National Center for Earth-surface Dynamicshydrolab.illinois.edu/people/parkerg/_private/CourseNotes/Renesse03Lecture1.pdfNational Center for Earth-surface Dynamics: Renesse 2003: Non-cohesive

National Center for Earth-surface Dynamics:Renesse 2003: Non-cohesive Sediment Transport

Summary of Lectures on Transport of Non-Cohesive Sediment

•What is Morphodynamics?•Sediment Properties•Modes of Transport of Sediment•Equations for Conservation of Bed Sediment•Overview of Fluid Dynamics•Threshold of Motion•Skin Friction and Form Drag•Relations for Bed Load Transport•Relations for Entrainment of Bed Sediment into Suspension•Formulation for Suspended Sediment•Sediment Transport in Wave Boundary Layers•Formulation for Wave-Current Boundary Layers


WHAT IS MORPHODYNAMICS?THE ORIGINS OF

MORPHODYNAMICS:DUNE ASYMMETRY

Felix Maria Exner, an Austrian physicist, asked the following question circa 1920.

Why do river dunes have gentle stoss (upstream) faces and steep lee (downstream) faces?

Looking upstream: Lab (SAFL)


MORE DUNES: NOTE THE ASYMMETRY

Looking downstream: Field (Amazon basin)Looking upstream: Lab (H. Ikeda)


THE PARAMETERSx = streamwise distance [L]t = time [T]η= bed elevation [L]qt = volume total sediment transport rate per unit stream width [L2/T]λp = bed porosity [1]g = acceleration of gravity [L/T2]H = flow depthU = depth-averaged flow velocity [L/T]Cf = bed friction coefficient [1]

The flow changes the bedThe bed changes the flow


THE STAGEEnxer equation of bed sediment

continuity

xq

t)1( t

p ∂∂

−=∂η∂

λ−FELIX EXNER WAS

THE FIRST MORPHODYNAMICIST

Sediment transport relation

)U(qq tt =

St. Venant shallow water equations

2f

2

UCx

gHxHgH

21

xHU

tUH

0x

UHtH

−∂η∂

−∂∂

−=∂

∂+

∂∂

=∂∂

+∂∂


EXNER REDUCED THE PROBLEM TO A PROBLEM OF NONLINEAR WAVE DYNAMICS

He found1. Dunes like Froude-subcritical flow.2. Dunes migrate downstream as mass waves.3. Dunes are nonlinear waves: migration speed changes with elev, c = c(η)4. In particular, wave speed increases with elevation5. Voilà, the asymmetry evolves on its own!


MORPHODYNAMICS: EXPLAIN HOW WATER AND SEDIMENT INTERACT TO MAKE THESE BEAUTIFUL PATTERNS


SEDIMENT PROPERTIES

Rio Cordon, Italy

ρs = density of sediment [ML-3]commonly 2.5 ~ 2.8 g/cm3

quartz: 2.65 g/cm3

ρ = density of water [ML-3], ~ 1g/cm3

R = ρs/ρ - 1, [1], ~ 1.65(submerged specific gravity)

D = characteristic grain size [L], mmvs = fall velocity of sediment [LT-1]


SEDIMENT SIZE: LOGARITHMIC PHI AND PSI SCALES

)2(n)D(n)D(n2

l

ll ==φ−=ψφ−ψ == 22D

D (mm) ψ φ

4 2 -2

2 1 -1

1 0 0

0.5 -1 1

0.25 -2 2

0.125 -3 3


SEDIMENT SIZE RANGES

Type D (mm) ψ φ

< -9 > 9

4 ~ 9

-1 ~ 4

-6 ~ -1

-8 ~ -6

< -8

-9 ~ -4

-4 ~ 1

1 ~ 6

6 ~ 8

> 8

Notes

Clay < 0.002 Usually cohesive

Silt 0.002 ~ 0.0625 Cohesive ~ non-cohesive

Sand 0.0625 ~ 2 Non-cohesive

Gravel 2 ~ 64 “

Cobbles 64 ~ 256 “

Boulders > 256 “

Non-cohesive coastal morphodynamics is mostly about sand


SEDIMENT GRAIN SIZE DISTRIBUTIONS

Sample Grain Size Distribution

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.01 0.1 1 10

Grain Size mm

Frac

tion

Fine

r

Characterize grain size distribution in terms of N+1 sizes Db,I such that ff,i denotes the fraction in the sample that is finer than size Db,i

i Db,I mm ff,i12345678

0.03125 0.0200.0625 0.0320.0125 0.100

1 0.9702 0.990

0.25 0.420.5 0.834

4 1.000Use logarithmic scale!

