1 00:00:03,189 --> 00:00:08,170 Water resulting from rainfall and snowfall that is not returning to the atmosphere by 2 00:00:08,170 --> 00:00:13,709 means of evapotranspiration, travels from mountains and elevated areas 3 00:00:13,709 --> 00:00:15,849 to the sea or ocean. 4 00:00:15,980 --> 00:00:21,340 During this trip, rivers are formed, enabling the transport of water and sediment 5 00:00:21,350 --> 00:00:22,710 to the sea. 6 00:00:22,710 --> 00:00:29,510 So a river system is a complex network composed of streams that drain earth’s land surface. 7 00:00:29,510 --> 00:00:32,710 The question we are addressing in this submodule on rivers is: 8 00:00:32,710 --> 00:00:35,499 Why does the river look as it does? 9 00:00:35,499 --> 00:00:40,760 The topography defines the limits of the basin or catchment of a river. 10 00:00:40,760 --> 00:00:43,940 Now we will focus on the basin of the Rhine river. 11 00:00:43,940 --> 00:00:50,319 This river system enables transport of water and sediment from the Alps to the North Sea 12 00:00:50,319 --> 00:00:55,260 The water that travels from the mountains to the sea through the river as its highway 13 00:00:55,260 --> 00:00:56,399 also carries sediment. 14 00:00:56,399 --> 00:01:02,569 This sediment is usually eroded over the river’s upper course, 15 00:01:02,569 --> 00:01:06,370 transported through its middle course, and deposited near its mouth. 16 00:01:06,370 --> 00:01:12,120 A river flows over the sediment that it transports at the same time. 17 00:01:12,120 --> 00:01:17,430 It is an alive entity, continuously changing its shape in all directions, 18 00:01:17,430 --> 00:01:21,830 eroding and accreting its banks, changing its course, 19 00:01:21,830 --> 00:01:24,720 abandoning channels, creating new ones, 20 00:01:24,720 --> 00:01:28,680 and aggrading and degrading its bed. 21 00:01:28,680 --> 00:01:34,110 If we analyze the longitudinal profile of the bed elevation of a river system, 22 00:01:34,110 --> 00:01:41,110 we observe that the steepness of the bed (called slope) gradually decreases in downstream direction 23 00:01:41,420 --> 00:01:45,900 leading to an upward concave profile of the river. 24 00:01:45,900 --> 00:01:51,610 This decrease in slope in downstream direction is related to the size of the sediment that 25 00:01:51,610 --> 00:01:54,270 is transported by the river. 26 00:01:54,270 --> 00:01:56,840 At the upstream part, in the mountains, 27 00:01:56,840 --> 00:01:58,980 the sediment is coarse. 28 00:01:58,980 --> 00:02:03,220 In other words the grain size is relatively large. 29 00:02:03,220 --> 00:02:08,250 While travelling, the particle size decreases due to abrasion. 30 00:02:08,250 --> 00:02:14,810 When particles are transported they hit each other and so loose material or turn into small pieces. 31 00:02:15,920 --> 00:02:22,760 Tributaries joining the main river lead to an increase of the water discharge in streamwise direction. 32 00:02:23,500 --> 00:02:27,980 Moreover, the discharge is not constant, varying over time, 33 00:02:27,980 --> 00:02:32,069 for instance, due to local precipitation. 34 00:02:32,069 --> 00:02:37,230 The more downstream the smaller the variability of water discharge. 35 00:02:37,230 --> 00:02:43,860 This is due to the relatively smaller influence of locally high precipitation rates. 36 00:02:45,240 --> 00:02:50,860 Let’s have a look at this river system at different locations. 37 00:03:05,760 --> 00:03:09,140 Here in the Alps, where the water has only traveled a few kilometers 38 00:03:09,340 --> 00:03:13,660 the river is still very steep, has a narrow channel and a limited water discharge. 39 00:03:14,160 --> 00:03:16,780 This discharge varies heavily throughout the year. 40 00:03:17,160 --> 00:03:19,020 During larger flowrates, 41 00:03:19,120 --> 00:03:23,500 the river transports larger particles which will be abraded further downstream. 42 00:03:24,280 --> 00:03:29,739 Downstream from the mountain streams, we usually see braided reaches governed by 43 00:03:29,739 --> 00:03:36,440 high sediment load coming from upstream and resulting from bank erosion. 