breaks away from the main flow. 00:20:22.610 --> 00:20:25.780 align:middle line:84% And what happens is that the flow has so much 00:20:25.780 --> 00:20:27.980 align:middle line:90% inertia that it keeps on going. 00:20:27.980 --> 00:20:34.480 align:middle line:84% It separates from the solid surface where it breaks away 00:20:34.480 --> 00:20:36.620 align:middle line:90% and falls away from the flow. 00:20:36.620 --> 00:20:39.240 align:middle line:84% And so you get very strong shear. 00:20:39.240 --> 00:20:41.440 align:middle line:84% And that shear develops turbulence on it. 00:20:41.440 --> 00:20:44.820 align:middle line:84% And you have an expanding turbulent shear layer. 00:20:44.820 --> 00:20:47.460 align:middle line:84% And you get a lot of mixing, a lot of entrainment. 00:20:47.460 --> 00:20:53.300 align:middle line:84% And down here, you get a counter-rotating, irregular 00:20:53.300 --> 00:20:55.100 align:middle line:90% turbulent vortex. 00:20:55.100 --> 00:20:56.740 align:middle line:84% And we're going to see a lot of this 00:20:56.740 --> 00:20:59.860 align:middle line:84% when we talk about bedforms, ripples, dunes, et 00:20:59.860 --> 00:21:02.620 align:middle line:84% cetera, because this is a classic kind of thing that 00:21:02.620 --> 00:21:03.320 align:middle line:90% goes on. 00:21:03.320 --> 00:21:05.940 align:middle line:90% 00:21:05.940 --> 00:21:08.140 align:middle line:84% And although I didn't mention it in the slide, 00:21:08.140 --> 00:21:11.580 align:middle line:84% it takes a long way down past the point 00:21:11.580 --> 00:21:15.420 align:middle line:84% of separation for the flow to adjust itself 00:21:15.420 --> 00:21:18.020 align:middle line:90% to conditions that are-- 00:21:18.020 --> 00:21:20.065 align:middle line:84% as if there had been no direction. 00:21:20.065 --> 00:21:22.440 align:middle line:84% That's a very complicated sense, but you see what I mean. 00:21:22.440 --> 00:21:24.780 align:middle line:84% You have to go a long way before the flow comes 00:21:24.780 --> 00:21:28.410 align:middle line:84% back to what it was before it approached this breaking away 00:21:28.410 --> 00:21:29.740 align:middle line:90% point. 00:21:29.740 --> 00:21:34.820 align:middle line:84% And that's painful for people studying flows 00:21:34.820 --> 00:21:38.900 align:middle line:84% around things in open channels, because the channel 00:21:38.900 --> 00:21:41.900 align:middle line:84% has to be very long before the effect of the thing that's 00:21:41.900 --> 00:21:43.220 align:middle line:90% there disappears. 00:21:43.220 --> 00:21:46.060 align:middle line:90% But you have to live with that. 00:21:46.060 --> 00:21:48.660 align:middle line:84% So this is what it would look like around a sphere. 00:21:48.660 --> 00:21:51.260 align:middle line:84% Now, this separation is not a line. 00:21:51.260 --> 00:21:54.780 align:middle line:84% It's a circle that goes around the flow transverse 00:21:54.780 --> 00:21:56.320 align:middle line:90% cross-section particle. 00:21:56.320 --> 00:22:00.220 align:middle line:84% And that's where flow-- there's a flow separation ring that goes 00:22:00.220 --> 00:22:01.900 align:middle line:84% away, goes downstream of the flow, 00:22:01.900 --> 00:22:03.700 align:middle line:84% with the kind of thing I described-- 00:22:03.700 --> 00:22:09.020 align:middle line:84% turbulent shear layer developing all around as is a-- 00:22:09.020 --> 00:22:15.720 align:middle line:84% with this blobby mass wake right behind the sphere. 00:22:15.720 --> 00:22:18.700 align:middle line:90% 00:22:18.700 --> 00:22:20.780 align:middle line:84% I want to introduce two terms here, 00:22:20.780 --> 00:22:22.830 align:middle line:90% skin friction and form drag. 00:22:22.830 --> 00:22:25.990 align:middle line:84% I used the term form drag in an earlier figure 00:22:25.990 --> 00:22:28.550 align:middle line:84% and I didn't think to define it for you. 00:22:28.550 --> 00:22:31.370 align:middle line:84% Skin friction is a viscous force that's on a solid boundary. 00:22:31.370 --> 00:22:33.350 align:middle line:84% And I've told you about viscosity. 00:22:33.350 --> 00:22:36.230 align:middle line:84% Form drag is the front and back pressure forces 00:22:36.230 --> 00:22:38.070 align:middle line:90% because of flow separation. 00:22:38.070 --> 00:22:43.990 align:middle line:84% It turns out that-- and I should go back to this slide. 00:22:43.990 --> 00:22:48.990 align:middle line:84% It turns out that the pressure is high is-- 00:22:48.990 --> 00:22:49.650 align:middle line:90% I'm sorry. 00:22:49.650 --> 00:22:51.310 align:middle line:90% It's high at the front. 00:22:51.310 --> 00:22:56.390 align:middle line:84% And then in the back, the low pressure above and all 00:22:56.390 --> 00:22:59.890 align:middle line:84% around that circle means low pressure. 00:22:59.890 --> 00:23:04.110 align:middle line:84% And so that creates a drag force just because 00:23:04.110 --> 00:23:06.270 align:middle line:90% of the structure of the flow. 00:23:06.270 --> 00:23:10.070 align:middle line:84% And I have another slide here to show you. 00:23:10.070 --> 00:23:10.930 align:middle line:90% Wait a minute. 00:23:10.930 --> 00:23:12.510 align:middle line:90% I have to go. 00:23:12.510 --> 00:23:13.230 align:middle line:90% OK. 00:23:13.230 --> 00:23:19.710 align:middle line:84% So things like the sphere or a sediment particle 00:23:19.710 --> 00:23:25.000 align:middle line:84% can be called a bluff body or a roughness element. 00:23:25.000 --> 00:23:28.640 align:middle line:84% Bluff bodies, your house is a bluff body in the wind. 00:23:28.640 --> 00:23:29.460 align:middle line:90% A semi-trailer. 00:23:29.460 --> 00:23:31.940 align:middle line:84% You come up behind a semi-trailer, it's a bluff body. 00:23:31.940 --> 00:23:35.000 align:middle line:84% And you're tailing him in the wake 00:23:35.000 --> 00:23:36.420 align:middle line:90% and you're feeling it like this. 00:23:36.420 --> 00:23:39.020 align:middle line:84% Then you go to pass him and you're hit with the flow. 00:23:39.020 --> 00:23:41.460 align:middle line:90% And we are bluff bodies. 00:23:41.460 --> 00:23:42.620 align:middle line:90% We are rough elements. 00:23:42.620 --> 00:23:44.740 align:middle line:84% Did you ever think of yourself as a bluff body 00:23:44.740 --> 00:23:45.580 align:middle line:90% and a rough element? 00:23:45.580 --> 00:23:47.480 align:middle line:90% Probably not. 00:23:47.480 --> 00:23:48.220 align:middle line:90% But we are. 00:23:48.220 --> 00:23:52.040 align:middle line:90% 00:23:52.040 --> 00:23:57.480 align:middle line:84% So for a low Reynolds number and not bluff body, smooth boundary, 00:23:57.480 --> 00:24:00.400 align:middle line:84% skin friction-- that is, the friction right at the boundary 00:24:00.400 --> 00:24:03.160 align:middle line:84% between the flow and the solid surface-- 00:24:03.160 --> 00:24:05.640 align:middle line:84% is much greater than this form drag 00:24:05.640 --> 00:24:08.560 align:middle line:84% that I mentioned on the last slide about the flow 00:24:08.560 --> 00:24:09.460 align:middle line:90% around a sphere. 