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Sediment Transport &Fluid Flow

• Downslope transport• Fluid Flow

– Viscosity– Types of fluid flow– Laminar vs. Turbulent– Eddy Viscosity– Reynolds number– Boundary Layer

• Grain Settling• Particle Transport

Loss of intergrain cohesion caused bysaturation of pores…

before…

…after

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Different kinds of mass movements,variable velocity (and other factors)

From weathering to deposition:From weathering to deposition: sorting and modification of sorting and modification of clastic clastic particlesparticles

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Effects of transport on rounding, sortingEffects of transport on rounding, sorting

How are particles transported by fluids?

What are the key parameters?

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Flow regimes in a stream

Fluid Flow• Fundamental Physical Properties of Fluids

– Density (ρ)– Viscosity (µ)Control the ability of a fluid to erode & transport

particles• Viscosity - resistance to flow, or deform under shear

stress.– Air - low– Water - low– Ice- high∆µ with ∆ T, or by mixing other materials

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Shear Deformation

Shear stress (τ) is the shearing force per unit area• generated at the boundary between two moving fluids• function of the extent to which the slower moving fluid retards

motion of the faster moving fluid (i.e., viscosity)

Fluid Viscosity and Flow

�

µ =!

du /dy

where,τ = shear stress (dynes/cm2)du/dy = velocity gradient

(rate of deformation)

dy

• Dynamic viscosity(µ) - theresistance of a substance (water)to ∆ shape during flow (shearstress)

• Kinematic viscosity(v) =µ/ρ

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Behaviour of Fluids

Increasedfluidity

Viscous

Types of FluidsWater - flow properties function of sediment concentrations• Newtonian Fluids - no strength, no ∆ in viscosity as shear rate∆’s (e.g., ordinary water)

• Non-newtonian Fluids - no strength, but variable viscosity(µ)as shear rate ∆’s (e.g., water w/ sand (>30% ) or cohesiveclay)– Muds flow sluggishly at low flow velocities, but display less viscous

flow at high velocities• Bingham Plastics - initial strength, must be overcome before

yield occurs (e.g., debris-flows)– No ∆ in viscosity after yield strength is exceeded– If µvaries, as with water laden sediment, or ice, this is referred to as a

pseudoplastic

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Flow regimes in a stream

Laminar to Turbulent flow

• What controls this change in flow?– Depth (L) & Velocity (U)

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Laminar vs. Turbulent FlowTwo modes of flow dependent upon:

1. Velocity2. Fluid viscosity3. Bed roughness

• Laminar Flow: streamlined, uniform current. Requires:– Low fluid velocity or– High viscosity or– Smooth beds

• Turbulent Flow: discontinuous, distorted, flow w/considerable motion perpendicular to primary flowdirection.

– Eddies - highly turbulent flow (water and air)• Eddy Viscosity - internal friction at a larger scale

– Turbulent flow resists distortion to a much greater degree thanLaminar flow

– Fluid under turbulent flow appears to have high viscosity

Eddy Viscosity• Shear stress for Fluid undergoing turbulence

require an extra term to account for e.v.– For laminar flow:

! = µdu

dy

– For turbulent flow:

! = (µ +")du

dy

– Where η is eddy viscosity

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What controls the transition from turbulent to laminar flow?

Reynolds Number (Re)• Laminar vs Turbulent differences arise from ratio

of inertial / viscous forces– Inertial forces (Uρ) - enhance turbulence– Viscous forces (µ/L) - suppress turbulence

• Relationship of inertial to viscous forces isdescribed by:

Re=UL!

µ

When µ dominates, Re is small (<500), flow is laminar-e.g., low velocity, shallow, or ice flows

At high U and/or L, flow becomes turbulent (>2000)

U = mean velocity, L = water depth, ρ=density

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Viscosity effects on Re:laminar vs. turbulent

• High viscosity - low Re• Low viscosity - high Re

Boundary Layers• Area of reduced flow: Fluid

flow over a stationary surface(the bed of a river)– fluid touching the surface is

brought to rest by the shearstress (boundary) at the wall.

– U increases to a maximum inthe main stream of the flow.

