Transcript Sedimentology Flow and Sediment Transport (1) Reading

Sedimentology
Flow and Sediment Transport (1)
Reading Assignment: Boggs, Chapter 2
Key Concepts
I. Earth surface transport systems
II. Properties of water, air & ice
III. Characterizing fluid flow
IV.Grain entrainment
V. Modes of grain movement
VI.Sediment-gravity flows
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
Earth Surface Transport Systems
• Driving force
• Water: gravity-driven for most natural flows
• Air: usually pressure-driven (high to low pressure), but gravitydriven 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
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
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
Characterizing Fluid Flow
U
= scale velocity
Fr =
L
= scale length
U
Froude Number
g L
Re =
U L
u
Reynolds Number
Characterizing Fluid Flow
U
= scale velocity
Fr =
L
= scale length
U
Froude Number
g L
Fr <1 => subcritical flow
Fr>1 => supercritical
flow
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.
Characterizing Fluid Flow
U
= scale velocity
L
= scale length
Re is measure of turbulence
Re =
U L
u
Reynolds Number
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)
https://www.youtube.com/watch?v=XeURH6Tpaeg
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!
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
Comparison of Velocity Profiles
End of part 1
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
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
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….
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
t
has been determined experimentally for a wide range of sediment in
Shield’s Diagram
cr
t
is often presented in the dimensionless form
t* = tcr /[(rs-r)gD]
cr
u* is shear velocity, is a form by
which a shear stress may be rewritten 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)
Relating tb to u
Force applied by moving fluid to bed
tb =
Areabed
t b = Boundary shear stress
u* = Shear velocity
Important definition:
def
t b = ru
2
*
Boundary shear stress can be related to the mean flow velocity, <u>
by
Also,
def
def
Cd = hydraulic drag
2
2
t b = ru* = rCd u
coefficient
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*
Ws calculated assuming:
1) density of quartz
2) Water temp = 20C
3) Spheroid grain shapes
4) 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.
Summary of Relationships
Key connections between solid and fluid phase
t cr  t b
ws  u*
Experimental Results:
Pure Bedload: tb > tcr & ws/u* > 3
Suspension: ws/u* ≤ 1
Fully suspended: ws/u* ≤ 1
Modes of Grain Movement
Bedload consists of creep and saltation
Bedload transport
https://www.youtube.com/watch?v=O9GVRKnMch8&list=PL4BwvUWoIyLNgTjmUEacM9tPIgcKq7JWA&index=30
Bedload and suspended load:
https://www.youtube.com/watch?v=7Z0XwYkqXy4&list=PL4BwvUWoIyLNgTjmUEacM9tPIgcKq7JWA&index=23
Saltation in Air:
Hop length and height can be 100-1000’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?
Suspended Sediment Load Concentration Profiles
Concentration of suspended sediment near bed
Grain trajectory Length >>> particle diameter
Suspended Grain Velocity ≈ Fluid flow velocity.
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)
All Three Modes of Transport
All Three Modes of Transport
Sediment Discharge per Unit Width:
qs =  s  us   s
s = average thickness of sediment transport layer
<us> = average velocity of moving sediment
<s> = average volume concentration of moving sediment
Sediment discharge per unit
width or Volume Flux of Sediment
= [(V×<s> )×us]/A
(units of Length2/Time)
z
y
z
Sediment-Gravity Flows
• Whole class of flow where sediment
concentration is much higher than in fluidgravity 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
Sediment gravity flow
https://www.youtube.com/watch?v=4r9ndJ80_1Y&list=PL4BwvUWoIyLNgTjmUEacM9tPIgcKq7JWA&index=19
Questions You Should be Able to Answer
1.
What are the global-scale drivers that cause re-surfacing of the Earth’s
surface?
2.
What are the roles of flowing water, air or ice in shaping the Earth’s
surface?
3.
How are sediment-gravity flows different from fluid-gravity flows?
4.
What usually makes water flow, the wind blow and glaciers move?
5.
What is a fluid? What is different about the fluids water and air?
6.
What is density? What are the densities of water, wind and ice? Why
does it matter in terms of sediment transport?
7.
What is dynamic viscosity? What does it measure? What is kinematic
viscosity?
8.
What is the Froude Number?
9.
What is the Reynolds Number?
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?
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?
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?