00:24:09.460 --> 00:24:10.820 align:middle line:90% Big pressure difference. 00:24:10.820 --> 00:24:16.640 align:middle line:84% And you get a lot of pressure, a lot of force on the particle. 00:24:16.640 --> 00:24:20.120 align:middle line:84% But relatively high Reynolds number around bluff bodies. 00:24:20.120 --> 00:24:22.900 align:middle line:84% Form drag is far greater than skin friction. 00:24:22.900 --> 00:24:24.140 align:middle line:90% So just keep that in mind. 00:24:24.140 --> 00:24:27.960 align:middle line:90% 00:24:27.960 --> 00:24:30.840 align:middle line:84% Now, there's something called an inviscid fluid. 00:24:30.840 --> 00:24:33.560 align:middle line:84% And there's no such thing as an inviscid fluid. 00:24:33.560 --> 00:24:39.020 align:middle line:84% But it's also called an ideal fluid. 00:24:39.020 --> 00:24:42.020 align:middle line:84% No viscosity, only pressure and velocity. 00:24:42.020 --> 00:24:43.520 align:middle line:90% That's all that's involved. 00:24:43.520 --> 00:24:46.960 align:middle line:84% And it turns out that for large Reynolds numbers, 00:24:46.960 --> 00:24:49.680 align:middle line:84% outside that thin, viscosity-dominated layer, 00:24:49.680 --> 00:24:51.560 align:middle line:84% the nature of the flow is pretty much like it 00:24:51.560 --> 00:24:52.860 align:middle line:90% is in an inviscid fluid. 00:24:52.860 --> 00:24:54.200 align:middle line:90% It's a good approximation. 00:24:54.200 --> 00:25:00.120 align:middle line:84% And that helps us because there's a relationship 00:25:00.120 --> 00:25:02.180 align:middle line:90% between pressure and velocity. 00:25:02.180 --> 00:25:07.240 align:middle line:84% That v is a velocity there, as the flow moves around an object. 00:25:07.240 --> 00:25:09.120 align:middle line:84% So there's an inverse relationship 00:25:09.120 --> 00:25:10.840 align:middle line:90% between velocity and pressure. 00:25:10.840 --> 00:25:12.320 align:middle line:84% And I'll show you why that could be 00:25:12.320 --> 00:25:16.320 align:middle line:84% useful by looking at an airfoil of an airplane wing. 00:25:16.320 --> 00:25:18.570 align:middle line:84% You're probably familiar with this. 00:25:18.570 --> 00:25:21.850 align:middle line:84% The shape is such that when the flow goes around, 00:25:21.850 --> 00:25:26.170 align:middle line:84% because of the stronger arching on the upper surface, 00:25:26.170 --> 00:25:29.190 align:middle line:84% the streamlines are crowded, velocity is higher, 00:25:29.190 --> 00:25:31.570 align:middle line:84% pressure is lower, so you get a lift. 00:25:31.570 --> 00:25:34.650 align:middle line:84% Maybe you knew that about how airplane wings work. 00:25:34.650 --> 00:25:36.570 align:middle line:84% The Wright brothers discovered this 00:25:36.570 --> 00:25:43.130 align:middle line:84% without knowing why back in 1900 or something like that. 00:25:43.130 --> 00:25:44.470 align:middle line:90% This is a complicated slide. 00:25:44.470 --> 00:25:47.010 align:middle line:84% And I'm going to show it in two parts, fluid forces 00:25:47.010 --> 00:25:48.890 align:middle line:84% on a sphere at low Reynolds numbers 00:25:48.890 --> 00:25:50.930 align:middle line:84% and at high Reynolds numbers, A and B. 00:25:50.930 --> 00:25:53.510 align:middle line:84% And just so you can read it more easily, 00:25:53.510 --> 00:25:56.317 align:middle line:84% I'll show you first the one at small Reynolds numbers. 00:25:56.317 --> 00:25:58.650 align:middle line:84% This is the one I defined for you, the boundary Reynolds 00:25:58.650 --> 00:25:59.370 align:middle line:90% number. 00:25:59.370 --> 00:26:06.290 align:middle line:84% And so there's some lift, but there's a lot of drag. 00:26:06.290 --> 00:26:08.822 align:middle line:84% And so the total fluid force is at a moderate sort 00:26:08.822 --> 00:26:11.450 align:middle line:90% of shallow angle. 00:26:11.450 --> 00:26:18.020 align:middle line:84% And the line of action is it is fairly high up on the particle. 00:26:18.020 --> 00:26:20.580 align:middle line:84% Those pluses and little arrows are-- 00:26:20.580 --> 00:26:24.020 align:middle line:84% the pluses and minuses are pressure differences. 00:26:24.020 --> 00:26:28.660 align:middle line:84% And the little single barbed arrows are some friction. 00:26:28.660 --> 00:26:31.100 align:middle line:84% But then I'll show you the other one. 00:26:31.100 --> 00:26:33.260 align:middle line:84% For large Reynolds numbers, this would 00:26:33.260 --> 00:26:37.620 align:middle line:84% be anything coarser than coarse sand up into the gravel range. 00:26:37.620 --> 00:26:40.540 align:middle line:84% And you can see there's a difference. 00:26:40.540 --> 00:26:41.860 align:middle line:90% It's rough flow. 00:26:41.860 --> 00:26:45.060 align:middle line:84% There's flow separation and a big pressure difference 00:26:45.060 --> 00:26:46.180 align:middle line:90% from front to back. 00:26:46.180 --> 00:26:47.720 align:middle line:90% Still some skin friction. 00:26:47.720 --> 00:26:50.340 align:middle line:84% So it's mainly dominated by form drag. 00:26:50.340 --> 00:26:53.420 align:middle line:84% And the lift-- lift is substantial. 00:26:53.420 --> 00:26:58.140 align:middle line:84% I mean, it's almost equal to the horizontal component 00:26:58.140 --> 00:27:00.540 align:middle line:90% of the flow. 00:27:00.540 --> 00:27:02.840 align:middle line:84% So very different, depending on the Reynolds number. 00:27:02.840 --> 00:27:04.820 align:middle line:84% And this is relevant to if we're looking 00:27:04.820 --> 00:27:08.280 align:middle line:84% at a bed of silt or fine sand at relatively slow flows. 00:27:08.280 --> 00:27:09.600 align:middle line:90% That would be the first case. 00:27:09.600 --> 00:27:11.142 align:middle line:84% If we're looking at coarser sediment, 00:27:11.142 --> 00:27:14.020 align:middle line:84% like medium to coarse sand up in the gravel range, 00:27:14.020 --> 00:27:17.380 align:middle line:84% and then strong and large Reynolds numbers-- strong 00:27:17.380 --> 00:27:19.640 align:middle line:90% flows-- we'd draw it like this. 00:27:19.640 --> 00:27:21.800 align:middle line:84% You get a lot of lift, which is important. 00:27:21.800 --> 00:27:24.420 align:middle line:90% We'll see that as time goes on. 00:27:24.420 --> 00:27:24.960 align:middle line:90% All right. 