44 00:03:36,440 --> 00:03:41,950 This means that the river here consists of several channels that bifurcate and join without 45 00:03:41,950 --> 00:03:44,099 a clear main channel. 46 00:03:44,099 --> 00:03:48,410 This part is highly dynamic leading to frequent changes. 47 00:03:48,410 --> 00:03:52,980 Once the river flows through a milder slope area with less energy, 48 00:03:52,980 --> 00:03:57,760 the river usually shows a highly curved single-thread channel. 49 00:03:57,760 --> 00:04:01,500 This pattern is called a meandering planform. 50 00:04:01,500 --> 00:04:05,569 In this part, the river has one main channel and is more 51 00:04:05,569 --> 00:04:06,459 stable. 52 00:04:06,459 --> 00:04:10,150 It shows a sinuous shape. 53 00:04:10,150 --> 00:04:14,280 Although it is less dynamic than the upstream braided reach, 54 00:04:14,280 --> 00:04:17,400 this does not mean it is fixed. 55 00:04:17,400 --> 00:04:23,430 Outer banks erode and inner banks accrete, which leads to bend migration and an increase 56 00:04:23,430 --> 00:04:27,220 in curvature until, during a flood, 57 00:04:27,220 --> 00:04:32,250 a river creates a shortcut and then the process restarts. 58 00:04:32,250 --> 00:04:38,990 The river continuously changes its planform and bed elevation over its alluvial plain. 59 00:04:38,990 --> 00:04:43,730 Let’s have a closer look at an individual bend. 60 00:04:43,730 --> 00:04:49,850 Water is turning in a bend, changing the direction of the flow velocity. 61 00:04:50,840 --> 00:04:55,500 If an object turns, Newton’s second law tells us that there 62 00:04:55,500 --> 00:05:01,010 must be a force making it turn, changing the direction of the velocity. 63 00:05:01,010 --> 00:05:08,010 This force, called the centripetal force, is directed to the center of curvature. 64 00:05:10,180 --> 00:05:17,180 Also in a bend there is a centripetal force, changing the direction of the flow velocity. 65 00:05:17,270 --> 00:05:22,520 In the carousel, the centripetal force is exerted by the chain. 66 00:05:22,520 --> 00:05:29,520 In the case of curved flow in a bend, the centripetal force necessary for changing 67 00:05:29,630 --> 00:05:34,870 the flow direction, originates from a water level gradient in 68 00:05:34,870 --> 00:05:36,900 lateral direction. 69 00:05:36,900 --> 00:05:42,840 This gradient in the water surface ultimately leads to a secondary circulation. 70 00:05:42,840 --> 00:05:48,419 In the upper part flow is directed to the outer bend and in the deeper part flow is 71 00:05:48,419 --> 00:05:51,400 directed towards the inner bend. 72 00:05:51,400 --> 00:05:57,660 This secondary circulation causes degradation in the outer bend and deposition in the inner 73 00:05:57,660 --> 00:06:01,270 bend, resulting in a cross section with a deeper 74 00:06:01,270 --> 00:06:04,199 outer bend and a shallower inner bend. 75 00:06:04,199 --> 00:06:07,550 Let’s go back to the entire river system. 76 00:06:07,550 --> 00:06:11,930 Now, moving downstream, close to the river mouth, 77 00:06:11,930 --> 00:06:14,490 the slope is mildest. 78 00:06:14,490 --> 00:06:22,510 These more quiet conditions have benefited civilizations which initiated many (now large) cities. 79 00:06:22,740 --> 00:06:27,380 Let’s see what the river looks like in this area. 80 00:06:42,200 --> 00:06:47,800 Like this one, Nijmegen, that since the Roman era has been situated along the southern bank of the Rhine. 81 00:06:48,420 --> 00:06:54,460 You can see how, after a 900 kilometer trip, the river slope is much milder and the discharge has increased. 82 00:06:54,860 --> 00:06:59,500 Moreover, this discharge varies much less significantly than in the upper course in the Alps. 83 00:06:59,860 --> 00:07:05,080 And the large sediment size that you could observe in the Alps has now been decreased to sand, 84 00:07:05,420 --> 00:07:10,600 and the river is much wider, which allows for shipping and transportation of goods. 85 00:07:11,080 --> 00:07:16,920 Notice how the ships here are taking the outer part of the bend to stay in the deepest part of the channel. 86 00:07:17,080 --> 00:07:22,980 and remember that this cross-sectional profile is related to the secondary circulation that was discussed before in the lectures. 