Db,4

ff,4


CHARACTERISTIC SIZES BASED ON PERCENT FINER


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.01 0.1 1 10

Grain Size mm

Frac

tion

Fine

r

Dx is size such that x percent of the sample is finer than DxExamples:D50 = median sizeD90 ~ roughness height

D50

D90 To find Dx (e.g. D50) find i such that

1i,fi,f f100

xf +≤≤

Then

x2D

f100

xff

x

i,fi,f1i,f

i,b1i,bi,bx

ψ

+

+

=

⎟⎠⎞

⎜⎝⎛ −

−ψ−ψ

+ψ=ψ

D50 = 0.286 mm; D90 = 0.700 mm


STATISTICAL CHARACTERISTICS OF SIZE DISTRIBUTION


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.01 0.1 1 10

Grain Size mm

Frac

tion

Fine

r

N+1 bounds defines N grain size ranges. The ith grain size range is defined by (Db,i, Db,i+1)and (ff,i, ff,i+1)

f4

f4 = 0.444; D4 = 0.354 mm

( )

( ) 2/11i,bi,bi

1i,bi,bi

DDD21

+

+

=

ψ−ψ=ψ

i,f1i,fi fff −= +

ψI (Di) = characteristic size of ith grain size range

fi = fraction of sample in ithgrain size range


STATISTICAL CHARACTERISTICS OF SIZE DISTRIBUTION


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.01 0.1 1 10

Grain Size mm

Frac

tion

Fine

r

= mean grain size on psi scaleσ = standard deviation on psi scaleψ

( )

σ

ψ

=

=

=σ

=

ψ−ψ=σ

ψ=ψ

∑

∑

2

2D

f

f

g

g

N

1ii

2i

2

N

1iii

Dg = geometric mean sizeσg = geometric standard deviation( ≥ 1)Sediment is well sorted if σg < 1.6Dg = 0.296 mm, σg = 1.71


SEDIMENT FALL VELOCITY IN STILL WATER

Assume a spherical particle with diameter DThe downstream impelling force of gravity Fg is:

( )ν

==⎟⎠⎞

⎜⎝⎛πρ=

Dv,cc,v2Dc

21F s

vpvpDD2s

2

DD ReRe

3

g 2DRg

34F ⎟

⎠⎞

⎜⎝⎛πρ=

The resistive drag force is

where ν is the kinematic viscosity of the water and cDis specified by the empirical drag curve for spheres

DF

gF

Condition for equilibrium:

gDvs

f R=R2/1

vpDf ]

)(c34[Re

R =Dg FF = where


2/1

pDf ]

)(Rec34[R =

SEDIMENT FALL VELOCITY IN STILL WATERUntangle the relation

ν=

DvsvpRe

gDvs

f R=R2/1

vpDf ]

)(c34[Re

R = where andDF

gF ν=

DRgDpRe

pfds

vpDRgD

RgDvDv ReRRe =

ν=

ν= where

Reduce to Rf = Rf(Rep)

Relation of Dietrich (1982):b1 2.891394b2 0.95296b3 0.056835b4 0.002892b5 0.000245

})](n[b)](n[b

)](n[b)(nbb{exp4

p53

p4

2p3p21f

ReRe

ReReR

ll

ll

+−

−+−=

Original relation also includes correction for shape


2/1

pDf ]

)(Rec34[R =

SOME SAMPLE CALCULATIONS OF SEDIMENT FALL VELOCITY (Dietrich Relation)

g = 9.81 ms-2

R = 1.65 (quartz)ν = 1.00x10-6 m2s-1 (water at 20 deg Celsius)ρ = 1000 kgm-3 (water)

D, mm vs, cm/s

0.0625 0.330

0.125 1.08

0.25 3.04

0.5 7.40

1 15.5

2 28.3


2/1

pDf ]

)(Rec34[R =

MODES OF TRANSPORT OF SEDIMENT

Bed material load is that part of the sediment load that exchanges with the bed (and thus contributes to morphodynamics).Wash load is transported through without exchange with the bed.In rivers, material finer than 0.0625 mm (silt and clay) is often approximated as wash load.

Bed material load is further subdivided into bedload and suspended load.

Bedload:sliding, rolling or saltating just above bedrole of turbulence is indirect

Suspended load:feels direct dispersive effect of eddiesmay be wafted high into the water column


2/1

pDf ]

)(Rec34[R =

TRANSPORT DOMINATED BY BEDLOAD(Delta progradation at SAFL: M. Kleinhans)

videoclip


2/1

pDf ]

)(Rec34[R =

TRANSPORT DOMINATED BY BEDLOAD(courtesy Vicenzo D’Agostino)

videoclip


TRANSPORT DOMINATED BY SUSPENDED LOAD(Sand-mud turbidity current at SAFL: J. Marr)

videoclip

Documents

National Center for Earth-surface Dynamicshydrolab.illinois.edu/people/parkerg/_private/CourseNotes/Renesse03Lecture1.pdfNational Center for Earth-surface Dynamics: Renesse 2003: Non-cohesive