00:27:24.960 --> 00:27:26.980 align:middle line:84% That's my pitch on oscillatory flow. 00:27:26.980 --> 00:27:30.620 align:middle line:84% Now I have to stop for a minute and you in the back 00:27:30.620 --> 00:27:33.900 align:middle line:84% will have to readjust because I want to take my sweater off. 00:27:33.900 --> 00:27:36.400 align:middle line:84% This is the other main topic we have to deal with. 00:27:36.400 --> 00:27:38.887 align:middle line:84% We've looked at unidirectional flows-- down a channel. 00:27:38.887 --> 00:27:39.720 align:middle line:90% It could be a river. 00:27:39.720 --> 00:27:42.620 align:middle line:84% It could be a tidal current, tidal flow, a longshore current 00:27:42.620 --> 00:27:44.300 align:middle line:90% in the shallow ocean. 00:27:44.300 --> 00:27:47.740 align:middle line:84% But there's also oscillatory flow, back and forth flow. 00:27:47.740 --> 00:27:50.287 align:middle line:84% And it's another important thing to deal with. 00:27:50.287 --> 00:27:52.620 align:middle line:84% The approach is going to be a little different from what 00:27:52.620 --> 00:27:55.900 align:middle line:84% I just gave you, but bear with me and see what you think. 00:27:55.900 --> 00:27:58.980 align:middle line:84% All right, so you probably know that that's a wave with a crest 00:27:58.980 --> 00:28:01.460 align:middle line:84% and a trough, a wave height and a wavelength. 00:28:01.460 --> 00:28:05.140 align:middle line:84% That's a typical wave that we would deal with. 00:28:05.140 --> 00:28:09.860 align:middle line:84% And this is a problem with this slide here. 00:28:09.860 --> 00:28:13.510 align:middle line:90% This is supposed to be a circle. 00:28:13.510 --> 00:28:14.690 align:middle line:90% And I know why it happened. 00:28:14.690 --> 00:28:17.350 align:middle line:84% I was resizing it, trying to make it bigger, 00:28:17.350 --> 00:28:18.530 align:middle line:90% and go up and down. 00:28:18.530 --> 00:28:21.790 align:middle line:84% And I don't know how on PowerPoint you 00:28:21.790 --> 00:28:24.117 align:middle line:84% can expand something without changing the dimensions. 00:28:24.117 --> 00:28:25.450 align:middle line:90% There must be a way of doing it. 00:28:25.450 --> 00:28:28.090 align:middle line:90% But I had to relearn PowerPoint. 00:28:28.090 --> 00:28:31.230 align:middle line:84% It's been 15 years since I made a PowerPoint. 00:28:31.230 --> 00:28:32.110 align:middle line:90% Literally, yes. 00:28:32.110 --> 00:28:32.850 align:middle line:90% I had to relearn. 00:28:32.850 --> 00:28:38.910 align:middle line:84% But anyway, so that's what we see when the wave goes by. 00:28:38.910 --> 00:28:40.550 align:middle line:84% But there's an important difference 00:28:40.550 --> 00:28:42.830 align:middle line:84% between the deep water waves and shallow water waves. 00:28:42.830 --> 00:28:45.790 align:middle line:84% And deep water waves, the sea bed 00:28:45.790 --> 00:28:49.682 align:middle line:84% is so far down that the orbits die out slowly with depth 00:28:49.682 --> 00:28:50.390 align:middle line:90% till you get to-- 00:28:50.390 --> 00:28:52.430 align:middle line:84% they disappear before you reach the bottom. 00:28:52.430 --> 00:28:54.990 align:middle line:84% And that's not relevant to our business here. 00:28:54.990 --> 00:29:01.472 align:middle line:84% But the shallow water waves, the orbits are ellipses. 00:29:01.472 --> 00:29:03.430 align:middle line:84% And I can't tell you why, but they're ellipses. 00:29:03.430 --> 00:29:05.590 align:middle line:90% And ellipses die back. 00:29:05.590 --> 00:29:09.510 align:middle line:84% But there's still back and forth motion right at the boundary-- 00:29:09.510 --> 00:29:12.280 align:middle line:84% even at the solid boundary, at the seabed. 00:29:12.280 --> 00:29:13.500 align:middle line:90% And so that's relevant to us. 00:29:13.500 --> 00:29:15.125 align:middle line:84% We're going to think about how sediment 00:29:15.125 --> 00:29:16.820 align:middle line:90% is moved by oscillatory flows. 00:29:16.820 --> 00:29:21.000 align:middle line:90% 00:29:21.000 --> 00:29:21.820 align:middle line:90% It's getting late. 00:29:21.820 --> 00:29:22.320 align:middle line:90% Boy. 00:29:22.320 --> 00:29:23.400 align:middle line:90% It's getting late. 00:29:23.400 --> 00:29:25.380 align:middle line:84% So what is the flow like at the bed? 00:29:25.380 --> 00:29:28.160 align:middle line:90% 00:29:28.160 --> 00:29:30.180 align:middle line:84% Well, again, we'll think about variables. 00:29:30.180 --> 00:29:32.760 align:middle line:84% Wave period, max orbital velocity-- the wave period, 00:29:32.760 --> 00:29:33.260 align:middle line:90% you know it. 00:29:33.260 --> 00:29:37.360 align:middle line:84% And orbital velocity, it moves this way and this way. 00:29:37.360 --> 00:29:39.720 align:middle line:84% And that's an orbital diameter, how far 00:29:39.720 --> 00:29:41.840 align:middle line:90% the it moves back and forth. 00:29:41.840 --> 00:29:45.680 align:middle line:84% And the maximum orbital-- in the middle of the orbit, that's 00:29:45.680 --> 00:29:46.940 align:middle line:90% the maximum velocity. 00:29:46.940 --> 00:29:49.923 align:middle line:90% So there's three variables. 00:29:49.923 --> 00:29:51.340 align:middle line:84% And actually, only two are needed. 00:29:51.340 --> 00:29:52.740 align:middle line:84% Now, I'm not going to prove this, 00:29:52.740 --> 00:29:54.960 align:middle line:84% but it's well-known that the velocity 00:29:54.960 --> 00:29:58.300 align:middle line:84% equals pi times the orbital diameter divided by the period. 00:29:58.300 --> 00:30:00.320 align:middle line:90% You just have to accept that. 00:30:00.320 --> 00:30:01.560 align:middle line:90% Only two of these are-- 00:30:01.560 --> 00:30:05.400 align:middle line:90% 00:30:05.400 --> 00:30:10.280 align:middle line:84% but it's U, m, and T that I and we as sedimentologists 00:30:10.280 --> 00:30:11.940 align:middle line:90% are mostly interested in. 00:30:11.940 --> 00:30:16.300 align:middle line:84% So we have four variables, U, m, T, rho, and mu. 00:30:16.300 --> 00:30:19.240 align:middle line:84% And of course, we get a dimensionless variable. 00:30:19.240 --> 00:30:22.240 align:middle line:84% But it turns out that this doesn't help us much. 00:30:22.240 --> 00:30:24.420 align:middle line:84% I just mentioned that you can do that. 00:30:24.420 --> 00:30:26.700 align:middle line:84% It holds for a smooth bed with no sediment, 00:30:26.700 --> 00:30:28.680 align:middle line:84% but we're dealing with the mobile bed case 00:30:28.680 --> 00:30:33.040 align:middle line:84% pretty soon for sediment transport. 00:30:33.040 --> 00:30:37.520 align:middle line:84% So here's an important point for shallow water 00:30:37.520 --> 00:30:40.920 align:middle line:84% waves with very small amplitude, the time history velocity 00:30:40.920 --> 00:30:42.600 align:middle line:90% is symmetrical. 00:30:42.600 --> 00:30:47.280 align:middle line:84% The forward velocity is equal to the back velocity. 