87 00:07:23,880 --> 00:07:29,840 At the river mouth the flow velocity decreases, enhancing deposition. 88 00:07:31,660 --> 00:07:35,280 The deposited sediment creates a delta. 89 00:07:35,289 --> 00:07:41,460 Here, the conditions of the sea play a decisive role in the dynamics of the river. 90 00:07:41,460 --> 00:07:44,560 Tides and waves govern the shape of the delta. 91 00:07:47,060 --> 00:07:52,250 Now we are going to focus on what happens at a specific cross section of the river. 92 00:07:53,620 --> 00:07:58,120 As we have said, the discharge varies in time. 93 00:07:58,130 --> 00:08:05,130 A cross section is usually characterized by a wide floodplain and a narrower main channel. 94 00:08:05,180 --> 00:08:11,240 During a flood event, the entire cross section is filled with water. 95 00:08:11,240 --> 00:08:16,580 Note how the width of the cross-section is much larger than its depth. 96 00:08:16,580 --> 00:08:21,860 In the main channel, water flows faster than over the floodplains. 97 00:08:21,860 --> 00:08:26,110 During mean flow conditions, the flow is normally constrained to the main 98 00:08:26,110 --> 00:08:29,610 channel with a more limited width. 99 00:08:29,610 --> 00:08:35,079 We are now going to use a schematic cross section in order to define some important 100 00:08:35,079 --> 00:08:37,229 variables in a river. 101 00:08:37,229 --> 00:08:43,130 The geometry can be characterized by a width and a flow depth. 102 00:08:43,130 --> 00:08:49,770 Another important variable is the mean grain size of the sediment that is being transported 103 00:08:49,770 --> 00:08:53,300 by the river at this specific location. 104 00:08:53,300 --> 00:09:00,000 The flow is characterized by the water discharge, which is the volume of water per unit time 105 00:09:00,000 --> 00:09:05,660 that passes through this specific location, and the velocity of the flow. 106 00:09:05,660 --> 00:09:12,000 The amount of sediment that passes through this specific location per unit time is called 107 00:09:12,000 --> 00:09:15,029 the sediment discharge. 108 00:09:15,029 --> 00:09:21,600 The bed and vegetation creates a resistance force to the movement of water. 109 00:09:21,600 --> 00:09:27,350 This is expressed by the friction coefficient that depends on the mean grain size, 110 00:09:27,350 --> 00:09:31,640 the presence of bedforms, vegetation and so on. 111 00:09:31,640 --> 00:09:37,140 Let’s focus on a one meter wide part of the cross section. 112 00:09:37,140 --> 00:09:40,580 Note that the depth, mean grain size, 113 00:09:40,580 --> 00:09:46,610 friction coefficient and velocity are considered the same as in the entire section. 114 00:09:46,610 --> 00:09:52,880 We now define the discharge of water and sediment over this one meter wide. 115 00:09:52,880 --> 00:09:58,240 The water discharge over one meter width is equal to the product of flow velocity and 116 00:09:58,240 --> 00:10:00,120 flow depth. 117 00:10:07,089 --> 00:10:13,529 The slope is a very important parameter because it is the slope that indicates the effectiveness 118 00:10:13,529 --> 00:10:17,110 of gravity in moving the water. 119 00:10:17,110 --> 00:10:21,000 The question we want to answer in the next section is: 120 00:10:21,000 --> 00:10:28,000 what are the flow depth and slope for a given and steady water and sediment discharge? 121 00:10:30,810 --> 00:10:36,339 If we let a river evolve when water and sediment discharge are steady, 122 00:10:36,339 --> 00:10:43,339 it will arrive at a situation in which the gravity force balances with the friction force. 123 00:10:43,860 --> 00:10:48,320 In this situation, the water surface slope is equal to the bed slope. 124 00:10:50,540 --> 00:10:55,470 The question is: How can we predict the normal flow depth that 125 00:10:55,470 --> 00:10:58,380 corresponds to this steady state? 126 00:10:58,380 --> 00:11:00,400 Well, let’s see. 127 00:11:01,950 --> 00:11:05,920 If we analyze a volume of water in steady state, 128 00:11:05,920 --> 00:11:09,250 gravity and friction balance each other. 129 00:11:09,250 --> 00:11:16,250 We know that the force of gravity is the product of mass and the gravitational acceleration. 