Streams

M. I. Bursik

ublearns.buffalo.edu

October 19, 2008

Contents

1 Streams 1

2 Longitudinal analysis of a river 1

3 Uniform flow 2

4 Reach morphology → overall morphology 2

5 Headwaters 2

6 Stream valley-head 3

7 Floodplain (much of the mature midsection) 3

8 The floodplain channel 4

9 The floodplain channel 4

10 Mouth 4

11 Summary: types of streams 4

12 Terraces 5

13 Terraces (cont.) 6

1

14 Fluvial Dynamics 7

15 Mass Wasting and Particle Physics 7

16 Channel Flow 7

17 Speed of water in reaches 7

18 Hydraulic radius and roughness parameter 8

19 Friction and drag 8

20 Stream power 8

21 Shape 9

22 Drag Coefficient 9

23 Drag Coefficient 10

24 Balance of gravity and friction forces 10

25 Derivation of Manning’s Equation 11

26 Velocity Distribution 11

27 Gradually- and Rapidly-varied Flow 12

28 Equations of Motion 12

29 Hydraulic Jump 13

30 Hydraulics, Transport and Landforms 13

31 Base Level 14

32 Longitudinal Profile 14

33 Three Sedimentary Processes 14

34 Stream Erosion 15

2

35 Lifting 1535.1

Schematic of drag on particle . . . . . . . . . . . 15

36 Lifting (cont.) 15

37 Sizes of Dislodged Particles 16

38 Transport 16

39 Ability to Transport 17

40 Deposition 17

41 Change in competence 17

42 The Hjulstrom curve 17

43 Bedforms 18

44 Effects on sediment transport of control structures 19

45 Man-made levees 19

46 Fluvial Landforms 19

47 Landscape Maturity 22

48 Complex drainage development 23

49 Drainage: consequent and antecedent 24

3

50 Superimposed drainage 25

51 Stream capture (piracy, abstraction) 26

52 Split Mountain, UT 27

53 Eroded landforms 27

54 Eroded landforms 28

55 Eroded foldbelt 28

1 Streams

• We are specifically interested in how streams move andcarry rocky material

• Let‘s first talk about the nature of streamflow

Stream the generic term for all channelized overland flow(rivers, creeks, etc.)

– Other forms of overland flow are sheetwash and rill-wash

• Streamflow can be either laminar or turbulent, with veloc-ity at a maximum in center top of the stream channel

2 Longitudinal analysis of a river

• At a lower level, the river is divided into separate sections,or reaches

• The primary division into reaches is based on whether flowstays the same

3 Uniform flow

Uniform flow flow that does not change with distance down-stream, neither in area nor velocity

4

• The major reaches are sections of uniform flow

• One slice through the flow looks the same as any otherslice, within reason

Dividing the major reaches of uniform flow are reaches of grad-ually varied and rapidly varied flow

4 Reach morphology → overallmorphology

• What are the major sections of meandering streams?

• What are the major features of braided and meanderingstreams?

5 Headwaters

• Few depositional features

– The valley margins are close to the channel

– Gravel bars

∗ Redeposited from mass wasting

• Mostly erosional features including V-shaped valley withbedrock channels

• Many streams also head in lakes

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6 Stream valley-head

• Most stream valley heads have a characteristic funnel-topform caused by knick-point migration or groundwaterreturn flow

Funnel top valley head

7 Floodplain (much of the maturemidsection)

• Inundated during high water

• Slackwater deposits

– Natural levees

Backswamps, backlands bayous poorly drained areas out-side of levees

– Annual mud deposition from suspension - over-bank flood deposits

Crevasse splay Local overbank bedload deposit

8 The floodplain channel

• For meandering streams

– Pool and riffle structure and downstream bars

– Point bar

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– Channel fill

∗ Deposition in abandoned or aggrading channelreaches

9 The floodplain channel

• For braided streams

– Total width of channels is greater, but depth is shal-lower and change can be rapid

– Slope steeper

– Anastomozing branches separated by stabilizinglongitudinal bars

10 Mouth

• Alluvial fans and deltas

– large velocity drop associated with change in gradient

Alluvial fans on land, mostly in arid environments; de-position from floods and debris flows from mountains