00:30:47.280 --> 00:30:49.800 align:middle line:84% But for large amplitude waves-- and that's 00:30:49.800 --> 00:30:52.920 align:middle line:84% pretty typical of large waves, when the troughs are broad 00:30:52.920 --> 00:30:55.360 align:middle line:84% and the crests are sharp-- it turns out 00:30:55.360 --> 00:31:00.520 align:middle line:84% that when the wave crests are sharper 00:31:00.520 --> 00:31:05.180 align:middle line:84% and the troughs are broader, it's not symmetrical, 00:31:05.180 --> 00:31:06.300 align:middle line:90% it's asymmetrical. 00:31:06.300 --> 00:31:10.650 align:middle line:90% 00:31:10.650 --> 00:31:12.810 align:middle line:90% We just did that. 00:31:12.810 --> 00:31:13.610 align:middle line:90% OK. 00:31:13.610 --> 00:31:16.470 align:middle line:84% So the thing is, if you look at the maximum velocity 00:31:16.470 --> 00:31:21.250 align:middle line:84% when the crest is passing over you forward, 00:31:21.250 --> 00:31:24.590 align:middle line:84% the velocity is higher, but the time of passage is smaller. 00:31:24.590 --> 00:31:27.410 align:middle line:84% And it's the opposite for when the trough is over you 00:31:27.410 --> 00:31:29.050 align:middle line:90% and it's moving backward. 00:31:29.050 --> 00:31:32.570 align:middle line:84% So there's no net movement of sediment. 00:31:32.570 --> 00:31:37.250 align:middle line:84% But it goes this way fast and this way back slow. 00:31:37.250 --> 00:31:39.810 align:middle line:84% And so because-- and I'm not going 00:31:39.810 --> 00:31:42.930 align:middle line:84% to tell you too much about it, but the sediment transport 00:31:42.930 --> 00:31:45.370 align:middle line:84% rate, how much sediment gets moved, 00:31:45.370 --> 00:31:48.890 align:middle line:84% is a very steeply-increasing function of the flow velocity. 00:31:48.890 --> 00:31:52.290 align:middle line:84% And so the consequence is that there's some net sediment 00:31:52.290 --> 00:31:55.130 align:middle line:84% movement under a purely oscillatory flow, which 00:31:55.130 --> 00:31:56.190 align:middle line:90% seems counterintuitive. 00:31:56.190 --> 00:31:57.430 align:middle line:90% But that's the way it works. 00:31:57.430 --> 00:32:01.243 align:middle line:90% 00:32:01.243 --> 00:32:03.410 align:middle line:84% And as you know, the waves come from the deep ocean, 00:32:03.410 --> 00:32:04.610 align:middle line:90% and they shoal. 00:32:04.610 --> 00:32:08.660 align:middle line:84% And when the depth gets to be less than about 00:32:08.660 --> 00:32:16.260 align:middle line:84% a half a wavelength of the wave, it begins-- the wave scrunch up. 00:32:16.260 --> 00:32:17.640 align:middle line:90% It's a technical term. 00:32:17.640 --> 00:32:21.860 align:middle line:84% The waves scrunch up and finally break, of course. 00:32:21.860 --> 00:32:24.780 align:middle line:84% But in this range from here to here, even 00:32:24.780 --> 00:32:26.380 align:middle line:84% in purely oscillatory flow, there 00:32:26.380 --> 00:32:31.440 align:middle line:84% is some net transport toward the shore. 00:32:31.440 --> 00:32:34.060 align:middle line:90% 00:32:34.060 --> 00:32:38.260 align:middle line:84% And this is a business about shoaling waves 00:32:38.260 --> 00:32:39.400 align:middle line:90% that I just mentioned. 00:32:39.400 --> 00:32:43.420 align:middle line:90% 00:32:43.420 --> 00:32:45.680 align:middle line:84% We're talking about a single oscillation. 00:32:45.680 --> 00:32:49.620 align:middle line:84% A single wave goes in, water moves back and forth. 00:32:49.620 --> 00:32:53.000 align:middle line:84% But you can have more than one oscillatory component. 00:32:53.000 --> 00:32:55.740 align:middle line:84% There can be-- let me get rid of this-- 00:32:55.740 --> 00:32:58.140 align:middle line:84% there can be waves running this way and waves running 00:32:58.140 --> 00:32:59.980 align:middle line:90% this way or maybe this way. 00:32:59.980 --> 00:33:02.080 align:middle line:84% And they superimpose on one another. 00:33:02.080 --> 00:33:04.020 align:middle line:90% They add to the effect. 00:33:04.020 --> 00:33:06.545 align:middle line:84% But they act at the same time, and it 00:33:06.545 --> 00:33:08.920 align:middle line:84% makes for very complicated water movements at the bottom, 00:33:08.920 --> 00:33:10.000 align:middle line:90% as you can imagine. 00:33:10.000 --> 00:33:13.700 align:middle line:90% 00:33:13.700 --> 00:33:16.520 align:middle line:84% So when the sea is fully developed under a storm, 00:33:16.520 --> 00:33:19.620 align:middle line:84% under a wind, how big the waves get 00:33:19.620 --> 00:33:22.100 align:middle line:84% depends on both wind strength, but also 00:33:22.100 --> 00:33:25.660 align:middle line:84% how far-- what greater distance that the wind has the chance 00:33:25.660 --> 00:33:28.980 align:middle line:90% to operate on the surface. 00:33:28.980 --> 00:33:32.860 align:middle line:84% And in a storm, if you've ever been out on a ship 00:33:32.860 --> 00:33:35.240 align:middle line:84% during a storm, there's pretty good size waves running. 00:33:35.240 --> 00:33:36.900 align:middle line:90% They're very complicated. 00:33:36.900 --> 00:33:39.622 align:middle line:84% So there's a spectrum of waves running in different directions 00:33:39.622 --> 00:33:41.080 align:middle line:84% and with different characteristics, 00:33:41.080 --> 00:33:43.180 align:middle line:90% and they all add together. 00:33:43.180 --> 00:33:44.820 align:middle line:90% But they're self-sorting. 00:33:44.820 --> 00:33:49.300 align:middle line:84% Because when the waves move out away from the storm, 00:33:49.300 --> 00:33:51.960 align:middle line:84% they sort themselves out by direction, obviously. 00:33:51.960 --> 00:33:54.820 align:middle line:84% But also, there's a low-pass filter effect. 00:33:54.820 --> 00:33:59.240 align:middle line:84% The bigger waves die out slower than the smaller waves. 00:33:59.240 --> 00:34:01.880 align:middle line:84% And so when you get well away from the storm, 00:34:01.880 --> 00:34:03.790 align:middle line:84% it gets simpler, because there's only usually 00:34:03.790 --> 00:34:07.850 align:middle line:84% one dominant oscillation component, 00:34:07.850 --> 00:34:09.870 align:middle line:84% unless there were a couple of subequal ones 00:34:09.870 --> 00:34:13.090 align:middle line:84% in different directions, which can happen in major storms. 00:34:13.090 --> 00:34:16.429 align:middle line:90% 00:34:16.429 --> 00:34:18.070 align:middle line:90% I just talked about this. 00:34:18.070 --> 00:34:21.449 align:middle line:84% But we have to think about the bottom water motions, 00:34:21.449 --> 00:34:23.590 align:middle line:84% because when we talk about the sediment movement 00:34:23.590 --> 00:34:25.710 align:middle line:84% by these oscillatory flows, that's 00:34:25.710 --> 00:34:27.250 align:middle line:90% an important consideration. 