1. Sedimentology Flow and Sediment Transport (1) Reading Assignment: Boggs, Chapter 2

2. Key Concepts
Earth surface transport systems
Properties of water, air & ice
Characterizing fluid flow
Grain entrainment
Modes of grain movement
Sediment-gravity flows

3. Earth Surface Transport Systems
Planet re-surfacing driven by tectonic, eustatic & climatic cycles
Resultant redistribution of sediment is by surface transport systems
Erosional landscapes
Depositional landscapes
Three sediment-transport systems
Water
Air
Glacial ice
There are also sediment-gravity flows where the fluid is NOT the primary transporter

4. Earth Surface Transport Systems
Driving force
Water: gravity-driven for most natural flows
Air: usually pressure-driven (high to low pressure), but gravity- driven winds (e.g., katabatic) can be important
Glacial ice: gravity-driven
Note: In sediment-gravity flows, gravity acting upon the body of sediment, the fluid acts more like pore fluid

5. Properties of Water, Air & Ice
Water & Air are fluids. Fluids have no shear strength so that they deform with every increment of shear stress.
Water is a liquid
Air is a gas
Glacial ice is a solid but it flows like a plastic & typically has a basal liquid surface
Density (r = M/V)
Water: ~ 1 g/cm3 or 1000 kg/m3
Air: 1.29 kg/m3 or ~ 1/800 as dense as water
Ice: : 917 kg/m3

6. Properties of Water, Air & Ice
Dynamic or Absolute Viscosity (m) - resistance of a fluid to deformation (flow) with applied shear stress; a measure of the internal friction of a fluid
Units of stress/strain rate → Pa/(1/t) = Ns/m2 = Pa s
Air μ ~ 10-5 Pa s
Water (20°C) μ = 10-3 Pa s
Ice μ ~ 1010 Pa s
Kinematic Viscosity
u = m/r

7. Characterizing Fluid Flow
= scale velocity
= scale length
Froude Number
Reynolds Number

8. Characterizing Fluid Flow
= scale velocity
= scale length
Fr <1 => subcritical flow
Fr>1 => supercritical flow
Froude Number
Toss a pebble into flowing water…
Do the expanding surface ripples travel upstream as well as downstream? If yes, then subcritical.
… Tells us about whether a flow can transmit information upstream.
Do the expand but all translate downstream? If yes, then supercritical
Fr is a measure of inertia versus gravitational forces.

9. Characterizing Fluid Flow
= scale velocity
= scale length
Re is measure of turbulence
Reynolds Number

10. Laminar vs. Turbulent Flow
In theory,
Re <1 Laminar flow: stable to small disturbances – perturbations decay with time.
Re >>> 1 Turbulent flow: unstable to small disturbances – perturbations grow with time.
In nature you always have disturbances, question is when do they decay versus grow?
Re < 500 laminar flow
Re > 500 turbulent flow (dominant style for natural flows of water and air)

13. Velocity Profiles in Laminar Flow
τ = μ(du/dy)
τ is linear with y
u is parabolic with y
A relationship that can be calculated!

14. Law-of-the-Wall Equation
Velocity Profiles in Turbulent Flow – Not as Simple Because of the Nature of Turbulence
Momentum transfer by turbulent eddies
Law-of-the-Wall Equation
uz = (u*/κ)(ln z/zo)
u* is shear or friction velocity (units of velocity)
κ is von Karman’s constant (0.4) of mixing length
zo is roughness height where u = 0

15. Comparison of Velocity Profiles

16. End of part 1

17. How Does Sediment Get Entrained?
Force of gravity is holding grains to surface and there is friction between the grains
Flowing fluid results in a drag force and lift force on the grains
Grains are transported when combined fluid forces > forces holding grain to the surface

18. Complexities & Need to Simplify!
Many grain factors influence how easily grains will be transported – grain density, size, shape, sorting, cohesion between grains, bed roughness ,……
Stochastic nature of turbulence means spatial and temporal deviations from mean stress exerted on bed
There is more organized turbulent structure caused by bed topography
Impractical / impossible to do a grain-by-grain calculation of transport for natural beds

19. Some More Simplifications
Basic questions
How can sediment entrainment be related to easily measured flow parameters?
How much of the sediment is moving as bedload vs. suspended load?
Experiments provide the basis for a simplified route….