Deltas the terminal region of a strean in oceans or lakes,characterized by a facies of topset, foreset and bot-tomset beds

The name for all features where a river enters the sea comes fromthis name from the Nile: a) floodplain, b) cataract, c) delta, d)Sudd swamp, e) meander

11 Summary: types of streams

Braided, meandering, anastomozing, straight; bedrock, boulder-bedded

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12 Terraces

• Generally a feature of bedrock and meandering streams

• Result from tectonic or climatic changes causing a changein stream parameters

Strath terraces terraces cut on bedrock

Alluvial terraces terraces molded by erosion and depostion onthe floor of an alluvial valley

Paired terraces terraces of same elevation occurring on bothsides of a valley, often depositional

Unpaired terraces unmatched terraces, often erosional

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13 Terraces (cont.)

Development of river terraces

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14 Fluvial Dynamics

• We want to understand a little of the basic physics of wa-ter flow and particle transport, as so much of the worldaround us is critically dependent on the flow of water andtransport of sediment in streams

15 Mass Wasting and Particle Physics

• Landslide phenomena can be treated with particle physics

– Sliding block problem

– Ballistics

– Method of Infinite Slope - each control volume ofmaterial treated independently

16 Channel Flow

Open channel flow the flow of water in streams or engineeredstructures in which the water has a free surface

• This is the most ubiquitous particle transport andlandscape modification system on the Earth’s surface

17 Speed of water in reaches

• Uniform flow easiest - not changing → forces are zero

• What does it seem like the speed of water in a channel willdepend on, intuitively?

– Gravity

– Gradient certainly

– Some measure of resistance

∗ This it turns out is related to the area of the bed,and a measure of the properties, mostly rough-ness, of the bed materials

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18 Hydraulic radius and roughnessparameter

• Measure of contact area is the hydraulic radius , R

R = A/P (1)

– Where A is cross-sectional area and P is the wettedperimeter

• Many measures of roughness

– Most common are Manning roughness parame-ter , Chezy constant , Strickler constant andfriction factor

– Manning roughness parameter most fully dependenton roughness alone (bed properties not channel ge-ometry)

19 Friction and drag

• Imagine bottom of stream with loosened clasts

Volume of water moved/time, V = U × A

20 Stream power

• Mass moved/time, m = ρwUA

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• So since energy (work), E = mU2/2

• Work/time = power, P = ρwUAU2/2 or P = ρwAU

3/2

– Remember this is the power that it takes to move thefluid out of the way of the obstacle

21 Shape

• Object shape is important

– Determines how water moves out of the way

– In a way, it affects the definition of A

• We need to differentiate between blunt objects and hydro-dynamically smooth objects

– Blunt - water meets object head-on, water forciblyripped away, turbulence

– Smooth - water is diverted around the object, thevolume diverted is more proportional to total exposedcontact area

∗ With smooth, there is a strong gradient of decel-eration next to the object· Gradient is to no-slip condition at object

surface

22 Drag Coefficient

• Drag coefficient, CD, characterizes the overall effect of theshape of the bed particles in counteracting flow motion

– CD varies with the change from form drag (blunt)to skin friction (smooth)

– CD is dimensionless

– What does its value depend on?

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23 Drag Coefficient

CD = F (U,A, µ, ρw)

• So:Pf = CDAρwU

3/2 (2)

24 Balance of gravity and friction forces

• Balance to get velocity for uniform flow

• That is:ma = F

ma = Fg − Ff

Fg − Ff = 0

Fg = Ff

13

25 Derivation of Manning’s Equation

• Equation of motion with friction factor

– By convention, when we deal with a stream, we usethe friction factor, ff , rather than the drag coefficient

Fg = Ff

Fg = Pf/U

(since Pf/U = Ff )

Fg = ffAρwU2/2

What is Fg?

– Chezy constant

– Manning roughness parameter

• The result is the Manning equation for uniform flow:

U =1

nM

R2/3S1/20 (3)

Or the Chezy equation:

U = C(RS0)1/2 (4)

– Question: NM = 0.03 s/m1/3, R = 100m, Sf =0.001. So mean stream velocity, U = . . . ?

