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
gravity-driven winds (e.g., katabatic) can be important
• Glacial ice: gravity-driven
• Sediment-gravity flow: 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
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
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
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