00:34:27.250 --> 00:34:30.310 align:middle line:90% 00:34:30.310 --> 00:34:33.110 align:middle line:84% So they can be at right angles, which is 00:34:33.110 --> 00:34:34.989 align:middle line:90% a fairly simple kind of thing. 00:34:34.989 --> 00:34:37.310 align:middle line:90% The ellipses would be-- 00:34:37.310 --> 00:34:40.310 align:middle line:84% the orbits would be ellipses rather than straight lines. 00:34:40.310 --> 00:34:44.389 align:middle line:84% And if you had two oscillations not at right angles, 00:34:44.389 --> 00:34:46.949 align:middle line:84% it gets a very complicated pattern 00:34:46.949 --> 00:34:48.949 align:middle line:90% which is infinitely repeating. 00:34:48.949 --> 00:34:50.969 align:middle line:84% Have you ever heard of Lissajous figures? 00:34:50.969 --> 00:34:54.610 align:middle line:84% How many people have heard of Lissajous figures? 00:34:54.610 --> 00:34:57.270 align:middle line:84% There's a nice Wikipedia entry on Lissajous figures. 00:34:57.270 --> 00:34:59.170 align:middle line:84% And to go and look at it sometime. 00:34:59.170 --> 00:34:59.890 align:middle line:90% It's clever. 00:34:59.890 --> 00:35:02.463 align:middle line:84% Some guy named Lissajous developed this. 00:35:02.463 --> 00:35:03.880 align:middle line:84% And I don't know who he is or when 00:35:03.880 --> 00:35:05.520 align:middle line:90% he lived or anything like that. 00:35:05.520 --> 00:35:10.060 align:middle line:84% Anyway, now we have to deal with combined flows. 00:35:10.060 --> 00:35:12.020 align:middle line:84% We've talked about unidirectional flows, 00:35:12.020 --> 00:35:14.260 align:middle line:84% various things about the forces and motions. 00:35:14.260 --> 00:35:16.260 align:middle line:84% And we've talked about oscillatory flows. 00:35:16.260 --> 00:35:18.840 align:middle line:84% But it's natural to think that there 00:35:18.840 --> 00:35:23.280 align:middle line:84% can be oscillatory flow with a superimposed unidirectional 00:35:23.280 --> 00:35:25.480 align:middle line:90% flow-- their combined flows. 00:35:25.480 --> 00:35:30.120 align:middle line:84% And in terms of sediment transport, it's a jungle. 00:35:30.120 --> 00:35:32.320 align:middle line:84% It's amazingly difficult to deal with all this. 00:35:32.320 --> 00:35:34.480 align:middle line:84% John Grotzinger, my long time colleague, 00:35:34.480 --> 00:35:36.800 align:middle line:90% would call it a dog's breakfast. 00:35:36.800 --> 00:35:39.600 align:middle line:84% He loved that expression, it's a dog's breakfast. 00:35:39.600 --> 00:35:41.260 align:middle line:90% Anyway, it's really complicated. 00:35:41.260 --> 00:35:42.120 align:middle line:84% And we're going to get to that when 00:35:42.120 --> 00:35:44.340 align:middle line:84% we talk about sediment transport and bed forms. 00:35:44.340 --> 00:35:46.640 align:middle line:90% But you have to live with that. 00:35:46.640 --> 00:35:48.980 align:middle line:84% The simplest case is they're collinear. 00:35:48.980 --> 00:35:51.200 align:middle line:84% And that's easy to do in the lab because you 00:35:51.200 --> 00:35:54.400 align:middle line:84% have a channel with a flow in it at the same time you're 00:35:54.400 --> 00:35:55.640 align:middle line:90% making waves. 00:35:55.640 --> 00:36:00.220 align:middle line:84% And you can look at the effects when they're collinear. 00:36:00.220 --> 00:36:02.960 align:middle line:90% 00:36:02.960 --> 00:36:06.560 align:middle line:84% And in this case, you can see that this is 00:36:06.560 --> 00:36:07.840 align:middle line:90% a steady-- this is a spectrum. 00:36:07.840 --> 00:36:12.778 align:middle line:84% Steady unidirectional flow, time and varying velocity. 00:36:12.778 --> 00:36:14.320 align:middle line:84% But it can be pulsing unidirectional. 00:36:14.320 --> 00:36:18.520 align:middle line:84% If you have a minor oscillatory component, the flow pulses-- 00:36:18.520 --> 00:36:21.040 align:middle line:90% slow fast, slow fast, slow. 00:36:21.040 --> 00:36:23.540 align:middle line:84% And then there's a middle thing, stop start. 00:36:23.540 --> 00:36:24.580 align:middle line:90% It flows and stops. 00:36:24.580 --> 00:36:26.080 align:middle line:90% It flows and stops. 00:36:26.080 --> 00:36:28.660 align:middle line:84% But in terms of sediment transport, 00:36:28.660 --> 00:36:30.200 align:middle line:90% it's not much different from-- 00:36:30.200 --> 00:36:31.680 align:middle line:84% the case of steady unidirectional 00:36:31.680 --> 00:36:34.240 align:middle line:84% is not much different from pulsing unidirectional stop 00:36:34.240 --> 00:36:34.740 align:middle line:90% and start. 00:36:34.740 --> 00:36:37.800 align:middle line:84% But if the oscillatory component dominates 00:36:37.800 --> 00:36:40.180 align:middle line:84% over the unidirectional component, 00:36:40.180 --> 00:36:42.480 align:middle line:84% you get an asymmetrical oscillatory flow 00:36:42.480 --> 00:36:45.060 align:middle line:84% until finally, you get to a symmetrical oscillatory flow. 00:36:45.060 --> 00:36:49.560 align:middle line:84% And any one of these unidirectional components 00:36:49.560 --> 00:36:52.480 align:middle line:84% and oscillatory components can be combined with each other 00:36:52.480 --> 00:36:53.900 align:middle line:90% because we have combined flow. 00:36:53.900 --> 00:36:56.960 align:middle line:90% 00:36:56.960 --> 00:36:58.950 align:middle line:84% Now, if they're at right angles to each other, 00:36:58.950 --> 00:37:01.290 align:middle line:84% that's a little more complicated. 00:37:01.290 --> 00:37:03.050 align:middle line:84% And I don't know of anybody who's 00:37:03.050 --> 00:37:06.330 align:middle line:84% done this in the laboratory, but I had an idea long ago-- 00:37:06.330 --> 00:37:09.770 align:middle line:84% and I thought about doing a research proposal on it-- 00:37:09.770 --> 00:37:14.130 align:middle line:84% have a channel flow flowing down it. 00:37:14.130 --> 00:37:16.970 align:middle line:84% But on the sides of the channel, all along 00:37:16.970 --> 00:37:20.410 align:middle line:84% the sides of the channel, there are reservoirs with entrances 00:37:20.410 --> 00:37:21.570 align:middle line:90% into the channel. 00:37:21.570 --> 00:37:24.350 align:middle line:84% So you tilt the channel back and forth, 00:37:24.350 --> 00:37:27.150 align:middle line:84% slosh the water sideways while it's flowing down that way. 00:37:27.150 --> 00:37:29.710 align:middle line:84% I never did it maybe I should have done it sometime. 