26 Velocity Distribution

• U from the Manning equation is the mean speed. How isthis related to the speed at the surface, which is easy tomeasure?

– within the fluid: ρwgz sinϑ = µeffdu(z)

dz

– ⇒u(z) = ρwg sinϑz2/(2µeff )

∗ parabolic velocity profile with depth for stream-flow

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∗ not quite correct because of turbulence

– one result though is that

Umax(surface) = 1.5U (5)

(the U from Manning’s equation)

• So through a vertical in uniform flow :

Umax(surface) =1

nM

1.5h2/3S1/20 (6)

27 Gradually- and Rapidly-varied Flow

• Uniform flow doesn’t occur everywhere

– Gradually varied flow occurs where stream depthand speed change smoothly

– Rapidly varied flow occurs where stream depthand speed change suddenly

∗ In gradually and rapidly varied flow, it is a rathercomplicated calculation to find speed ⇒ need tolook at equations of motion a bit, and perhapsuse a numerical program

• One can map out the reaches of any stream, such as the Ni-agara River defined by stretches of Uniform Flow and sep-arated by short stretches of Gradually Varied or RapidlyVaried Flow

• To analyze motion in these changing stretches, Manning’sEquation and its assumptions do not hold

28 Equations of Motion

Continuity equation conservation of mass

ρwUA = Q (7)

which is discharge , and is constant for no inflow or out-flow (either by tributaries, through groundwater, or byevapotranspiration)

15

• Assumes no inflow or outflow (no tributaries or dis-tributaries; losses or gains with groundwater; evapo-ration)

Momentum equation expresses Newton’s second law or Bernoulli’sequation

ρwgh+ ρwgy + (1/2)ρwU2 = E (8)

which is a constant called the Bernoulli integral or totalmechanical energy

• Bernoulli’s equation works within a streamtube -tube made up of mean stream lines , which areparallel to channel walls and the free water surfacein the case of streams

29 Hydraulic Jump

• In a region of rapidly varied flow, the height above a datum(y in the Bernoulli equation) does not change significantly,thus E = h+ U2/(2g) is a constant.

– Either h can be big, or U can be big, to get the sameE

– What happens on a graph of h (y-axis) versus E (x-axis)?

∗ There are two solution branches, defined by theFroude number, Fr = ratio of kinetic energy topotential energy:

Fr2 =U2

2gh(9)

30 Hydraulics, Transport and Landforms

• Now we want to discuss river mechanics, and the materialeroded/carried/deposited by a river

• We want to be able to address the questions:

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– What is the natural connection between hydraulicsand sediment movement?

– What is the relationship between sediment movementand landforms?

31 Base Level

Base level Level below which stream cannot go, at least tem-porarily

• Local

– lake– main stream channel– resistant rock

• Ultimate

– sea level

32 Longitudinal Profile

Longitudinal stream profile the topographic profile along streamcenterline

The Graded Stream a stream in which erosion is balanced bydeposition everywhere; a stream in quasi-equilibrium

• A graded stream maintains its profile

A view of a river valley cutting through the earth along thelength of the river is called a: a) channel, b) floodplain, c) lon-gitudinal profile, d) cross section

33 Three Sedimentary Processes

• Three processes affecting sediments (and the profile) occurin a stream:

– Erosion (picking up)

– Transport (carrying)

– Deposition (dropping)

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34 Stream Erosion

Lifting prying of large rock fragments by hydrodynamic pres-sures

Abrasion wearing of small fragments from bed by tooling ac-tion of streamborn fragments

Impact knocking of pre-existing grains from streambed by stream-born fragments

Solution dissolving of rock in contact with streamwater

35 Lifting

• Just as the bed particles exert a drag force on the water,the water exerts a stress on the bed particles

35.1

Schematic of drag on particle

Chalkboard

36 Lifting (cont.)

• It is usually thought that there is a critical bed shear stressabove which particles of a given size are lifted by the water

– Called Shield‘s stress or Shield‘s parameter (Θ)

18

• The ability to lift can be expressed as

DS

(1.65d)= 0.06 (10)

where D is water depth, S is slope and d is particle diam-eter. For a rectangular channel, D ≈ R