– Laminar flow transitions to anarea of turbulent flow

Umax

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U is low, Re is low, flow is laminar

AB

Boundary Layer (BL) Transition:laminar vs. turbulent

• Turbulent flow - thins BL• Rough bed - thins BL

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Surface Waves & Froude NumberFluid Flow variables:

– Viscosity (ignore for water)– Inertial forces– Gravity & depth (surface wave velocity)

Froude # (Fr) - ratio of inertial forces to gravity,

Fr=

U

gLFr=

100cm / s

9.8m / s2* 50cm

=

Froude # < 1, max wave velocity exceeds current, tranquil (sub-critical)>1, current velocity exceeds max wave velocity (supercritical)

Froude Number

• If flow U > wave U (Fr>1) flow is supercritical. lower U(Fr<1), flow subcritical (i.e., waves can travel upstream)

• A spatial transition from subcritical to supercritical flow (orvice versa) is characterized by a ‘hydraulic jump’

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 20 40 60 80 100 120 140 160

Fr (1 m/sec)

Fr

(1 m

/se

c)

water depth (cm)

subcriticalsupercritical

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DeeperSubcritical

(Fr<1)

ShallowSupercritica

l(Fr>1)

FLOW REGIMES

Flow

vel

ocity

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Sediment Transport

Two critical steps1. Erosion and entrainment• Lifting• Critical velocity threshold

2. Down current/wind transport• Rolling/bouncing/suspension• Critical velocity

Particle Entrainment:Forces acting on a grain Lift component:

flow lines compress

Drag (FD) Increase velocity =lower pressure

FL - Bernoulli Effect - Pressure diff. top & bottom of a grain

FD ~ τ (shear stress) /# of grains

Lift (FL)

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Modes of sediment transport inwater

Bedload Transport

Courtesy Dietrich, UCB

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Particle Transport3 Modes1. Traction (rolling, sliding)2. Saltation (bouncing)3. Suspension (floating)

Traction + Saltation = Bedload

Particle SettlingStokes’ Law (settling velocity in a static fluid)

• Stokes’ Law only applies to fine (<200 µm), quartz-densitygrains in water

V = CD2

V=settling velocity; D=grain diameter;Constants: ρg=grain density;ρf=fluid density; µ=dynamic viscosity

V =gD

2[!g " ! f ]

18µ

C =g[!g " ! f ]

18µ

http://www.ajdesigner.com/phpstokeslaw/stokes_law_terminal_velocity.php

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Sediment transport varies with flow velocity…

•Velocity to pluck (lift) grain > velocity needed to maintain suspension

Entrainmentvelocity

…and leads to characteristic bedforms(the geologic record)

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Deposition by Fluid Flows(water/wind)

• Deposition - Decrease in velocity– Decrease in slope– Increase in bed roughness– Low of water volume

• Deposition - permanent or temporary– River channels, point bars, beaches, reentrained& transported

• Sediment deposits characteristics:– Layers, Lack of size grading– Variable sorting

Different kinds of mass movements,variable velocity (and other factors)

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Deposition by Mass Transport• Transport by gravity

– Fluid is a lubricant (reduces), supports particles– Flow stops when sediments are deposited– Subaqueous or subaerial

• Categories:1. Rock Fall2. Slide3. Sediment Gravity flows

– Debris flows– Grain flows– Fluidized flows

Deposition by Sediment Gravity Flows(water/wind)

• Mass Flows (grain supported, cohesionless flow)1. Debris/Mud - slurrylike flows of highly concentrated,

poorly sorted mix of sediment/water (>10°) - Binghamplastics

2. Grain - avalanching of cohesionless sediment (sand) onsteep slope (>30°)

• Fluid Flows (fluid and grain supported flow)1. Liquefied2. Fluidized3. Turbidity

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Gravity flows

• Debris flows• Sediment/water >50%• both subaerial and subaqueous• Low Reynolds numbers

• Turbidity currents• Sediment/water <50%,• always subaqueous,• move due to density contrasts• Higher Reynolds numbers

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Modes of sediment transport inwater

Turbidity Currents

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Bouma Sequence

MIGRATION OF CROSS-BEDS

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REACTIVATION SURFACES

SedimentarySedimentaryrock textures,rock textures,sorting, sizesorting, size

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Sediment transport: forming graded bedding

Depth/Velocity & Sediment Size

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shear-stress can be used to predict the velocity 1 m above the bed (U100) caused bywaves of various heights and lengths (expressed as period, T)

Fluid Viscosity and FlowKinematic Viscosity (v) -

ratio of the dynamicviscosity to density

Determines the extent towhich fluid flows exhibitturbulence

�

! =µ

"

dy

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Rocks lose sharp edgesRocks lose sharp edges……