130 00:11:16,440 --> 00:11:23,440 The component of the gravitational force that is balanced by friction is the one parallel 131 00:11:23,470 --> 00:11:25,230 to the bed surface. 132 00:11:26,860 --> 00:11:33,300 Considering again the one meter wide and now the one meter long section, 133 00:11:33,300 --> 00:11:38,690 the mass is equal to the flow depth times the water density. 134 00:11:38,690 --> 00:11:44,500 The unit of the gravitational force is Newton per square meter. 135 00:11:44,500 --> 00:11:48,350 On the other hand, the friction force is represented by the bed 136 00:11:48,350 --> 00:11:53,839 shear stress, which is defined by the product of water density, 137 00:11:53,839 --> 00:11:59,510 the friction coefficient and the square of flow velocity. 138 00:11:59,510 --> 00:12:05,700 Setting these two forces equal to each other and using the equation of the discharge in 139 00:12:05,700 --> 00:12:12,490 a one meter wide section shown before, we arrive at an expression for the flow depth 140 00:12:12,490 --> 00:12:18,270 depending on the friction coefficient, water discharge, gravity, and slope. 141 00:12:21,480 --> 00:12:25,680 However, the bed is rarely flat. 142 00:12:25,680 --> 00:12:33,100 Depending on the flow conditions, ripples, dunes, antidunes, or bars may appear. 143 00:12:35,200 --> 00:12:39,000 The river bed is not fixed, it is not concrete, 144 00:12:39,450 --> 00:12:43,579 it is evolving, and it is continuously adjusting its shape 145 00:12:43,579 --> 00:12:48,209 in order to transport the sediment coming from upstream. 146 00:12:48,209 --> 00:12:54,690 The amount of sediment that can be transported mainly depends on the flow velocity (the faster 147 00:12:54,690 --> 00:12:57,760 the flow, the more sediment is transported), 148 00:12:58,560 --> 00:13:02,640 and the grain size of the particles (the larger the sediment, 149 00:13:02,649 --> 00:13:05,959 the more difficult it is to transport it). 150 00:13:05,959 --> 00:13:12,959 The river will adjust in order to transport the amount of sediment coming from upstream. 151 00:13:13,190 --> 00:13:18,190 Combining these two equations, we arrive at an expression of the equilibrium 152 00:13:18,190 --> 00:13:20,399 or normal slope. 153 00:13:20,399 --> 00:13:25,980 This is the slope which enables the river to transport the sediment coming from upstream. 154 00:13:26,680 --> 00:13:32,980 If, for example, the amount of sediment delivered to the river through landslides, 155 00:13:33,250 --> 00:13:41,430 bank erosion, bed degradation and so on, increases, the bed slope will increase to enable the 156 00:13:41,450 --> 00:13:45,980 river to transport the larger amount of sediment downstream. 157 00:13:45,980 --> 00:13:49,760 At the same time, if the amount of sediment delivered to the 158 00:13:49,760 --> 00:13:56,529 river and so the slope increases, the flow depth will decrease. 159 00:13:56,529 --> 00:14:02,929 The study of such changes in bed elevation is called river morphodynamics. 160 00:14:05,800 --> 00:14:10,269 As we previously said, the water discharge in the river varies with 161 00:14:10,269 --> 00:14:10,920 time. 162 00:14:10,920 --> 00:14:17,920 After a period of heavy rainfall, the river has to transport more water downstream. 163 00:14:18,110 --> 00:14:24,420 Let’s start in a situation where we are in equilibrium after a long time with a constant 164 00:14:24,420 --> 00:14:26,840 and limited water discharge. 165 00:14:28,200 --> 00:14:35,200 In this situation we can expect the water surface nearly parallel to the bed. 166 00:14:37,450 --> 00:14:41,230 The heavy rainfall initiates a flood wave. 167 00:14:41,230 --> 00:14:46,930 The water surface elevation increases locally due to the flood wave. 168 00:14:47,720 --> 00:14:53,190 At the locations where the water surface elevation is larger, 169 00:14:53,190 --> 00:14:55,450 the river may flood a city. 170 00:14:57,220 --> 00:15:02,960 This flood wave travels downstream over time, potentially increasing the number of towns 171 00:15:03,110 --> 00:15:05,209 and cities affected. 172 00:15:06,860 --> 00:15:13,180 While travelling, the peak is smoothed, decreasing the maximum water surface elevation 173 00:15:13,320 --> 00:15:16,660 but increasing the time a city experiences the flood.