00:37:29.710 --> 00:37:33.570 align:middle line:84% But I never got into actually writing a proposal for it. 00:37:33.570 --> 00:37:36.170 align:middle line:84% So that's pretty easy to deal with. 00:37:36.170 --> 00:37:38.530 align:middle line:84% The most difficult case is when there are currents 00:37:38.530 --> 00:37:40.313 align:middle line:90% plus multi-directional waves. 00:37:40.313 --> 00:37:41.730 align:middle line:84% And the only thing I can think of, 00:37:41.730 --> 00:37:43.570 align:middle line:84% if you want to do experiments, you'd 00:37:43.570 --> 00:37:48.650 align:middle line:84% have to build a very large wave tank with wave makers 00:37:48.650 --> 00:37:50.090 align:middle line:90% at various angles. 00:37:50.090 --> 00:37:51.728 align:middle line:84% Plus you pump water in at one end 00:37:51.728 --> 00:37:53.270 align:middle line:84% and you pull it out of the other end. 00:37:53.270 --> 00:37:55.010 align:middle line:84% And I don't think anybody has done that. 00:37:55.010 --> 00:37:57.890 align:middle line:84% But an experimentalist like me thinks in terms 00:37:57.890 --> 00:38:00.370 align:middle line:90% of doing something like this. 00:38:00.370 --> 00:38:02.350 align:middle line:84% And you could instrument the seabed. 00:38:02.350 --> 00:38:04.890 align:middle line:84% People do that and look at sediment transport and bed 00:38:04.890 --> 00:38:08.090 align:middle line:84% configurations, ripples on the seabed. 00:38:08.090 --> 00:38:10.370 align:middle line:84% But it's difficult and expensive. 00:38:10.370 --> 00:38:13.210 align:middle line:84% And it's especially difficult in major storms 00:38:13.210 --> 00:38:15.450 align:middle line:84% where much of the action takes place. 00:38:15.450 --> 00:38:21.170 align:middle line:90% So it's difficult. 00:38:21.170 --> 00:38:22.250 align:middle line:90% And that's it. 00:38:22.250 --> 00:38:25.052 align:middle line:90% So now I have to go to-- 00:38:25.052 --> 00:38:26.510 align:middle line:84% let's deal with sediment transport. 00:38:26.510 --> 00:38:28.010 align:middle line:84% Now that all about fluid flow, let's 00:38:28.010 --> 00:38:29.270 align:middle line:90% deal with sediment transport. 00:38:29.270 --> 00:38:31.810 align:middle line:90% 00:38:31.810 --> 00:38:34.667 align:middle line:84% And the obvious place to start is initiation of motion. 00:38:34.667 --> 00:38:37.250 align:middle line:84% How strong does the flow have to be before the sediment starts 00:38:37.250 --> 00:38:37.750 align:middle line:90% to move? 00:38:37.750 --> 00:38:39.550 align:middle line:84% It's an important thing to deal with. 00:38:39.550 --> 00:38:40.750 align:middle line:90% It's a classic problem. 00:38:40.750 --> 00:38:43.490 align:middle line:84% Much has been written about it over the many, many decades. 00:38:43.490 --> 00:38:47.170 align:middle line:84% So here's a thought experiment for you, an imaginary field 00:38:47.170 --> 00:38:49.810 align:middle line:90% trip. 00:38:49.810 --> 00:38:52.270 align:middle line:84% You can shrink yourself down to microscopic size. 00:38:52.270 --> 00:38:54.058 align:middle line:90% You're a micro person. 00:38:54.058 --> 00:38:56.600 align:middle line:84% And if you're doing it in water, you have to have scuba gear, 00:38:56.600 --> 00:38:57.380 align:middle line:90% obviously. 00:38:57.380 --> 00:38:59.700 align:middle line:84% And you have shoes that are equipped 00:38:59.700 --> 00:39:02.600 align:middle line:84% so that you can grab onto any surface down there. 00:39:02.600 --> 00:39:04.960 align:middle line:84% We're dealing with sediment particles on a sediment bed. 00:39:04.960 --> 00:39:06.840 align:middle line:84% You want to be able to get your feet onto it. 00:39:06.840 --> 00:39:09.940 align:middle line:84% And so you go down among the particles sitting there 00:39:09.940 --> 00:39:13.660 align:middle line:84% on the bed and below the bed as the flow is flowing. 00:39:13.660 --> 00:39:14.640 align:middle line:90% What would you see? 00:39:14.640 --> 00:39:15.780 align:middle line:90% What would you feel? 00:39:15.780 --> 00:39:18.800 align:middle line:84% Well, clearly there'd be flow around the surface particles, 00:39:18.800 --> 00:39:21.680 align:middle line:84% but there'd also be slower flow around some of the particles, 00:39:21.680 --> 00:39:23.780 align:middle line:84% fairly well down in the sediment. 00:39:23.780 --> 00:39:27.740 align:middle line:84% And it would be viscosity-dominated flow. 00:39:27.740 --> 00:39:29.220 align:middle line:84% But there would be irregularities, 00:39:29.220 --> 00:39:35.500 align:middle line:84% because overhead, above the sedimentary bed, 00:39:35.500 --> 00:39:37.420 align:middle line:90% there'd be turbulent flow. 00:39:37.420 --> 00:39:40.260 align:middle line:84% And so there'd be velocity fluctuations 00:39:40.260 --> 00:39:44.740 align:middle line:84% that would be transmitted down into the subsurface. 00:39:44.740 --> 00:39:46.040 align:middle line:90% That's my field trip. 00:39:46.040 --> 00:39:49.940 align:middle line:84% But there's more to it than that because if you-- 00:39:49.940 --> 00:39:52.510 align:middle line:84% now I'll turn into a fluvial geomorphologist. 00:39:52.510 --> 00:39:56.150 align:middle line:84% Do you know about effluent streams and effluent streams? 00:39:56.150 --> 00:39:57.130 align:middle line:90% Maybe not. 00:39:57.130 --> 00:39:59.510 align:middle line:90% OK, so look at the stream. 00:39:59.510 --> 00:40:02.430 align:middle line:84% And the groundwater table comes down 00:40:02.430 --> 00:40:04.190 align:middle line:90% to the surface of the stream. 00:40:04.190 --> 00:40:08.090 align:middle line:84% And so if the groundwater table slopes up from the channel, 00:40:08.090 --> 00:40:12.310 align:middle line:84% water is coming in from the subsurface up into the channel. 00:40:12.310 --> 00:40:16.048 align:middle line:84% And it's not a small-- it's a small effect, 00:40:16.048 --> 00:40:17.590 align:middle line:84% but it's not negligible, because that 00:40:17.590 --> 00:40:21.070 align:middle line:84% would tend to move the particles upward and entrain them. 00:40:21.070 --> 00:40:25.710 align:middle line:84% An effluent stream, the groundwater table 00:40:25.710 --> 00:40:29.358 align:middle line:84% slopes away from the channel and you're losing water. 00:40:29.358 --> 00:40:30.650 align:middle line:90% And so there's a downward flow. 00:40:30.650 --> 00:40:32.920 align:middle line:84% And that would tend to inhibit the particle transport. 00:40:32.920 --> 00:40:34.170 align:middle line:90% I don't think it's a big deal. 00:40:34.170 --> 00:40:39.150 align:middle line:84% I should talk with Taylor Perron about that sometime. 00:40:39.150 --> 00:40:43.030 align:middle line:84% So I told you about the boundary shear stress. 00:40:43.030 --> 00:40:44.810 align:middle line:90% Averaged over time and space. 