• Holds for noncohesive sediments (i. e., not clay)

37 Sizes of Dislodged Particles

Clay microscopic, feels smooth, < 4µm

Silt microscopic, feels gritty, 4− 62.5µm

Sand can see with the unaided eye, 62.5µm −2 mm

Gravel large, smallest is grus size, > 2 mm

Note: 1 µm = 10−6 m

38 Transport

• All material transported by a stream is called the load

– Three types, depending on mode of formation (weath-ering) and size

Bed load carried along bed of stream, consisting ofcoarse particles with high fall velocities, particlesroll, slide or saltate∗ The bed load consists of particles that are

able to be moved by the streamflow only in-termittently because their weight is close tothe bed shear stress

Suspended load carried within streamflow by tur-bulence, consisting of smaller particles with lowfall velocities

Dissolved load mostly ions that have been chemi-cally weathered from rock

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39 Ability to Transport

• Two measures of a stream‘s ability to carry material:

Capacity how much material altogether the stream cancarry, mostly dependent on stream size or discharge

Competence the largest particles that the stream cancarry, mostly dependent on stream speed or turbu-lence

40 Deposition

• Release of particles from flow, and inability of a stream toapply enough shear stress to particles to dislodge them

• Occurs when capacity or competence are exceeded

• Overloaded streams (load > capacity) are often braidedstreams

– presence of braiding also seems to correlate with highergradient

– common in streams issuing from glaciers because oflarge amounts of available sediments

41 Change in competence

• Changes in competence result in many major depositionalfeatures in great rivers = meandering streams

– As most streams are meandering streams, compe-tence is generally a much more important factor in de-termining erosion, transport and deposition behaviourthan is capacity

42 The Hjulstrom curve

• The result of all this is that a picture can be imaginedwhich expresses the relationships among stream power (usu-

20

ally expressed with velocity) and erosion, transport anddeposition

Hjulstrom Curve

43 Bedforms

• Small landforms?

• Although bedforms are strictly part of a sedimentologycourse, they do give indicators of streamflow character-istics (as in laboratory), and they cannot be completelyseparated from the landforms of which they form a part

• Bedform movies

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44 Effects on sediment transport ofcontrol structures

• Decrease discharge→ capacity and competence decreased→ deposition

• Increase discharge → capacity and competence increased→ erosion

• Increase load → stream over capacity → deposition

• Decrease load → stream further from capacity → erosion

• Decrease velocity → competence decreased → deposition

• Increase velocity → competence increased → erosion

45 Man-made levees

• What is the difference between leveed and unleveed streamsduring flood?

• Annual mean streamflow in Ellicott Creek is 100-200 cfs(median 25 cfs); typical maximum annual streamflow is1000-2000 cfs; very large flood of 1985 was 3700 cfs; Sept10, 2004 was 2940 cfs

– Thought problem: assume 3× average flow

∗ Across floodplain∗ In low-flow channel constrained by artificial lev-

ees

46 Fluvial Landforms

• Fluvial landforms occur over a wide range of scales becauseof the ubiquity of streams

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Largest scale is continental, then mountain-range, drainage basin,

23

local, and finally bedform

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47 Landscape Maturity

Varying landscape maturity due to influence of rock and timeon stream erosion

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48 Complex drainage development

Numerous relationships of drainage to structure

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49 Drainage: consequent andantecedent

Anaglyph (NASA) of Wheeler Ridge, CA. It is actively folding.Note the stream crossing the structure.

27

50 Superimposed drainage

Schematic diagram showing development of superimposed drainagein the Lake District, UK

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51 Stream capture (piracy, abstraction)

Progression of stream capture

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52 Split Mountain, UT

Split Mountain again. Why does the Green River go throughthe mountain?

53 Eroded landforms

Relationship of plateaus near Grand Canyon and Zion, a regionof widespread, subhorizontal bedrock strata

30

54 Eroded landforms

What is the difference between the drainage development in theAllegheny Plateau and along the Niagara Escarpment?

55 Eroded foldbelt

Valley and ridge system developed by fluvial erosion of tec-tonized bedrock

31