20. The Route: Step #1- Sediment Entrainment
tb = boundary shear stress (force exerted upon sediment bed)
tcr is the critical shear stress to move sediment, so that entrainment occurs when tb > tcr
We need to know tcr for a bed of sediment
tb needs to be related to the mean flow velocity u

21. cr has been determined experimentally for a wide range of sediment in Shield’s Diagram
cr is often presented in the dimensionless form
* = cr /[(s-)gD]
u* is shear velocity, is a form by which a shear stress may be re-written in units of velocity. It is useful as a method in fluid mechanics to compare true velocities, such as the velocity of a flow in a stream, to a velocity that relates shear between layers of flow
Wiberg and Smith (1985)

22. Relating tb to u Important definition: = Boundary shear stress
= Shear velocity
Boundary shear stress can be related to the mean flow velocity, <u> by
Also,
Cd = hydraulic drag coefficient

23. The Route: Step #2 – Bedload vs. Suspended Load
Ws = grain fall velocity, suspension occurs when upward component of fluid motion = downward pull of gravity
Ws has been experimentally related to u*

24. Ws calculated assuming:
density of quartz
Water temp = 20C
Spheroid grain shapes
Subrounded grains
Particle settles at constant speed when the gravitational force is exactly balanced by the sum of resistant forces
This constant speed = settling velocity or fall velocity of the particle.

25. Summary of Relationships
Key connections between solid and fluid phase
Experimental Results:
Pure Bedload: tb > tcr & ws/u* > 3
Suspension: ws/u* ≤ 1
Fully suspended: ws/u* ≤ 1

26. Modes of Grain Movement
Bedload consists of creep and saltation

27. Bedload transport

28. Bedload and suspended load: https://www. youtube. com/watch

29. Saltation in Air:
Hop length and height can be ’s
of grain diameters
Saltation in Water:
Hop Height < 10 particle diameters
Hop Length <100 particle diameters
In air or water saltation grain speed < fluid speed (but is greater in air).
Why?

30. Suspended Sediment Load Concentration Profiles
Concentration of suspended sediment near bed
Grain trajectory Length >>> particle diameter
Suspended Grain Velocity ≈ Fluid flow velocity.

31. Concentration Profiles of Suspended Load
Volume of fluid >> volume of suspended sand – rarely more than a few percent
When greater than 10% turbulence is completely damped (more on this in sediment gravity flows)

32. All Three Modes of Transport

33. All Three Modes of Transport

34. Sediment Discharge per Unit Width:
s = average thickness of sediment transport layer
<us> = average velocity of moving sediment
<s> = average volume concentration of moving sediment z y
Sediment discharge per unit
width or Volume Flux of Sediment = [(V×<s> )×us]/A
(units of Length2/Time)

35. Sediment-Gravity Flows
Whole class of flow where sediment concentration is much higher than in fluid- gravity flows that are addressed above.
Sediment/fluid form a single phase that gravity acts upon
A range from dilute turbidity currents to debris flows
Much more when we talk about slope and basin transport

36. Sediment gravity flow

37. Questions You Should be Able to Answer
What are the global-scale drivers that cause re-surfacing of the Earth’s surface?
What are the roles of flowing water, air or ice in shaping the Earth’s surface?
How are sediment-gravity flows different from fluid-gravity flows?
What usually makes water flow, the wind blow and glaciers move?
What is a fluid? What is different about the fluids water and air?
What is density? What are the densities of water, wind and ice? Why does it matter in terms of sediment transport?
What is dynamic viscosity? What does it measure? What is kinematic viscosity?
What is the Froude Number?
What is the Reynolds Number?

38. Questions You Should be Able to Answer
10. What is the difference between laminar and turbulent flow? How/why can these be characterized by the Reynolds Number? 11. What do flow pathlines look like in laminar and turbulent flow? 12. How do the velocity profiles in laminar and turbulent flow compare? 13. Why can the velocity profile in laminar flow be analytically calculated in laminar flow, but not in turbulent flow? 14. What is the Law-of-the-Wall? What does it do for you? 15. What are the forces acting upon grains subject to flowing fluid? 16. If we know the forces acting upon grains with fluid flow, why don’t we just directly calculate sediment transport? 17. What is the Hjulstrom Diagram? What does it show? Why are beds of clay harder to erode than beds of sand? 18. What is boundary shear stress? What is the critical shear stress to move sediment? How are these related to initiate sediment movement?

39. Questions You Should be Able to Answer
19. How has the critical shear stress to move sediment been determined? What is a Shield’s Diagram? What does it tell you about grain transport? 20. How is the boundary shear stress related to the mean flow velocity? 21. What is the grain fall or settling velocity? How is it determined? When does grain suspension occur? 22. Simplifications have been made to make it practical to calculate sediment transport for flowing fluids. What are the key connections that have been made? 23. Under what conditions of boundary shear stress and setting velocity does transport occur as pure bedload? 24. Under what condition of settling velocity does suspension occur? 25. What are the modes of grain movement? What are the components of bedload? 26. In typical suspended transport, where are most of the grains?

40. Questions You Should be Able to Answer
27. What concentration of suspended sediment might you expect in a flowing river? 28. How is total sediment discharge calculated? 29. What are examples of sediment-gravity flows? How are grain concentrations different in sediment-gravity flows than in fluid-gravity flows?