00:40:44.810 --> 00:40:46.490 align:middle line:90% Skin friction formed lift. 00:40:46.490 --> 00:40:49.723 align:middle line:84% We did this in the previous part. 00:40:49.723 --> 00:40:51.390 align:middle line:84% But you can look at things a little more 00:40:51.390 --> 00:40:53.670 align:middle line:84% closely and look at a sediment bed 00:40:53.670 --> 00:40:55.370 align:middle line:90% as a flow over the sediment bed. 00:40:55.370 --> 00:40:56.490 align:middle line:90% And here are particles. 00:40:56.490 --> 00:41:00.873 align:middle line:84% They have contact points, usually three contact points. 00:41:00.873 --> 00:41:01.790 align:middle line:90% They're sitting there. 00:41:01.790 --> 00:41:03.190 align:middle line:90% And they have a weight. 00:41:03.190 --> 00:41:05.820 align:middle line:84% And there's a fluid force of the kind I just talked about. 00:41:05.820 --> 00:41:07.570 align:middle line:84% And so that's what we have to think about. 00:41:07.570 --> 00:41:10.390 align:middle line:84% If we're thinking about making the move start happen, 00:41:10.390 --> 00:41:14.110 align:middle line:84% this is the kind of picture we have to think about. 00:41:14.110 --> 00:41:16.870 align:middle line:84% And in more detail, we could say there's this particle maybe 00:41:16.870 --> 00:41:17.830 align:middle line:90% ready to move. 00:41:17.830 --> 00:41:20.710 align:middle line:84% And so there are skin friction forces. 00:41:20.710 --> 00:41:24.870 align:middle line:84% There are front-to-back pressure forces. 00:41:24.870 --> 00:41:27.230 align:middle line:84% And that's what actually moves the particle. 00:41:27.230 --> 00:41:30.110 align:middle line:84% And which are more important, the viscous forces 00:41:30.110 --> 00:41:31.288 align:middle line:90% or the pressure forces? 00:41:31.288 --> 00:41:33.330 align:middle line:84% Depends on a Reynolds number, as you might guess, 00:41:33.330 --> 00:41:36.390 align:middle line:84% because that's what Reynolds numbers are all about. 00:41:36.390 --> 00:41:38.810 align:middle line:84% So this is from what I gave you before. 00:41:38.810 --> 00:41:39.710 align:middle line:90% You've seen this. 00:41:39.710 --> 00:41:44.430 align:middle line:84% And just to remind you that the nature of forces on a particle 00:41:44.430 --> 00:41:49.000 align:middle line:84% that might be ready to move is very strongly a function of this 00:41:49.000 --> 00:41:53.600 align:middle line:84% Reynolds number Re*, boundary Reynolds number. 00:41:53.600 --> 00:41:55.040 align:middle line:90% So let's do more. 00:41:55.040 --> 00:41:56.820 align:middle line:84% I am a lover of dimensional analysis. 00:41:56.820 --> 00:41:59.720 align:middle line:90% I guess you can see that. 00:41:59.720 --> 00:42:03.640 align:middle line:84% So here's a flow over a loose granular bed. 00:42:03.640 --> 00:42:05.180 align:middle line:84% And what do we need to worry about? 00:42:05.180 --> 00:42:07.100 align:middle line:84% We need the boundary shear stress. 00:42:07.100 --> 00:42:09.280 align:middle line:90% That's what moves the sediment. 00:42:09.280 --> 00:42:11.480 align:middle line:90% We need the particle size. 00:42:11.480 --> 00:42:14.020 align:middle line:84% You also need rho and mu, the field properties. 00:42:14.020 --> 00:42:16.540 align:middle line:84% But we also need the specific weight, 00:42:16.540 --> 00:42:19.360 align:middle line:84% the weight per unit volume of the sediment. 00:42:19.360 --> 00:42:23.360 align:middle line:84% Now, you might be saying to yourself, why do we 00:42:23.360 --> 00:42:29.412 align:middle line:84% have to have the fluid density rho and the specific weight? 00:42:29.412 --> 00:42:31.620 align:middle line:84% And I'm going to run through a little thing with you. 00:42:31.620 --> 00:42:34.160 align:middle line:84% It'll probably be the last thing I can do. 00:42:34.160 --> 00:42:36.040 align:middle line:84% Let's think about the threshold as a function 00:42:36.040 --> 00:42:40.560 align:middle line:84% of fluid properties, specific weight of the particles, size, 00:42:40.560 --> 00:42:41.720 align:middle line:90% and shear stress. 00:42:41.720 --> 00:42:44.820 align:middle line:84% And so as before, we have four of them. 00:42:44.820 --> 00:42:46.580 align:middle line:84% We have two dimensionless variables. 00:42:46.580 --> 00:42:51.690 align:middle line:84% This is a kind of a dimensionless shear stress. 00:42:51.690 --> 00:42:54.810 align:middle line:84% And the other is another kind of Reynolds number. 00:42:54.810 --> 00:42:56.990 align:middle line:84% This is called the shields parameter. 00:42:56.990 --> 00:43:00.010 align:middle line:84% And I'm going to tell you about Albert F. Shields in a minute. 00:43:00.010 --> 00:43:04.330 align:middle line:84% And u* is a kind of a fake velocity. 00:43:04.330 --> 00:43:09.590 align:middle line:84% It's a tau 0 divided by rho to the 1/2. 00:43:09.590 --> 00:43:12.710 align:middle line:84% And if you figured out, that sets the dimensions of velocity. 00:43:12.710 --> 00:43:13.910 align:middle line:90% So it's not really velocity. 00:43:13.910 --> 00:43:17.390 align:middle line:90% It's a shear stress in disguise. 00:43:17.390 --> 00:43:19.650 align:middle line:84% But anyway, that's the basic thing. 00:43:19.650 --> 00:43:26.330 align:middle line:84% Now, suppose you have a smooth granular bed 00:43:26.330 --> 00:43:29.090 align:middle line:84% and you slowly increase the flow velocity. 00:43:29.090 --> 00:43:31.490 align:middle line:84% A few grains start to move, rolling, sliding. 00:43:31.490 --> 00:43:34.490 align:middle line:84% And they find new pockets here and there. 00:43:34.490 --> 00:43:36.110 align:middle line:90% But you know what that is? 00:43:36.110 --> 00:43:38.630 align:middle line:90% That's called a printer's fist. 00:43:38.630 --> 00:43:39.390 align:middle line:90% Did you know that? 00:43:39.390 --> 00:43:40.590 align:middle line:90% It's a printer's fist. 00:43:40.590 --> 00:43:42.390 align:middle line:90% I love those printer's fists. 00:43:42.390 --> 00:43:44.750 align:middle line:84% It's to emphasize something this important. 00:43:44.750 --> 00:43:46.930 align:middle line:90% It's a printer's fist. 00:43:46.930 --> 00:43:50.270 align:middle line:84% The cutoff between no movement and established movement, 00:43:50.270 --> 00:43:51.850 align:middle line:90% there's no well-defined point. 00:43:51.850 --> 00:43:53.963 align:middle line:84% It's first a few grains start to move, 00:43:53.963 --> 00:43:55.630 align:middle line:84% and then some more grains start to move, 00:43:55.630 --> 00:43:58.130 align:middle line:84% and more and more, and pretty soon a lot of them are moving. 00:43:58.130 --> 00:43:59.550 align:middle line:84% Oh, well, it's past the threshold. 00:43:59.550 --> 00:44:01.370 align:middle line:84% But there's no way to actually put 00:44:01.370 --> 00:44:04.202 align:middle line:84% a value on the particular threshold. 00:44:04.202 --> 00:44:05.910 align:middle line:84% This is probably the last thing I can do. 00:44:05.910 --> 00:44:09.570 align:middle line:84% But here's a nice graphic way of thinking about how it works. 00:44:09.570 --> 00:44:13.330 align:middle line:84% This distribution is a distribution 00:44:13.330 --> 00:44:15.673 align:middle line:84% of instantaneous shear stress on the bed. 00:44:15.673 --> 00:44:17.090 align:middle line:84% And it ranges from small to large, 00:44:17.090 --> 00:44:19.210 align:middle line:84% depending on the turbulent eddies. 00:44:19.210 --> 00:44:22.370 align:middle line:84% Over the bed, that's the size distribution 00:44:22.370 --> 00:44:23.730 align:middle line:90% of the particles in the bed. 00:44:23.730 --> 00:44:25.330 align:middle line:84% So when there's no movement, clearly 00:44:25.330 --> 00:44:29.690 align:middle line:84% even the strongest flow doesn't move the most easily-moved 00:44:29.690 --> 00:44:30.350 align:middle line:90% sediments. 00:44:30.350 --> 00:44:33.570 align:middle line:90% But you finally get to a point-- 00:44:33.570 --> 00:44:35.650 align:middle line:84% as you increase the flow velocity, 00:44:35.650 --> 00:44:39.050 align:middle line:84% the bed size distribution stays the same and the flow 00:44:39.050 --> 00:44:41.170 align:middle line:84% distribution shifts to the right. 00:44:41.170 --> 00:44:42.790 align:middle line:90% And it starts to overlap. 00:44:42.790 --> 00:44:44.752 align:middle line:84% And that's what we'd call incipient motion. 00:44:44.752 --> 00:44:46.460 align:middle line:84% And then eventually, it gets to the point 00:44:46.460 --> 00:44:48.520 align:middle line:84% where the flow overlaps the bed quite a bit 00:44:48.520 --> 00:44:51.740 align:middle line:90% and we have general motion. 00:44:51.740 --> 00:44:55.940 align:middle line:84% So there's a famous diagram called the Shields diagram. 00:44:55.940 --> 00:44:58.080 align:middle line:84% I don't have a slide about Shields, 00:44:58.080 --> 00:45:00.660 align:middle line:84% but there's a nice interesting Wikipedia 00:45:00.660 --> 00:45:02.580 align:middle line:90% entry for Albert F. Shields. 00:45:02.580 --> 00:45:03.360 align:middle line:90% Read it sometime. 00:45:03.360 --> 00:45:05.020 align:middle line:84% He had an interesting and varied career 00:45:05.020 --> 00:45:06.760 align:middle line:84% and I won't spend time talking about it. 00:45:06.760 --> 00:45:10.220 align:middle line:84% But anyway, this is a plot, basically dimensionless boundary 00:45:10.220 --> 00:45:13.040 align:middle line:84% shear stress versus the boundary Reynolds number, 00:45:13.040 --> 00:45:14.660 align:middle line:90% which I told you about before. 00:45:14.660 --> 00:45:18.260 align:middle line:84% And he plotted a number of data points from the literature. 00:45:18.260 --> 00:45:20.420 align:middle line:90% Ignore these diagonal lines. 00:45:20.420 --> 00:45:23.020 align:middle line:84% And he fitted a curve through it. 00:45:23.020 --> 00:45:24.740 align:middle line:90% And it looks pretty reasonable. 00:45:24.740 --> 00:45:28.780 align:middle line:84% But he extended the curve up to very small boundary Reynolds. 00:45:28.780 --> 00:45:30.820 align:middle line:90% That is small particles. 00:45:30.820 --> 00:45:33.660 align:middle line:84% And it climbs without any data in there. 00:45:33.660 --> 00:45:36.640 align:middle line:84% And the last thing I want to do is talk about that. 00:45:36.640 --> 00:45:39.220 align:middle line:90% 00:45:39.220 --> 00:45:41.830 align:middle line:84% Fine particles tend to be cohesive, 00:45:41.830 --> 00:45:45.590 align:middle line:84% because large particles-- any cohesive forces 00:45:45.590 --> 00:45:48.570 align:middle line:84% between electrostatic cohesive forces are negligible. 00:45:48.570 --> 00:45:51.310 align:middle line:84% But when you get down to really fine sizes, 00:45:51.310 --> 00:45:53.550 align:middle line:84% they dominate the situation and the particles 00:45:53.550 --> 00:45:55.630 align:middle line:90% tend to clump together. 00:45:55.630 --> 00:45:59.790 align:middle line:84% And so that makes it more difficult for the flow to move. 00:45:59.790 --> 00:46:02.190 align:middle line:84% And although there's no data here, 00:46:02.190 --> 00:46:04.910 align:middle line:84% that's a reasonable way of looking at what happens. 00:46:04.910 --> 00:46:07.950 align:middle line:84% In fine sediments, you have to really have a strong flow 00:46:07.950 --> 00:46:13.990 align:middle line:84% to overcome those interparticle forces. 00:46:13.990 --> 00:46:17.090 align:middle line:84% And I think-- oh, one more thing. 00:46:17.090 --> 00:46:18.210 align:middle line:90% I mentioned this to you. 00:46:18.210 --> 00:46:18.850 align:middle line:90% Look him up. 00:46:18.850 --> 00:46:20.910 align:middle line:90% He's an interesting guy. 00:46:20.910 --> 00:46:25.950 align:middle line:84% And I will mention in the notes-- 00:46:25.950 --> 00:46:28.090 align:middle line:84% you all got copies of the notes, right? 00:46:28.090 --> 00:46:29.690 align:middle line:84% Just in case you want to look at them. 00:46:29.690 --> 00:46:34.590 align:middle line:84% And I'm referring these things to a particular page. 00:46:34.590 --> 00:46:37.410 align:middle line:84% There's something called the Hjulstrom diagram. 00:46:37.410 --> 00:46:38.410 align:middle line:90% I think he was Swedish. 00:46:38.410 --> 00:46:39.310 align:middle line:90% I'm pretty sure. 00:46:39.310 --> 00:46:42.430 align:middle line:84% And Sundborg, I know he was Swedish. 00:46:42.430 --> 00:46:46.530 align:middle line:84% Variants or extrapolations of the Shields diagram. 00:46:46.530 --> 00:46:49.630 align:middle line:84% So this is standard initiation of motion stuff. 00:46:49.630 --> 00:46:53.127 align:middle line:84% So I think I'm going to quit because-- 00:46:53.127 --> 00:46:54.210 align:middle line:90% well, I'll return to this. 00:46:54.210 --> 00:46:54.850 align:middle line:90% I got to stop. 00:46:54.850 --> 00:46:56.650 align:middle line:90% It's 4 o'clock, so I'll stop. 00:46:56.650 --> 00:46:59.790 align:middle line:84% But we'll pick that up to what we 00:46:59.790 --> 00:47:05.012 align:middle line:84% do to deal with initiation motion better. 00:47:05.012 --> 00:47:05.970 align:middle line:90% And I'll go from there. 00:47:05.970 --> 00:47:07.590 align:middle line:84% When we have established motion, you 00:47:07.590 --> 00:47:09.090 align:middle line:84% have a lot of things to talk about. 00:47:09.090 --> 00:47:10.390 align:middle line:90% So I have to quit. 00:47:10.390 --> 00:47:14.070 align:middle line:90% And I'll see you next week. 00:47:14.070 --> 00:47:16.600 align:middle line:90% Same time, same place, right? 00:47:16.600 --> 00:47:40.000 align:middle line:90%